NASA Institute for Advanced Concepts

Phase I Study of Self-Transforming Robotic Planetary Explorers Final Report

Reporting Period: 11/98 - 5/99

Steven Dubowsky, PI

Field and Space Laboratory Department of Mechanical Engineering Massachusetts Institute of Technology Abstract The exploration and development of the planets and moons of the solar system in the next 10 to 40 years are stated goals of NASA and the international space science community. These missions will require robot scouts to lead the way, exploring, mapping and constructing facilities. The fixed configuration planetary robots of today will not be able to meet the demands of these missions forecast for the coming millenium. This Phase I study explorered preliminary feasibility issues in preparation for future studies related to the concept of self-transforming robotic planetary explorers to meet the needs of future missions. A self-transforming system would be able to change its configuration to overcome a wide range of physical obstacles and perform a wide range of tasks. In order to achieve self-transforming robots for planetary exploration, conventional complex and heavy physical components, such as gears, motors and bearings, must be replaced by a new family of elements. We propose light weight, compliant elements with embedded actuation are proposed. The actuation would be binary in nature, simplifying the control architecture. The physical system would allow the robot to make both geometric and topological configuration changes. We have examined configuration planning through the implementation of genetic algorithms. This Phase I research developed concepts and technologies that will be relevant to the needs of NASA in the 10- 40 year period. This program has focused on the preliminary study of the underlying, fundamental physics and feasibility of self-transforming robotic planetary explorers.

Program Overview The exploration and development of the planets and moons of the solar system in the next 10 to 40 years are stated goals of NASA and the international space science community, including Human Exploration and Development of Space – HEDS [NASA, 1999] and similar programs [NASDA, 1999]. These missions will require robot scouts to lead the way, exploring, mapping and constructing facilities. Current planetary rovers (Sojourner) [Bickler, 1992] and those under development are relatively conventional fixed configuration vehicles carrying a simple mechanical manipulator [Schenker, 1997]. This technology, while well conceived for current and near-term science objectives, will not meet the demands of missions forecast for the coming millennium. Present technology would not be able to explore rough terrain, such as cliff sides, deep ravines and craters, where the most interesting scientific samples and information are probably located. Nor will they be able to perform even the simplest assembly or construction tasks. New robot technology concepts are required to meet the needs of future planetary exploration and development programs. This research program has begun the study of the concept of self-transforming robotic planetary explorers to meet the needs of future missions. A self-transforming system would be able to change its configuration to overcome a wide range of physical obstacles and perform a wide range of tasks. It would also replace the heavy and complex conventional physical components, such as gears, motors, bearings, cables and connectors, with elements that use compliant members with embedded actuators, sensors, and information and power networks, called Articulated Binary Elements, or ABEs. This would result in more reliable and robust systems that are also easier to control than conventional systems. The development of future robotic systems presents a number of important technical challenges, such as in the areas of sensor technologies, communications and artificial intelligence. This research has focussed on the problems associated with the design of the physical system and its control. Further, the charge of the NIAC program is to develop technology and concepts that are relevant to the needs of NASA in the 10 to 40 year period. Clearly, this 6 month study has not been able to begin to address all the technical issues relevant to the problem in this time frame.

Page 2 It has focussed instead on studying the underlying fundamental physics of self-transforming robotic systems. The approach has been to develop the concept of a self-transforming robotic planetary explorer, called the STX, that could be used in exploration missions in 10 to 15 years. The STX is a hybrid system composed of a combination of conventional system components and ABEs. The addition of small-scale binary actuation (2-4 binary states) to enhance conventional fixed configuration robots with some limited configuration change has also been pursued. The projection into 30 to 40 years would be a system of very large-scale binary actuation (VLSBA; 103 to 104 binary states) which can also deliver the changing topology necessary for truly effective planetary robots. The study has identified some of the key enabling technologies required for the successful implementation of the STX and future work will assess the feasibility of the approach, its potential and its fundamental limitations. Future study would also attempt, consistent with the NIAC charge, to project this technical approach into the 30 to 40 year timeframe.

Review of the State of the Art In order to understand the inherent need for self-transforming robotic planetary explorers, it is necessary to understand the current state of the art in planetary exploration. Current planetary exploration is conducted with fixed configuration rovers capable of traversing benign terrain, performing specific surveying and small sample collection. They are composed of discrete mechanical and electrical components such as gears, motors, bearings, encoders, and sensors. A model Mars rover, based on the Jet Propulsion Laboratory’s Light Weight Survivable Rover (LSR shown in Figure 1) has been designed and built in the Field and Space Robotics Laboratory at Massachusetts Institute of Technology (FSRL Mod 2 shown in Figure 2.)

Figure 1 LSR (Left) and Sojourner (right) (Schenker, P., et al.)

Page 3 Figure 2 FSRL Mod 2 Rover, view of discrete components

Force Torque IF

Encoder IF

PC/104 Stack Arm RAM Amplifiers Motherboard Harddrive

Wireless Modem Body Central Frame Figure 3 Block Diagram of Electrical Components of Mod 2 Rover The FSRL rover has been used to study such things as local path planning, soil tire interaction, and the implementation of a smart traction control scheme using fuzzy logic (Hacot 1998, Burn 1998), see Appendix B. It is based on a PC/104 computer, uses several different I/O modules, and is powered by nickel cadmium batteries. The system controls 12 motors via pulse width modulation, reads four encoders and six tachometers, and uses a six axis force-torque sensor. (Figure 3 shows a block layout for the interaction of the individual components and subsystems.) This descriptive list, which is representative of the numbers and kinds of discrete elements in any rover, begins to show some of the limitations of current rover technology. The focus of initial work with telerobotics has been related to building highly robust systems capable of receiving and implementing basic commands received from Earth-based control. To

Page 4 this end, current technologies suffice. Figure 2 demonstrates the complexity of systems composed of these components of current technology. Particularly confounding is the necessity for so many wires. While the size of individual electronic components will decrease progressively as integration and miniaturization processes improve, the size of the electronics as a whole will likely increase as more demanding tasks are slated for planetary rovers. And with this increase in the number of discrete components will come an increase in number of wires necessary for controlling the system. Even with these evolutionary advances in planetary robotics, a natural limit to the types of tasks capable of being performed by rovers exists. This limit results from the fact that regardless of how small the components become, they are still individual, discrete components in a fixed configuration system. The tasks they are capable of performing will always be limited by the number and nature of the discrete implements they are able to carry. Exit velocity and the cost of propulsion will limit these implements by weight criteria. It becomes clear that any hope of thorough planetary exploration will depend upon the development of robots that are capable of taking a limited number of elements and reconfiguring them in an efficient and useful manner. In the next 10 to 40 years, it is possible to imagine robots that will be able to explore and help prepare the way for human exploration and even habitation. In order to accomplish these goals, planetary robots will have to be able to scout, mine, conduct science experiments, construct ground facilities and aid human planetary explorers and settlers. These tasks necessitate robots that are extremely flexible and adaptive to varying terrain, environments and duties. This requirement of adaptability calls to mind the “robot” from the movie Terminator 2; a transforming metal system that can assume the shape required to accomplish its task and Odo, a shape shifter from Deep Space Nine. Science fiction aside, there is validity in the idea of moving from a paradigm of fixed configuration robots with discrete components to one of continuous systems and components. Fixed configuration systems are suited for a narrow range of simple tasks. As the tasks grow in complexity, the robot complexity also increases. The objective of this research has been to explore the notions of continuous mechanical elements, simplified control architectures and configuration planning that would potentially allow robots to be self- transforming. The Research Approach The focus of this phase I study has been concentrated on the preliminary development of concepts for future robotic planetary explorers and on the identification of enabling technologies that will allow these concepts to become realities in a 10 to 40 year period. To this end, the concept of Self-Transforming Explorers (STX) has been pursued. This research program has begun to study the feasibility of self-transforming robotic planetary explorers. The physical design of such systems will be based on the use of Active Binary Elements (ABEs) which are compliant members with embedded actuators, sensors, and information and power networks. Future research would focus on studying the design of the physical system and the control of self-transforming systems. It will address the underlying fundamental physics of this class of system in attempting to assess the concept feasibility. Such systems also present important technical challenges in a number of areas, such as sensor technologies, communications and artificial intelligence, which, while important, are beyond the scope of this 6 month study. First, working with NASA experts from JPL, a set of potential missions for planetary exploration, and for precursor human missions that might occur in the next 10 to 15 years, has been formulated. Concepts for a class of self-transforming robotic planetary explorers, called

Page 5 STXs, which could meet the objectives of these representative missions begun to be investigated. An STX system is a hybrid system composed of a combination of conventional system components and elements that can be fabricated from elastic materials with embedded actuators, sensors and information and power networks, ABEs. As discussed below, the binary nature of the articulation results in a significant reduction of system complexity, while maintaining a high degree of functionality. The move to ABEs can be thought of as being analogous to the landmark replacement of analog electronic circuits by digital circuits that occurred twenty years ago. Figure 4 shows a representation of an STX system with an idealization of a system composed entirely of a very large number of highly integrated, non-conventional binary elements. Figures 5 and 6 suggest two STX topological configurations of an STX performing future tasks.

Figure 4. STX concept

Figure 5. STX Constructing a Ground Facility

Page 6 Figure 6. STX Traversing a Boulder Field Using basic analysis, simulations and laboratory experiments, the STX concept will be studied in future work to determine its potential and its fundamental limitations. An essential objective of the work has been to identify some of the key enabling technologies that will be required for the successful implementation of self-transforming robot planetary explorer concepts. Figure 7 shows a diagram of the enabling technologies that are expected, based on our Phase I work, to be considered in proposed Phase II research. These technologies will be studied to assess the underlying feasibility of self-transforming robotic planetary explorers. To be consistent with the NIAC charge, the study has attempted to project this technical approach into the 30 to 40 year timeframe.

Figure 7. Enabling technologies required for self-transforming robotic planetary explorers.

Page 7 Concept Overview The key technical idea with self-transforming explorers (STX) is that by building systems with Articulated Binary Elements (ABEs), systems that can change their configuration by simply contracting and relaxing individual elements within their structure can be realized. A given ABE, shown in Figure 10, can achieve large motions by choosing which internal actuator element to actuate in a binary or discrete fashion. The result is a system that can change its geometry in order to perform a task without involving continuous motion actuators, such as motors. Such motions can be achieved with very low complexity devices such as Shape Memory Actuators (SMAs) or conducting polymers. The system would not require internal motion sensors, such as encoders, to provide feedback, since its multiple actuators are only moved from one state to the next. Finally, since individual, large, angular motions of the system consist of relatively small sub-motions, any sub-element might be limited to 450, then conventional bearings are not required. Their function can be achieved through elastic hinges. This study has been structured on the assumption that self-transforming technology (STX) will become practical in a series of stages. In the 10-15 year time frame these systems will be hybrid systems, with some change in topology, see Figures 5 and 6. In the 20-30 year period we expect these systems to incorporate very large-scale binary actuation and to display substantial changes in topology. In the 30-40 year period these systems might achieve the seamless shape shifting of the science fiction robot from Terminator 2. The objective of this study is to consider all of these. Clearly, the most substantial technical work can be done on the 10-15 year systems. However, the study has begun to consider the feasible technology route for the next 15-40 years. Laboratory experiments conducted during the completed Phase I of this study have demonstrated the feasibility of a robot that can make limited configuration changes. This was achieved by adding 2-4 binary states to the 6-18 continuous degrees of freedom of conventional fixed- configuration planetary rover design. The objectives of a Phase II study would be to study the feasibility of a hybrid STX system which would have 50-100 binary degrees of freedom, in addition to 6-18 conventional angular joint degrees of freedom. The projection into 30-40 years would be a system of very large-scale binary actuation (VLSBA) achieving 103 to 104 binary states. This VLSBA design would permit the changing topology necessary for truly effective planetary robots. Furthermore, these VLSBA systems may have many of their functions, such as power, processing and electronics, distributed throughout the structure. Overview of Technologies In order to achieve the objective of hybrid self-transforming planetary robots in the next 10 to 15 years, and true, self-transforming robots in the 15-40 year time frame, some key technologies will need to be developed. Figure 7 shows these technologies and their relationship to the entire system concept. This initial research has and will continue to focus on three main areas: 1. Physical System: The Structure of the System Active Binary Muscles Reconfigurable Information and Power Networks 2. Discrete, Binary Motion Control 3. Physical System Configuration Planning

Page 8 The following sections will describe the type of research which has been conducted in each of these areas under this phase I study as well as to detail what future work will be done on this project. Physical Structure Consider, first, the physical structure of the self-transforming robotic planetary explorer (STX), see Figures 4 through 6. The body of the STX is composed of a network of node elements. The role of these nodes is multifunctional. They act as connection points for the system. They also house the system intelligence, power storage and carry science apparatus and geological samples. Conceptually, they are many faceted (possibly rhombic dodecahedrons) each face representing a different point of connection, for the ABEs. These connection points allow the STX to change its topology. With this increased number of connection points, the possible number of topological configurations expands from that of the basic fixed configuration shapes used today. Each robotic system is a set of multiple nodes. The larger the number of nodes available to the system, the more configurations and, therefore, the larger the effective workspace of the robot. Each node may have a specific task or responsibility. This network of nodes would rely on Articulated Binary Elements, ABEs, for connection to each other as well as for mobility and manipulation. The following sections will explain how these ABEs will be realized based on emerging technologies. ABEs will allow the topological changes necessary for completing a wide and varying range of tasks in systems in the 10-15 year time frame, see Figures 4 through 6. In the 15-40 year time frame, many of the functions of robotic systems will become distributed throughout these ABEs, and the ABEs themselves will evolve into more generalized members. In the STX concept, the nodes are joined by Articulated Binary Elements, ABEs, which are composed of compliant mechanisms and contain their own internal actuation. The actuation methods will be discussed below. ABEs are capable of accomplishing many diverse tasks, such as mobility and manipulation. They also form the skeleton of the system. Whereas today’s robots are structurally rigid (and heavy), the ABEs will exploit their flexibility, eliminating the need for bearings and traditional joints. In addition to simplifying some of the mechanical complexity of today’s robots, the ABEs will allow the STX to undergo topological changes through connecting and reconnecting to different nodes, in different configurations, see Reconfigurable Information and Power Networks. Favoring compliance over rigidity is, in fact, the way of nature [Vogel, 1995]. As discussed earlier, ABEs are lightweight structures, possibly made from non-metallic materials, which achieve points of relative motion through optimized material minimization. Thus forming compliant joints. Instead of having two rigid links coupled by a complex rotary actuator and bearing, compliant joints provide relative motion with minimal complexity. Ideally, each compliant machine is a continuous structure, manufactured from a single piece of material, and designed to have multiple points of flexure, or joints. Figure 8 shows a model of an initial design of a 3DOF compliant leg developed during this phase I study. It demonstrates the simplicity of compliant joints while still remaining in the realm of discrete components designed for a specific task, in this case ambulating.

Page 9 Figure 8. Model of a 3DOF Compliant Leg Figure 9 shows a prototype compliant gripper developed during this phase I study that is mechanically simple but capable of lifting geological samples. The base of this compliant gripper is manufactured from a single piece of delrin, achieving flexibility at its joints through material minimization. In this design, the material selection was a matter of strength and weight optimization. The base of the gripper which contains the joints is made from delrin allowing optimized flexure. The “fingers” are constructed from brass which contain the strength and rigidity necessary for lifting heavy samples, as well as being able to hold a machine point at their tips. It is actuated with shape memory alloy (NiTi) wires that act antagonistically. See Appendix A for further details of this model and previous smart gripper designs as well as for the “squatting” suspension. This development work provides the foundation for ABE development.

Figure 9. Compliant SMA Gripper with no bearings Because of the simplicity of compliant joints, it is possible to construct members (ABEs) with many of these joints that are actuated in a simple binary fashion. The advantage of this type of structure over rigid manipulators, is that they are lightweight, simple to control (see section on Binary Motion Control), and multifunctional. They would be used not only for manipulation but also for mobility, walking, climbing and rolling for example, and in the STX, as a skeletal structure for connecting the various node bodies.

Page 10 In the Field and Space Robotics Laboratory, a first generation ABE has been built [Oropeza] (Figure 10(a)). It consists of five stages, each composed of two discs interconnected by three flexure-hinged links. The links were made out of Ultra High Molecular Weight (UHMW) polyethylene and the discs were machined out of Delrin. The links were press-fit to the discs and the stages were connected to each other with nylon screws. The structure is actuated by shape memory alloy (SMA) wires. Also built at the FSRL and shown in Figure 10(b) is a prototype of a "squatting" suspension that can change its geometric configuration by activating antagonistic SMAs.

Figure 10. (a) Articulated Binary Element, ABE; (b) SMA "Squatting" Suspension Future research will focus on finding materials for the skeletal structure that are optimally strong and elastic. This may involve hybridizing materials as in the case of the compliant gripper. Future research will also concentrate on addressing the issues of how these materials will perform in space environments, including microgravity, temperature and contamination issues. In a 10 to 15 year timeframe, it is believed that this work in compliant structures will grow to represent an entirely new family of engineering components for terrestrial as well as space applications. This group of mechanical materials will be an integral step toward the realization of a continuously transformable planetary explorer. In the 15-40 year timeframe, the number of compliant joints will increase, approaching the very large scale binary actuation (VLSBA) systems with more distributed functions. Embedded Active Binary Muscles The concept of ABEs, as discussed above, requires actuators that have only two states. In a sense they will be artificial muscles, but with less complexity. Control is achieved by having many of these binary actuators (see section on Binary Motion Control.) There have been many advances in recent years in active materials for artificial muscles. Among these materials are shape memory alloys, conducting polymers, polymer gels, piezoelectrics, magnetostrictives, and many more. As most of these materials are still in their infancy, extensive use of them in practical robotic systems has not yet been realized. A limitation of some active materials is that they can only be used for small deflections in short periods of time. For robotic systems such as the STX, active materials will have to be able to achieve large motions. Since these robots will

Page 11 be used in space exploration, fast action is not expected to be a critical performance criterion on most missions. This phase I study has concentrated on identifying materials that will be useful to self- transforming explorers and on understanding their fundamental properties, capabilities and expected developmental advances. Initial use of active binary muscles is projected to include using bundles of these muscles attached to the skeleton, similar to mammalian musculature. This segment of the research is amenable to the current state of technology and will be pursued in the 10-15 year timeframe. Central to the research for the 15-40 year time frame is the idea of embedding matrices of these muscles within the material of the skeletal structure itself, as shown in Figure 11. This idea contributes to the development of the active mechanical material family mentioned in the last section. By embedding the muscles, a clear development path from embedded discrete actuators in mechanical materials to continuously adaptable materials will be established. As discussed, below, two very promising actuator technologies for self- transforming robots are SMAs and conducting polymers. The study of the feasibility of these actuators for robots used for exploration will be the focus of phase II research.

Figure 11. Embedded Actuation [Hagood, amsl.mit.edu] Conducting Polymers. Conducting polymers are a class of materials that can be used as electromechanical actuators by achieving large dimensional changes through electrochemical doping. Applying a voltage across two conducting polymer electrodes of similar electrochemical potential generates a strain. For a few volts, conducting polymer actuators can achieve linear dimensional changes on the order of 10%. This can be compared with piezoelectric and electrostrictive actuators which require on the order of 30 volts to achieve a 0.1% dimensional change [Baughman, 1996]. Conducting polymer response time is an order of magnitude faster than the fastest natural muscles; ant jaw closure: 0.3 ms and flea jumping: 1ms [Baughman, 1996]. The maximum force of conducting polymers is 80-100 times that of natural muscles (790kgf/cm2 compared with 8kgf/cm2 for crawfish muscle – [Baughman, 1996]). Given these metrics, it is likely that conducting polymers will be an integral part of robotics in the coming century. They would allow robotic actuation to reach, and surpass, that of biological systems. Together with the compliant mechanical skeleton, these conducting polymer actuators will be fundamental in the development of adaptable generalized appendages. Bundles of conducting polymers, used in parallel but controlled individually would be able to adjust the force and compliance of the appendage, similar to the adjustable rigidity of the human ankle that can be achieved by

Page 12 contracting multiple muscles [Baughman, 1996]. This idea of controllable compliance, studied in connection with ABEs, would be used by embedding conducting polymers into the compliant mechanical skeleton of the self-transforming robotic planetary explorers. Research into conducting polymers is ongoing in conjunction with the Bioinstrumentation Laboratory at MIT. This work has begun to address a number of engineering versus basis science issues that need to be considered, such as temperature and environmental effects. Conducting polymer actuators promise to be very useful to robotics in the long-run, however, in the next 15 years SMA may prove to be a more feasible option for binary actuation in the ABEs. Shape Memory Alloys. Another class of actuators, which have been under consideration in this study of self-transforming robotic planetary explorers, are shape memory alloys. Whereas conducting polymers are in their infancy in terms of development, SMAs have been well studied and are commercially available. SMAs are important to the study of self-transforming robotic planetary explorers for several reasons. First, SMAs represent a substantial improvement in strength to weight ratio over traditional hydraulic and electromechanical actuators, (600Mpa/3.166E-4kg/m). They can be actuated in a binary fashion that simplifies the control aspect, as will be discussed in a later section. While SMAs are considered inefficient for most applications, it is believed that for planetary and space applications, where fast action is not critical, SMAs will exhibit better efficiency when well insulated and actuated slowly. Finally, they are readily available and low cost. They have been used to actuate the compliant mechanical structure and a clear progression from early work done with SMAs on the ABEs to later development of conducting polymer musculature can be seen. Reconfigurable Information and Power Networks In order for the STX to be able to topologically transform, the information and power networks will, themselves, have to be reconfigurable. The idea of hard wiring does not work within the context of this application because it limits the system to a fixed configuration. There are several issues that require research in this area. These include: 1. Determining if these information and power pathways that make up these networks can be consolidated. 2. Determining if the same muscles used for actuation can be used to carry signals. 3. Addressing the issues related to reconnecting the information and power pathways to allow reconfiguration of the STX. Possible solutions to these issues that have begun being studied include: 1. Establishing a “Bus” structure for the networks or “multiplexing” the pathways. 2. Developing a methodology for an electronic handshake. As the physical systems mate, the power and information re-connections would be made as well, as shown conceptually in Figure 12. The physical mating will be accomplished through the releasing and locking of bistable compliant mechanisms at the ends of the ABEs and on the node faces. For the sake of visualization, view these links as gripping “hands”. On the “palm” of each “hand” would be an electrical grid pad. When these two pads come together and are locked in place by the physical grip, they would meet up in some arbitrary configuration. Some portions of each grid would have counterparts on the other grid and some would not. Once the physical connection is in place, the system intelligence would query the point of connection. It would be able to establish its new connectivity by detecting which grid point received which signal. Through an “electronic handshake” the very electrical system itself becomes transformable

Page 13 3. Exploring new ways to actuate ABEs at a distance, such as magnetic field, lasers, eddycurrents.

Figure 12. Bi-stable Compliant Latch with Electronic Handshake Motion Control Binary Actuated Robotics. Binary actuation constitutes a new paradigm that may have an impact for mechanical and robotic systems as profound as the impact that digital devices have had for electronic systems. In traditional approaches to robotics, relatively heavy continuous-motion actuators such as electric motors and hydraulic cylinders are used. While such actuation is reasonable in the context of factory automation, the weight requirements are prohibitive for missions in space. On the other hand, technologies such as micro electrostatic combs, shape memory alloy (SMA), and electro-polymer gels have very good force to weight ratios, but are rather difficult to control using traditional PID and/or adaptive control schemes. By driving these actuators from one hard stop to another, a cost (and weight) effective actuator results. As an example of a mechanical device constructed from binary actuators, consider the platform manipulator shown below.

Figure 13. 3 Bit Stewart Platform Manipulator Here each leg has two states, and so the platform has 2^3 = 8 configurations. In general, if there are N actuators, 2^N states result. Hence, as N becomes large, a binary robot can perform the vast majority of tasks that a continuous-motion robot can. For planetary surface the following operations are possible: (1) docking and locking of self-transforming robotic modules; (2) discrete-step locomotion of a collection of self-transforming modules. For such applications as discrete-state robotic devices have several advantages over traditional continuous-motion robots. These include:

Page 14 1. Reduced need for feedback control and its associated computation and hardware; 2. Reduced need for high bandwidth communications for remotely controlled robots. In the past, our team (Chirikjian) has focused on the design, workspace properties, and motion planning of binary-actuated manipulator arms ranging from 3 to 36 bits. In future work, his subcontract will be responsible for: 1. Simulation of discrete-state locomotion processes; 2. Analysis of self-transforming maneuvers for discrete-state mechanical modules; 3. Investigation of control strategies for self-transforming binary robots; The metrics for demonstrating how this technology is an improvement over conventional robotics include: (1) quantitative comparison of the discrete-state locomotion scheme with other modes of locomotion used in practice (e.g., wheels, tracks, legs, and continuous snake-like robots), and (2) comparison of the communications bandwidth requirements for remote control of continuous-motion vs. discrete-state robots. Physical System Configuration Planning Physical system configuration planning applies to both reconfiguration and path planning that are determined by the system intelligence of the STX. First, consider the problem of reconfigurability. The goal is for the self-transforming robotic planetary explorer to reconfigure itself as to achieve the optimal configuration for accomplishing any given task. A physical system can change its configuration in two ways. The first is through geometric changes; that is, changes to the dimensionality of the existing physical system such that the system appears to “grow” or “shrink” or shift its center of mass. The ABE shown in Figure 10(a) is capable of undergoing geometric reconfiguration through extension or contraction of itself. The second way to make physical changes of configuration is to change the topology of the system; that is, how the individual elements of the system are connected such that the entire shape and functionality of the system change. The arrangement of the nodes and ABEs in the STX are subject to topological configuration changes. The question for the system intelligence is how to come up with the optimal configuration. One way is to “program” the many different configurations into the system, initially. While this would appear to be a relatively easy task, it would be impossible and impractical to preprogram all of the possible eventualities the robot might encounter. What is more realistic, is to somehow train the robot to come up with its own solutions to the problems and tasks it faces. It has been demonstrated through research into modular robot design conducted at the Field and Space Robotics lab that a large number of unique system configurations can be realized with a small inventory of parts, as shown in Figure 14. The result is that a highly capable robotic system can be achieved composed of simple elements. (Details of this work are contained in Appendix C)

Page 15 Inventory

Power Module

Joints

Connecting Links

Robot Assemblies End Effectors move limb 1 forward move limb 1 forward move limb 2 forward move body forward

grasp object retrieve sample move limb 2 forward communicate with retrive sample move body forward ground station Action Modules Action Plan Figure 14. A Modular Design Approach to Robotics This work in modular planning has used genetic algorithms in order to determine the best modular design for a system given a particular task. Configuration planning builds on the results of modular planning, in that similar techniques can be used to allow a robot to decide which topological configuration of its given elements would be optimal for completing a task. Self- transformability takes this planning one step further by requiring not only that the robot figure out the best configuration, but that it also figure out how to physically change into this configuration. Genetic algorithms can be used for both stages of planning. The feasibility of using genetic algorithms to accomplish these goals begun to be studied in this phase I research. The inventory of nodes and ABEs make up the set of usable assets for accomplishing any task. These assets are represented by chromosomes in the genetic algorithm. Each possible configuration is described by a script of these chromosomes. The robot’s intelligence initially picks several candidate scripts arbitrarily and runs them through a simulation of the task to see how proficiently the task is accomplished. The quantitative measure of this proficiency is termed the performance measure. If the performance measure does not meet some predetermined value for any of the candidate configurations, this generation is sent back to the GA. At this point, the GA performs cross breeding from the parent generation to establish a new generation of candidate designs to be evaluated (Figure 15). In addition to crossbreeding, mutations are randomly introduced to speed the selection process. This cycle continues until the performance measure is met by one of these candidates.

Page 16 Tail Crossover Cris-Crossover Figure 15. Genetic Crossover Methods [Farritor, 1998] Once the optimal configuration is found, the STX must physically reconfigure. This is a path planning issue, which can also be addressed with genetic algorithms. In this application, each possible action is considered a chromosome, and each representative plan is a script or a series of these chromosomes. The same iterative process is followed until the system intelligence finds the optimal way to physically change from its current configuration to the chosen configuration. After this transformation is completed, the system intelligence uses the same path planning genetic algorithm to choose a path to accomplish the given reconfiguration.

Page 17 References Ananthasureth, G., and Kota, S., “Designing Compliant Mechanisms,” Mechanical Engineering, Vol. 117, No. 11, pp93-6, 1995. Baughman, R., “Conducting Polymer Artificial Muscles,” Synthetic Metals No. 78, pp. 339-53, 1996. Bickler, D., “The New Family of JPL Planetary Surface Vehicles,” Proceedings of Missions, Technologies, and Design of Planetary Mobile Vehicles, Toulouse, France, 1992. Burn, R., “Design of a Laboratory Planetary Exploration Rover, MS Thesis, MIT, Cambridge, MA 1998. Chirikjian, G. “Kinematics of Metamorphic Robotic System,” IEEE International Conference on Robotics and Automation, pp. 449-55, 1994. Chirikjian, G., ``Kinematic Synthesis of Mechanisms and Robotic Manipulators with Binary Actuators,'' ASME Journal of Mechanical Design, 117(Sept):573-580. Chirikjian, G., “Inverse Kinematics of Binary Manipulators Using a Continuum Model,” J. Intelligent and Robotic Systems, 19:5-22, 1997. Chirikjian, G. and Ebert-Uphoff, I., “Discretely Actuated Manipulator Workspace Generation Using Numerical Convolution of the Euclidean Group,” IEEE International Conference on Robotics and Automation, Belgium, 1998. Chirikjian G. and Burdick, J., “The Kinematics of Hyper-Redundant Robot Locomotion,” IEEE Transactions on Robotics and Automation, Vol. 11, No. 6, 1995. Dubowsky, S., Cole, J., Rutman, N. and Sundana, C., “Mobile Autonomous Robotic Systems for Unstructured Environments – With Applications to the USS Constitution” Proceedings of the NSF Design and Manufacturing Grantees Conference, San Diego, CA, 1995, Invited. Farritor, S., “On Modular Design and Planning for Field Robotic Systems,” PhD Thesis, MIT, Cambridge, MA, 1998. Farritor, S., Dubowsky, S. Rutman, N., and Cole, J., “A System Level Modular Design Approach to Field Robotics,” 1996 IEEE International Conference on Robotics and Automation, Minneapolis, pp2890-5, 1996. Farritor, S. and Dubowsky, S., “A Self-Planning Methodology for Planetary Robotic Explorers,” 1997 International Conference on Advanced Robotics, Monterey, CA, 1997. Farritor, S., Hacot, H., and Dubowsky, S., “Physics-Based Planning for Planetary Exploration,” 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium, 1998. Frecker, M., Kikuchi, N., and Kota, S., “Optimal Synthesis of Compliant Mechanisms to Meet Structural and Kinematic Requirements – Preliminary Results,” Proceedings of the 1996 ASME Design Engineering Technical Conferences, 96-DETC/DAC-1497, 1996. Hacot, H., and Dubowsky, S., “Analysis and Simulation of a Rocker-Bogie Exploration Rover,” Proceedings of XII CISM-IFToMM Symposium on Theory and Practise of Robots and Manipulators (ROMANSY ’98), Paris, 1998. Hamlin, G., and Sanderson, A., “Tetrobot Modular Robotics: Prototype and Experiments,” Proceedings of Intelligent Robots and Systems, 1996. Hirose, S. Shirasu, T., and Fukushima, F., “A Proposal for Cooperative Robot “Gunryu” Composed of Autonomous Segments,” Proceedings of Intelligent Robots and Systems pp. 1532-8, 1994. Janos, B., and Hagood, N., “Overview of Active Fiber Composites Technologies,” Proceedingsof the Sixth International Conference on New Actuators, ACTUATOR98, Bremen, Germany, June 1998. Kawauchi, Y., Inaba, M., Fukuda, T., “Self-Organising Intelligence for Cellular Robotic System (CEBOT) with Genetic Knowledge Production Algorithm,” Proceedings of IEEE International Conference on Robotics and Automation, pp. 813-8, 1992. Kotay, K., Rus, D., Vona, M., and McGray, C., “The Self-Reconfiguring Robotic Molecule,” Proceedings of the IEEE Conference on Robotics and Automation, Leuven, Belgium, pp. 424-31, 1998. Koliskor, A., 1986. ``The l-coordinate approach to the industrial robots design,'' in Information Control Problems in Manufacturing Technology. Proceedings of the 5th IFAC/IFIP/IMACS/IFORS Conference, pp. 225-232, USSR.

Page 18 Kotay, K. and Rus, D., “Task Reconfigurable Robots: Navigators and Manipulators,” Proceedings of Intelligent Robots and Systems, 1997. Kumar, A., Waldron, K. J., ``Numerical Plotting of Surfaces of Positioning Accuracy of Manipulators,'' Mech. Mach. Theory, Vol. 16, No.4, pp.361-368, 1980. Latombe, J. “Robot Motion Planning,” Kluwar Academic Publishers, Boston, MA 1991. Lee, C., and Sun, C., “The Nonlinear Frequency and Large Amplitude of Sandwich Composites with Embedded Shape Memory Alloys,” Journal of Reinforced Plastics and Composites, Vol. 14, pp. 1160-74, November 1995. Madden, J., Lafontaine, S. and Hunter, I., “Fabrication by Electrodeposition: Building 3D Structures and Polymer Actuators,” Proceedings of the Sixth Symposium on Micro Machine and Human Science, 1995. Murata, S., Kurokawa, H., and Kokaji, S., “Self Assembling Machine,” Proceedings IEEE International Conference on Robotics and Automation, Vol. 1, pp. 441-8, 1994. Mars Pathfinder Website, http://www.mpf.jpl.nasa.gov. NASA Strategic Plan, 1998 NASA Policy Directive (NPD)-1000.1, http://www.hq.nasa.gov/office/nsp Opdahl, P., Jensen, B., Howell, L., “An Investigation into Compliant Bistable Mechanisms,” ASME Bienniel Mechanisms Conference, Atlanta, GA, 1998. Oropeza, G., “The Design of Lightweight Deployable Structures for Space Applications,” BSME Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1999. Pamecha, A, Ebert-Uphoff, I. and Chirikjian, G., “Useful Metrics for Modular Robot Motion Planning,” IEEE Transactions on Robotics and Automation, Vol. 13, No. 4, pp. 531-45, 1997. Pieper, D.L., 1968 (Oct). The Kinematics of Manipulators under Computer Control, PhD Thesis, Stanford Univ. Polypod Website, http://www.parc.xerox.com/spl/members/yim/polypod Roth, B, Rastegar, J., and Scheinman, V., 1973. ``On the Design of Computer Controlled Manipulators,'' First CISM-IFTMM Symp. on Theory and Practice of Robots and Manipulators, pp. 93-113. Saggere, L., and Kota, S., “Synthesis of Distributed Compliant Mechanisms for Adaptive Structures Applications: An Elasto-Kinematic Approach,” Proceedings of the 1997 ASME Design Engineering technical Conferences, DETC97/DAC-3861. Salamon, B., and Midha, A., “An Introduction to Mechanical Advantage in Compliant Mechanisms,” Advances in Design Automation, DE-Vol. 44-2, 18th ASME Design Automation Conference, 1992. Schenker, P., "Lightweight Rovers for Mars Science Exploration and Sample Return," Intelligent Robots and Computer Vision XVI, SPIE Proc. 3208, Pittsburg, PA, October, 1997. Sen, D., Mruthyunjaya, T.S., ``A Discrete State Perspective of Manipulator Workspaces,'' Mech. Mach. Theory, Vol. 29, No.4, pp.591-605, 1994. Sreenivasan, S. and Wilcox, B., “Stability and Traction Control of an Actively Actuated Micro-Rover,” Journal of Robotic Systems, Vol. 11, No. 6, 1994. Tesar, D., and Butler, M., “A Generalized Modular Architecture for Robotic Structures,” manufacturing Review, Vol. 2, No. 2, 1989. Vogel, S., “Better Bent Than Broken,” Discover May 1995, pp. 62-7. Wang, G., and Shahinpoor, M., “A New Design for a Bending Muscle with an Embedded SMA Wire Actuator,” SPIE Vol. 2715, pp. 51-61, 1996. Yim, M. “Locomotion with a Unit Modular Reconfigurable Robot,” PhD Thesis, Stanford Univ, Palo Alto, 1995. Youyi, C. and Tu., H., “Shape Memory Materials ‘94”, Proceedings of the International Symposium of Shape Memory Materials, Beijing, China, 1994.

Page 19 Appendix A

Reconfigurability

This appendix presents work done to improve the mobility of a Mars exploration rover, thus decreasing the chance of mission failure. By increasing the amount of terrain that can be navigated, the rover will be able to select from a larger set of science objectives to investigate. The rover’s mobility can be enhanced by giving it the capability of reconfiguring its geometry. The goals of a reconfigurability mechanism will be described in more detail in the next section. Section A.2 discusses shape memory alloy actuation and its use in a reconfigurability system. Section A.3 presents the design of the experimental reconfigurability system, with results in Section A.4. Finally, a next generation design based on our experimental findings is covered in Section A.5.

A.1 Motivation for Reconfigurability The two most basic ways for a rocker bogie rover to vary its geometry are by changing the link lengths and by changing the rocker and bogie angles. Implementation of a reconfigurability mechanism will allow the rover to shift its weight to vary each wheel’s traction with the ground, as well as increase the rover’s stability for a given configuration. During operation in rugged terrain, the rover could easily become trapped in a position that could lead to tipping. Unseen objects, crumbling terrain, or incorrect terrain data can all lead to undesirable predicaments for the rover. One purpose of a reconfigurability mechanism is to allow the rover to squat one or both sides and increase its stability margin if it finds itself in a perilous position.

Figure A.1: Rover Close to Tipping

Page 20 Figure A.2: Squatting Left Side Increases Stability In addition to increasing stability, the rover can shift its weight to perform traction control. When one wheel begins to slip, the rocker or bogie angle can be changed to move the center of mass vector closer to the wheel with the largest normal force vector in the direction of the center of mass vector.

A.2 Shape Memory Alloy Actuation

A.2.1 Background

The key element to the design of a variable geometry mechanism to change rocker or bogie angles is developing an appropriate actuator. The actuator must have a high force/weight ratio in order to keep the system lightweight. Planetary applications limit the variety of actuator types. Hydraulic actuators, for example, can exert very high forces, but they have too many problems. Pumps, hoses and seals would increase weight, and keeping the fluid from freezing or leaking would add complexity as well. Pneumatics would have similar problems with pumps, seals and hoses. Electric solenoids would not be able to exert enough force, without consuming large amounts of power. The common method of actuation is a geared electric motor, but this adds weight, bulk and reliability problems to the design. Another possible, but less common, method of actuation is shape memory alloy. Due to its light weight and simplicity as an actuator, shape memory alloy actuation is being investigated for a reconfigurability mechanism.

Page 21 A.2.2 SMA Properties

Shape memory alloys posses unique stress-strain properties. An SMA can be deformed plastically, and then returned to its original shape by being heated. The most common alloy is Nitinol (NiTi). A NiTi SMA is in its martensite phase at room temperature. When stressed, the martensite crystal structure slips causing up to 8% strain (Figure A.3). When the alloy is heated above 68 °C, the alloy transforms into the austentite phase and its original crystal structure is restored. Figure A.4 shows the stress-strain curves of the two different phases. This special alloy can be used as an actuator, because the ratio of the deformation stress to the actuated recovery stress can be higher than 10 to 1.

Figure A.3: Austentite and Martensite Crystal Structures (Duerig, 1990)

Page 22 Figure A.4: NiTi Stress-Strain Curve (Duerig, 1990) There are some important design considerations in working with SMAs to take into account. To avoid fatigue, the useful strain of an SMA should only be 3-5%, depending on the quality of the wire used. Also, there is a minimum bend radius for an SMA wire, depending on its diameter. Using a tighter radius will cause excess strain and failure in the wire.

Figure A.5: Large Bend Radius Causes Overstrain (Gilbertson, 1994) Fixing the wire at each end is another design consideration. A thin wire has little surface area to clamp, yet exerts high force. Therefore, the clamp must hold enough of the wire to keep it from slipping. Soldering to a NiTi wire is difficult, because the heat associated with soldering can change the wire’s properties. When using multiple wires in parallel, to increase force, each wire must be the same length, requiring special care in designing an SMA mechanism. If one wire is shorter than the others, it will bear all of the load when heated and break. Finally, care must be taken in the design of an SMA mechanism, to insulate the SMA wire. An electrical short across the SMA wire will make it useless.

Page 23 A.3 Experimental Design

A.3.1 Goals

The goal of this reconfigurability work is to develop a shape memory alloy actuated mechanism to allow the rover to change geometry. Many concepts for changing rover geometry were looked at and evaluated. A mechanism that would simply change the rocker or bogie angle appeared to be more feasible with SMA’s to implement than one that would actually extend or retract rocker or bogie links. Before choosing a design to be implemented on the rover, an initial test mechanism was developed to evaluate SMA performance and to learn more about implementation of shape memory alloys. The goals of initial work, therefore, are to use shape memory alloys to raise and squat a device similar to a rocker or bogie, and to test control of this mechanism’s angle.

A.3.2 Force and Strain Requirements

Table A.1 gives the requirements chosen for the reconfigurability mechanism. Since shape memory alloys only have a small useful strain, they must be attached close to the pivot point of a lever, to give that lever a useful range of motion. However, as the wires are moved closer to the pivot point, more wires will be required to achieve the necessary force. One way to “assist” the wires in lifting heavy load, is by using a bias spring to help offset some of the required force. Several different configurations of springs and wires allow the mechanism to raise and squat, while loaded or unloaded (Figure A.6). Configuration 1 simply uses SMA wires to raise the mechanism. Configuration 2 uses a spring that keeps the mechanism in a raised position. Wires above the pivot point allow the mechanism to squat when actuated. However, both of these configurations require many and/or thick wires to achieve enough force to either lift the weight or stretch the spring. Using many wires adds complexity to the system. Using thick wires requires a larger bending radius. Both require more power to actuate.

Page 24 Figure A.6: SMA and Spring Configurations An unloaded mechanism would use different configurations of wires and springs. Configuration 3, because it is unloaded, uses a spring that is only stiff enough to stretch the SMA wire when not actuated. Since SMA’s have a high ratio of actuated stress to passive deformation stress, the unloaded system will use less power. Configuration 4 shows two sets of SMA wires. One set raises the system and one set squats. The solution for the preliminary design is a combination of 3 and 4. In order to make the system behave like an unloaded system, a spring is be added with the correct stiffness to offset the payload weight. Then two sets of wires are used, one to raise and one to squat. The system can then be modified to test an unloaded condition, by removing the payload and using only the squat wires and the spring, as shown in number 3. Position control work using only one set of wires is simpler, and therefore a better starting place.

Page 25 A.3.3 SMA Calculations

To implement the above design, several parameters would need to be determined: length and number of wires, distance from wires to pivot, wire diameter, and spring force. The useful length of wire deformation follows the strain equation, (A.1)

DL = Le max -useful where L is the length of the wire. The minimum force required to achieve this deformation is

pns d 2 F = def . deformation 4 calculated using equation (A.2),

(A.2) where n is the number of wires and d is the wire diameter. The maximum contraction force can be calculated using equation (A.2) by substituting the max. contraction stress for the deformation stress. Finally the resistance, R, of the set of wires is obtained using equation (A.3), (A.3) 4LR R = pnd 2 where R is the resistivity of the wire in Ohm*m. Preliminary calculations showed that to use a reasonable amount of power and number of wires, the wire length would have to be an order of magnitude higher than the approximate wire length in Figure A.6. The approach taken was to run the wires from one wheel, over or under the pivot, and back down to the other wheel (Figure A.7). Rollers near the pivot point allow the full length of the wire to stretch and contract. This idea has the same effect as the one shown in Figure A.6, but it allows for much higher strains due to longer wires.

Page 26 Figure A.7: Longer Wires Design Spring force is another concern. A standard extension spring follows the rule F=Kx. However, since the payload weight provides a constant force, an extension spring would provide excessive force at full extension and adequate or inadequate force in its retracted position. To simplify the model and reduce the work required by the SMA’s at full spring extension, a constant force spring would be incorporated into the design.

A.3.4 Design Implementation

Figure A.8 shows a schematic of the reconfigurability design, with a photograph of the mechanism in Figure A.9. The same size aluminum tubes as used in the rover, were used as the structure of this device. The rollers are grooved aluminum cylinders. To insulate the wires, the aluminum rollers use Phenolic shafts (a polymer based composite) instead of tradition steel shafts. The wires are friction clamped at each end using fiberglass plates, again for insulation. The constant force spring is wrapped around an aluminum drum that is free to rotate. A potentiometer mounted at the pivot point measures the angle of the mechanism.

Page 27 Figure A.8: Mechanism Schematic

Figure A.9: Mechanism Prototype A.4 Experimental Results

Page 28 A.4.1 Bipolar Position

The system was first tested in a loaded configuration (Figure A.6: Solution). Without the SMA wires, the system was stable in either the fully raised or fully squatted position, as predicted. Upon actuation of the wires, the mechanism raised and squatted with rise times on the order of ½ second for the full 60° of motion.

A.4.2 Position Control

Position control experiments were performed with the reconfigurability configuration shown below (Figure A.10). The one pound payload was removed and the lower (raise) wires were not used. This is the simpler of the two configurations to control, and therefore a better starting point. A proportional position control loop was written in C++, and position measurements were read from a potentiometer mounted to the joint. The high current needs of the SMA’s were met by a custom built transistor circuit (Troisfontaine, 1998).

Figure A.10: Position Control Configuration

Figure A.11: Transition Phase

Page 29 Figure A.12: Position Control Block Diagram The first task was to determine the holding current. This is the current required to keep the SMA between the austentite and martensite phases, as illustrated in Figure A.11. This current would be the current sent from the amplifier when the position error (desired position – actual position) was 0. Then the proportional gain, Kp, was tuned to optimize performance. Figures A.13-A.15 presents test results for three different desired angles. The peak power used was 1.9 Watts.

Figure A.13: 10° Step

Page 30 Figure A.14: 30° Step

Figure A.15: 50° Step

A.4.3 Analysis

These plots show a rather typical P control response. Due to low damping, there is some overshoot in the two larger steps. Also there is some steady state error. If position accuracy better than a few degrees is required, than an integrator term would be necessary. Another observation is the one-half second lag before the mechanism begins to move. This lag is due to a “cold start” by the system. The current being sent to the wires was zero, not the holding current,

Page 31 when the test began. Therefore, the lag is the time it took for the wires to heat up from room temperature. One key observation that is not shown in Figures A.13-A.15 is that this system exhibits very poor disturbance rejection, typical of P control. Using higher gains, however, cause the system to oscillate. PID control may solve this problem as well as the steady state error problem. Many design improvements will need to be made, however, before this system can be incorporated into the rover. First, the wires may have slipped in the friction clamps. The issue will need further investigation and possibly a better method of fixing the wires will be necessary. Also, this test system uses free rolling wheels, where as the wheels may not be free to move on the rover if it is stuck. Also, as mentioned earlier, the position control tests above were done with the system unloaded. Further tests will have to be performed with different payloads and possibly using both sets of wires and a more robust control scheme. Power considerations dictate that this system cannot be actively running all of the time. To keep power usage down, control should only be done for one or two seconds at a time, just enough time to achieve the desired position. The two sets of wire acting against each other will both be in the stress-strain curve location shown in Figure A.11. Therefore, small outside force will cause the mechanism to change angle. One solution to this problem is to incorporate a brake that passively locks the system in place. When a new angle is desired, the brake is released momentarily by another SMA wire, and the angle can be changed. Then the brake is released and the system locks. Thus only a few seconds of power would be used. The next section presents a new design based on these results.

A.5 Second Generation Design The new design for rover reconfigurability is shown in Figure A.16. Illustrated is the rocker of the rover’s left side. One key feature is the Delrin© wire guides, which replace the aluminum rollers. Delrin gives the wires a low friction, insulated surface to slide on. The guides also protect the wires, which were exposed in the first generation design. The second key feature is the addition of a brake. A multi-jaw coupling locks the rocker links in place, fixing the angle. The jaws are held together by a compression spring located underneath the other side of the brake pivot lever. An SMA wire is hidden inside the aluminum tube next to the spring. When the SMA wire is heated, it pulls the brake pivot lever towards the tube, opening the jaws and allowing the other SMA wires to change the rocker angle.

Page 32 +

Figure A.16: Second Generation Design

Figure A.17: Brake Close-up

Page 33 A.6 End-Effector

A.6.1 Introduction One of the main purposes of the manipulator arm is to acquire and manipulate rock samples. The arm therefore needs an end-effector to grasp rocks. The Sojourner rover did not have a manipulator, so no end-effectors have been tested yet on Mars. JPL is testing a multi-purpose end-effector on Rocky 7 (Volpe, 1998), which is another experimental test bed rover. JPL’s end- effector, shown in figure A.18, is a two DOF tool that can dig, grasp, and point instruments. The double scoop can dig and pick up sand. If the two sides of the scoop are flipped around, they can be used to grasp rocks. Since the FSRL will not be doing digging work in the near future, an end-effector with such a diverse capability is not necessary for the experimental system.

Figure A.18: Rocky 7 with End-Effector (Volpe, 1998) The first purpose of this end-effector research is to design and build an experimental test bed for manipulator control work. Part of this manipulator control work involves manipulation of rocks. The second purpose of this research, as mentioned in A.1, is to develop new, lightweight mechanisms to manipulate these rocks. Section A.6.2 shows six new concepts for end-effector design, and selects the two most promising designs. Sections A.6.3 and A.6.4 detail the two best designs and section A.6.5 presents some experimental results.

A.6.2 Concept Selection There are three functional requirements for the end-effector. First, it must be light weight, which is a main goal of this mechanism design work. Second, it must be able to pick up rocks reliably, and third, it should be able to pick up a variety of rock sizes and weights. With these requirements in mind, six different end-effector concepts were generated. For purposes of weight, any actuation of the concepts is to be done by shape memory alloy wires.

Page 34 Figure A.18: End-effector Concepts Figure A.18 displays these six concepts. Concept 1 uses three spring loaded rigid fingers, with compliant pads at the tips. SMA wires pull the fingers open, and the springs close the fingers when the wires cool. This configuration allows for short duration SMA use. Concept 5 is similar to concept 1, except that is uses three sharp metal points to contact the rocks instead of the pads. Concept 3 Uses three flexible fingers with the SMA’s embedded in the fingers, which would be made of a polymer material. Concept 6 utilizes two plates that each have a matrix of spring loaded pins. These pins would be pushed up against the rock, forming the contour of the sample. Again, the plates would be spring loaded closed, and an SMA would be used for momentary opening of the plates. Concepts 2 and 4 take a different approach by not requiring actuation. Concept 2 is a hollow cylinder that contains many different sizes of pivoting teeth. When the device is pushed over the sample, some of the teeth lift up and then flip back down underneath the rock, and the rock can be lifted. To let go of the rock, the end-effector is turned upside down and the rock falls out the top. Concept 4 is similar to concept 2, except that it uses spring steel teeth that flex instead of pivot. Also, concept 4 uses essentially two halves of a cylinder that can be pushed open to accommodate a large variety of rock sizes. All six concepts were rated based to ten different categories, as shown in Table A.1. Each different criterion was given a weighting and five concepts were rated on a scale of 1 to 5 against Concept 1, which was chosen as the baseline concept. The category “Durable Materials” refers to the concepts’ use of certain polymers. Low Martian temperatures can cause polymer flexures to become brittle, and the low atmospheric pressure causes degradation of some materials. From the selection matrix, the two best designs emerged, concepts 4 and 5. Since these two designs have very different approaches to acquiring samples, both were built and tested. Table A.1: Concept Selection

Page 35 Concepts Selection Criteria Weight 1 2 3 4 5 6 3 Pads Ratchet Cup Flexible Fingers Ratchet Clamshell 3 Points Contour Pins % Rating Score Rating Score Rating Score Rating Score Rating Score Rating Score

Sample Size Flexibility 5 3 0.15 1 0.05 3 0.15 2 0.1 3 0.15 2 0.1

Sample Shape Flexibility 15 3 0.45 2 0.3 4 0.6 3 0.45 3 0.45 3 0.45

Reliability of Grip 10 3 0.3 2 0.2 3 0.3 3 0.3 2 0.2 3 0.3

Creativity 10 3 0.3 5 0.5 4 0.4 4.5 0.45 3 0.3 4 0.4

Appearance 10 3 0.3 2 0.2 5 0.5 2.5 0.25 3.5 0.35 2.5 0.25

Durable Materials 5 3 0.15 5 0.25 1 0.05 2 0.1 4 0.2 4 0.2

Complexity 15 3 0.45 1 0.15 1 0.15 2 0.3 4 0.6 1 0.15

Actuation 15 2 0.3 5 0.75 1 0.15 5 0.75 2 0.3 2 0.3

Machining Time 5 3 0.15 2 0.1 1 0.05 2 0.1 3.5 0.175 1 0.05

Weight 10 3 0.3 3 0.3 3 0.3 3 0.3 3 0.3 2 0.2

Total Score 2.85 2.8 2.65 3.1 3.03 2.4

A.6.3 Design 1 The first concept built was the three pointed fingers gripper. Each of the three fingers was made from 1/8” steel shaft. The fingers pivot about steel slip fit pins which are clamped onto the main plate by socket cap screws. The main plate is a circular piece of plastic, so that the fingers are electrically insulated. An elastomer was wrapped around the three fingers to serve as a spring. The SMA wires are tied through holes in the top of the fingers. The wires then run over Delrin guides and meet in the middle underneath the plate. The wires are routed over the plate and back underneath to give more deformation length, allowing more finger travel. The Delrin guides provide low friction, insulated channels for the wires to follow. Figure A.19 shows the design, with one of the wires and Delrin guides shown. An aluminum bracket bolted to the plate mates with the end of the manipulator. The 3 finger gripper is designed to be able to grasp rocks up to 2 ½" in diameter, and be able to hold the weight of a typical rock of that size. The end-effector weighs a remarkably light 2 ounces.

Page 36 Figure A.19: Three Fingers Design

Page 37 Figure A.20: A Three Fingers Prototype Gripper

A.6.4 Design 2 The second concept to be constructed is the ratchet/clamshell design. Figure A.21 shows the design. The two halves of the gripper are made of Lexan. Two spring steel beams support each half and hold it in the closed position, and the thickness of the beams can be varied to adjust the clamping force of the gripper. The flexible teeth are made of spring steel as well and are epoxied to the Lexan halves. The teeth are bent at a 135° angle so that as the gripper is pushed on top of a rock, the teeth and the halves are forced open. To release the sample, the gripper is turned upside down and the rock slides out the top. Again, an aluminum bracket bolted to the gripper mates with the end of the manipulator. This end-effector is also designed to accommodate up to 2 ½" rock diameters and can be modified for SMA actuation if necessary. The end-effector weighs one ounce.

Page 38 Figure A.21: Ratchet Clamshell Design

Figure A.22: Ratchet Clamshell Prototype Gripper

A.6.5 Test Results The two end-effectors were tested picking up rock samples. Two different kinds of rocks were used. Red volcanic lava rocks represent possible Mars samples. They are very porous and lightweight, being less dense than water. Silicon nuggets were also tested. They are much more dense, 2.33 g/cm3, and have much smoother surface characteristics than the lava rocks. Figure A.23 shows the two types of samples tested. Examination of terrain maps of Mars suggests that many of the small rocks on mars will be partially buried in fine sand. Therefore, the lava and

Page 39 silicon rock samples were buried about halfway, as seen in Figure A.24. The end-effectors were tested picking up a variety of samples of each kind of rock.

Figure A.23: Test Samples

Figure A.24: Sample Placement The results of the tests are shown in Figure A.25. If the rock was not picked up by the gripper in the first or second attempt, then it was considered a failure. For both end-effectors, the lava rocks proved to be easier to pick up, because they were lighter and had a rougher surface, which is easier to grip. The three finger gripper was very successful at probing into the sand, to reach the lower half of the samples. The samples that it usually failed at picking up were either of a long, thin shape or were heavy and had a very smooth, regular surface which was difficult to grip. The ratchet/clamshell gripper was the most successful at picking up the lava rocks. The only lava rocks that it had problems with were the ones that the gripper had to push deep into the sand to get a reasonable grip. This gripper didn’t probe into the sand nearly as easily as the 3 finger end- effector. However, this end-effector had some problems picking up many of the silicon rocks because of their smooth surface. Often, the teeth would just slip right over the rock. Thus, surface texture seems to be an important factor in this end-effector’s performance.

Page 40 90

80

70

60

50

40

30 Percent of Rocks 20

10

0 1st Try 2nd Try Fail

3 fingers Lava 3 fingers Silicon Clamshell Lava Clamshell Silicon Figure A.25: Test Results

Page 41 Appendix B Rover Force analysis and Simulation This appendix presents the force analysis of the rover. The 3-D balance is delineated in Section B.1. Ground-tire interaction models are used to introduce additional equations. Section B.2 presents a planar analysis of the rover. Section B.3 details a solution method to the problem. Useful evaluation parameters are defined and computed in Section B.4. The graphic interface has been developed and is presented in Section B.5.

B.1 Force Analysis

B.1.1 Main Assumptions The force analysis determines if the rover is physically able to perform a task. An easy way to evaluate this is to determine if the rover can stay in static equilibrium in its current position. This evaluation method is consistent with the fact that the rover is going to move at slow speeds: a quasi-static approximation is appropriate. Moreover, under this hypothesis, if the different evaluation positions of the rover are closely distributed in space and time, the torque distribution on the wheels that verifies the rover’s balance can be approximated as the actual commanded torques and can be used to calculate power consumption.

B.1.2 Rover center of mass and input force computation The position of the center of mass affects the load distribution on the wheels and the stability of the vehicle. It is therefore critical to compute its location. From this, the input force to the system can be deduced.

Page 42 B.1.3 Rover Masses Distribution

Figure B.1: Rover Mass Distribution. The rover mass distribution is shown in Figure B.1. Contribution to the system mass can be summarized as follows: · The main body, which will contain the science experimental equipment, the computer and power supplies. · The wheels. The motors’ masses are not negligible. This is why the LSR-1 design does not include any steering wheels. Extra actuators are not desirable. · The manipulator represents approximately 15% of the mass of the rover and whose range of motion is large enough to affect the center of mass position (Schenker et al., 1997-3). The position of the center of mass of this subsystem is computed with the knowledge of the kinematics of the arm. · Additional masses are rock samples gripped by the arm and those loaded or carried into the rover. Their influence must be taken into account too. The locations of all these elements are fully determined by the kinematics of the rover. Moreover, the masses of the rover’s parts are known, and it is assumed that rover sensors can estimate the masses of the rocks quite well. Volume estimates can lead to such mass estimations. All these systems and sensor readings are taken into account for the computation of the center of mass position. While simple, this task is important since it affects the rover’s stability and balance equations.

Page 43 B.1.3.1 Input Forces to the System Since the rover’s force analysis is performed under the quasi-static assumption, the input forces can be expressed as a wrench that will be located at the center of the body. This input wrench T vector is composed of six components computed in (x”, y”, z”) : [ Fxi, Fyi, Fzi, Mxi, Myi, Mzi ] .

The quantities Fxi, Fyi and Fzi are the components of the sum of all the externally applied forces in x”, y” and z” respectively. Mxi, Myi and Mzi are the components respectively in x”, y” and z” of the moment created by the sum of the externally applied forces on the center of the body. These external forces can be arbitrary forces or moments along the direction of motion of the system. Forces resulting from the manipulator’s interaction with its environment can be represented too. In the following sections, the lumped input wrench vector will be referred to as Fi.

B.1.4 Transversal Forces Computation

With the input force Fi to the system considered to be known, the three-dimensional analysis can be developed. The rover mechanics are quite complex. Since there are six contact points with the ground, the system is statically indeterminate. Modeling it as a solid results in 36 unknowns (six per wheel), that have to be computed with only six equilibrium equations! (see Figure B.2). The problem can then not be uniquely solved. Some simplifications help to reduce the number of unknowns. The moments created by the ground are small with respect to the moment that are induced by the rover transversal forces and can ignored, leaving only the friction forces.

Figure B.2: Force Analysis Unknowns (Represented on one wheel only).

Page 44 Even with these simplifications, the system remains statically indeterminate, with 18 unknowns (three per wheel) for six balance equations. The most common way to eliminate the extra unknowns is to make some elements of the structure compliant (Beer et al., 1981). Then, additional equations can be written. In the case of the rover, the most compliant elements of the structure are the tires, since the rocker-bogie structure is intended to be very rigid. The following model is used to represent the wheel/terrain interactions.

First, the longitudinal forces (Tir or Til) are controlled by the wheel torques, where i refers to the wheel number. The normal forces (Nir or Nil) are defined by the system and are not friction forces. But the transverse forces (Fyir or Fyil) can only be computed using a model of soil-tire interaction, more specifically the compliance of the wheels.

Figure B.3: System Compliance. Naturally, the transverse forces need to equilibrate the transverse input force Fyi.(see Figure B.3). They are also modeled to create no net moment on the body. This assumption is plausible. Indeed, when the rover is sitting exactly perpendicular to a slope and that no external forces other than gravity are exerted, it will not turn in place. The compliance of the wheels is represented by a spring of stiffness k and is assumed to be the same for all the wheels. Therefore, the problem is to find the relations between the relative displacements yi of the wheels. The equations are: k y y y y y y F 0 ×( 1r + 2 r + 3 r + 1 l + 2 l + 3 l )+ yi = (B-1)

i = 3 x y x y 0 (B-2) å( ir × ir + il × il ) = i =1

where xi is given by the kinematics of the rover. Equation (B-1) is the balance of forces in the y” direction, and Equation (B-2) is the moment balance equation along z”.

Since the rest of the body is relatively more rigid than the tires, all the displacements yir or yil are related to each other. This problem is similar to the balance of a beam on three compliant points. The displacement of the springs are linearly coupled because the beam is rigid (under small angle approximation). Here, the rover is taken as a rigid element too. Therefore, the

Page 45 displacements yir and yil are linearly coupled, as shown in Figure B.3, inducing Equations (B-3) through (B-6): y y (x x ) 2 r = 1 r + x × 2 r - 1 r (B-3)

y3 r = y1r + x ×( x3 r - x1r ) (B-4)

y2 l = y1l + x × ( x2 l - x1l ) (B-5) y y ( x x ) 3 l = 1l + x × 3l - 1l (B-6) The parameter x is the slope of the line joining all the relative displacements on the same side, see Figure B.3. There are six equations and seven unknowns: another constraint is added. y y 1 l = 1r (B-7) This constraint means that both rear wheels have the same contribution to the force balance. If the rover is such that all the wheels are at the same relative positions (i.e. x1r=x1l, x2r=x2l, x3r=x3l), then by symmetry, the forces will be the same on each pair of wheels. Equation (B-7) verifies this.

It is then possible to solve for x and y1r. Their expressions are given in Equations (B-8) and (B- 9). F x x (B-8) yi ×å( i × D i ) y i 1 r = æ ö k ç x x 6 x x ÷ × åå( i D j )- × å( i × D i ) è i j i ø F x yi × å( i ) (B-9) x = - i æ ö k ç x x 6 x x ÷ × å å( i D j )- × å( i × D i ) è i j i ø

where xi represents any xir or xil, and Dxi =(xi -x1 ). This model gives the values of the transverse forces acting on the wheels and reduces the hyperstaticity of the system. The remaining unknowns are the normal forces Nir and Nil and longitudinal forces Tir and Til. They can be deduced using free body diagrams as is described below.

B.1.5 Main body balance The rest of the analysis is conducted using free-body diagrams (see Figure B.4). The main body is separated from the rest of the rover. By writing the balance equations for the body, it is possible to calculate the forces that are applied to each side of the rover. This section describes the main body balance. The body’s balance is written in the R” frame, defined in section Error! Reference source not found.. The unknowns of the static equilibrium of the rover are Fzr, Fzl, Fyr, Fyl, Fxr, Fxl, and Mzr, Mzl, Myr, Myl, Mxr, Mxl. Here, the subscripts x, y, and z refer to the x”, y” and z” directions respectively. The equilibrium equations are scalar and the sign convention used is that the unknowns are positive in the directions shown in Figure B.4.

Page 46 Figure B.4: Rover Balance. The input Fi is a vector of three forces and three moments which are applied at the center of the body (more precisely, in the middle of the two body-rocker joints). They are positive in the directions defined by R”. The influence of the transverse forces are also taken as inputs to the static body balance. These forces induce forces in the y” direction that exactly compensate for Fyi, (therefore Fyr and Fyl are known) and moments in the x” and z” directions. The sum of the moments in the z” direction is zero because of the model used in the previous section. The moments in the x” direction should be affected by the longitudinal and normal forces on the wheels as well, but in the model, the width of the rocker-bogie mechanism is zero. Consequently, these moments are only functions of the transverse forces and are input to the body balance equations. Using the directions of the forces defined in Figure B.4 and using the components of the vectors u, v and w (defined in Figure B.5) along the z” axis (referred to as uzr, vzr and wzr for the right side and uzl, vzl and wzl on the left side), Fyr, Fyl , Mxr, Mxl, Mzr and Mzl can be deduced, since they are functions of the transverse forces only, and are given by: F F F F yr = y1 r + y2 r + y3 r (B-10) F (F F F ) yl = - y1 l + y 2 l + y 3l (B-11) M M 0 zr + zl = (B-12)

Page 47 M F u F v F w (B-13) xr = -( y1 r × zr + y2 r × 2 r + y 3 r × 3 r )

M F u F v F w (B-14) xl = -( y1 l × zl + y 2 l × 2 l + y3 l × 3l )

Figure B.5: Transverse Forces Influence. The remaining unknowns to the body balance are then : Fzr, Fzl, Fxr, Fxl, Myr and Myl. The quantities Fzl and Fzr are the forces in the z” direction acting from the rocker to the body. Fxr and Fxl are in the x” direction. The balance equations of the system are: F + F = F xr xl xi (B-15)

w w F F M M M xr × - xl × = zi + zr + zl (B-16) 2 2

M + M = M yr yl yi (B-17)

F + F = F zr zl zi (B-18)

w w F × - F × = M - M - M (B-19) zl 2 zr 2 xi xr xl

There are only five equations to solve for the six unknowns (the force equation in y” does not provide any new information and is not considered here). An additional equation is needed to solve for the moments in the y” direction. Here, it is assumed that both sides have the same contribution to that balance, hence the additional equation: M M yr = yl (B-20) The forces acting on the body can then be calculated and expressed as functions of the input forces and of Fyr, Fyl , Mxr, Mxl, Mzr and Mzl , that are defined by the transverse forces only. Their expressions are : F M F = xi - zi (B-21) xl 2 w

Page 48 F M xi zi (B-22) F = + xr 2 w M yi (B-23) M = yr 2 M yi (B-24) M = yl 2 F M - M - M F = zi + xi xr xl (B-25) zl 2 w F M - M - M F = zi - xi xr xl (B-26) zr 2 w These results can be checked intuitively. For example, if the center of mass is shifted to the right side of the body then Mxi increases and, from (B-25), Fzr becomes more negative. Also, if the roll of the body is positive, more weight should be transferred to the right side. What happens then is that the transversal forces Fyi become more positive. Therefore, Mxr and Mxl become more negative (from (B-13) and (B-14)) and so does Fzr from (B-26). Such rapid tests suggest that the equations are correct. From these solutions, the forces that will be applied to each rover side can be deduced. The rocker-bogie mechanism is modeled as a two-dimension system. The following sections present the force analysis of the rocker-bogie, address the issue of actuator redundancy, and present a method to find an optimum wheel torque distribution.

B.2 Planar Analysis of the Rocker-Bogie This section presents the planar quasi-static force analysis of the rocker-bogie mechanism. Some planar analysis has been developed for mobility evaluation of the rocker-bogie design in (Linderman et al., 1992). This analysis is a general tool to accommodate any sort of input of rocker-bogie configuration. It can then be used to study the effect of the kinematic parameters on the load distribution.

The model is shown in Figure B.6. In this model, there are six unknowns (Ti, Ni, i=1,2,3) and four independent static equilibrium equations. There are indeed two equilibrium equations for the forces in the x” and z” directions, and two moment equations on the rocker-bogie pivot joint. The moment equation must be zero at that point for both the rocker and the bogie, hence two equations. i i i The inputs to the system are Fx , Fz and My . They are related to the parameters calculated in the previous section (Fxr, Fzr, etc.) based on the free body diagram in Figure B.4. The geometry of the ground, and therefore the directions of the traction and normal forces are known. The direction of these forces are defined by the inverse kinematics procedure that locally considers the ground as a plane under each wheel. To perform the force analysis, the positions of the wheel contact points with respect to the rocker-bogie joint are required. The vectors u, v and w connect the wheel/ground contact points to the rocker-bogie joint (see Figure B.6). Vector z connects the rocker/body joint to the rocker/bogie joint. Their components along x” and z” are written with x and z subscripts respectively.

Page 49 Figure B.6: Rover Planar Analysis. The static equilibrium equations are:

T c T c T c N s N s N s F i 0 (B-27) 1 × 1 + 2 × 2 + 3 × 3 - 1 × 1 - 2 × 2 - 3 × 3 + x =

T s T s T s N c N c N c F i 0 (B-28) 1 × 1 + 2 × 2 + 3 × 3 + 1 × 1 + 2 × 2 + 3 × 3 - z =

T c u T s u N s u N c u M i F i z F i z 0 (B-29) 1 × 1 × y - 1 × 1 × x - 1 × 1 × y - 1 × 1 × x + y + x × y + z × x =

T c v T s v N s v N c v (B-30) 2 × 2 × y - 2 × 2 × x - 2 × 2 × y - 2 × 2 × x T c w T s w N s w N c w 0 + 3 × 3 × y - 3 × 3 × x - 3 × 3 × y - 3 × 3 × x = where ci = cos(ai) and si = sin(ai), i=1,2,3. These equations can also be expressed in matrix form (see Equation (B-31)).

T T A T T T N N N F i F i M i F i z F i z 0 (B-31) ×[ 1 2 3 1 2 3 ] = [- x z - y - x × y - z × x ] where A is a 4x6 matrix (four equations, six unknowns). Hence the system of equations is underdetermined and its null space is at least of dimension two.

Page 50 This system cannot be uniquely solved. However, it is very important to note that some of the unknowns can be controlled or constrained. Equilibrium of a wheel is given by Equation (B-32) (assuming that the wheel is not slipping). rad T ti = × i (B-32)

where rad is the radius of the wheel, Ti the traction force and ti is the torque applied to the wheel by the motor. It is equivalent to consider the traction forces or the wheel torques, since they are related by the constant rad. Since there are two infinities of solutions, two traction forces can be arbitrarily chosen. The rear and middle wheel traction forces are considered as command inputs. The other forces, including the third traction force and the other normal forces are uniquely determined by these inputs. For example, if the rover is standing on a flat terrain, two traction forces can be applied on the wheels 1 and 2. To obtain equilibrium, the third force must be equal to the opposite of the sum of the other two. This intuitively verifies the double infinity of solutions.

The problem can then be restated by using the traction forces T1 and T2 as parameters and inputs to the system :

T B T N N N C T D T E (B-33) ×[ 3 1 2 3 ] = × 1 + × 2 + where B is 4x4, and C, D and E are 4x1 vectors.

If B is invertible, T3, N1, N2 and N3 are linear functions of T1 and T2. T c' d' e' é 3 ù é 1 ù é 1 ù é 1 ù (B-34)

ê N 1 ú êc ' 2 ú ê d' 2 ú ê e' 2 ú = × T1 + × T2 + ê N 2 ú ê c' 3 ú ê d' 3 ú ê e' 3 ú ê N ú êc ' ú ê d' ú ê e' ú ë 3 û ë 4 û ë 4 û ë 4 û

Any couple (T1 , T2 ) defines a solution to the equilibrium equations. However, the solution must satisfy the physical constraints such as motor saturation, wheel slip and that the normal forces must be positive. Firstly, constraints on the sign of the normal forces must be verified: N 0 i 1) i ³ " (B-35)

Clearly, the normal forces must be positive. The condition Ni < 0 implies that the ground would have to pull down on the wheel to maintain equilibrium. Secondly, the motors cannot create an infinite torque. Physical limitations of the system have to be taken into account. rad T , i 2) × i £ tsat " (B-36)

Page 51 Thirdly, a limitation on the traction force due to wheel slip must be verified. The maximum traction force is limited by the product of the coefficient of friction and the normal force on the wheel. T N , i 3) i £ m × i " (B-37)

These three constraints must be satisfied at all times and for all the wheels. Finding a couple (T1 , T2) that satisfies these three constraints is challenging. A common way of finding a solution to such over determined problems is the pseudo-inverse method. An advantage of this method is that it is very simple to implement and it is computationally efficient. The pseudo inverse of a matrix A is defined as A#=AT (A AT)-1. The 2 solution to A x = b given by this method is: x = A# b. The method minimizes x (Doty, 1993). In the case of the rover, however, some of the unknowns cannot be directly actuated (the normal forces). Hence the optimum solution found with the pseudo-inverse would have little relation to the power consumption. Also, there is no guarantee that the physical constraints are verified. Another method must be used that fully considers the physics of the system. It is described in the following section.

B.3 Force Analysis Solution

B.3.1 Solution Space

Page 52 Figure B.7: 3-D Solution Space. To solve for the underdetermined force analysis while verifying all the physical constraints, a good representation of the problem is necessary. The previous section describes how to express T3, N1, N2 and N3 as linear functions of T1 and T2 . A 3-D visualization of the solution space is shown in Figure B.7. Here, the plane defined by T3=c’1 T1 +d’1 T2 +e’1 is represented. This plane is the solution space which contains the two infinities of solutions. Other planes are drawn that represent the physical constraints of the system. These constraint planes are represented by such equation as rad Ti = tsat or Ti = m Ni (see Table B-1). It is easier to view the orthogonal projection of the solution plane onto the (X,Y) plane. The plane (X,Y) will be referred to as P (see Figure B.8).

The constraints are also projected into P. They are functions of T1 and T2 only, therefore they become lines in P (see Equation B-34). There are nine constraints (three per wheel). Since some of these constraints are represented using absolute values, they are broken into two constraint equations (one if the term inside the absolute value is negative, and the other if the term inside the absolute value is negative). Six of the nine constraints are represented with absolute values, leading to 12 equations. In total, 15 equations must be computed. They are represented on Table B-1. Table B-1: Physical Constraints rad T rad T 1 × 1 £ tsat 2 × 1 ³ -tsat rad T rad T 3 × 2 £ tsat 4 × 2 ³ -tsat rad T rad T 5 × 3 £ tsat 6 × 3 ³ -tsat T N T N 7 1 £ m × 1 8 1 ³ -m × 1 T N T N 9 2 £ m× 2 10 2 ³ -m × 2

11 T3 £ m × N 3 12 T3 ³ -m× N 3 N 0 N 0 13 1 ³ 14 2 ³ N 0 15 3 ³

Page 53 Figure B.8: 2-D Visualization of the Solution Space. This fully defines the solution space. The following method uses this representation to find a suitable solution to the underdetermined system of equations.

B.3.2 Solution Search for the Statics of the Rover The solution space contains either zero or an infinity of solutions. It is then necessary to define criteria to choose the best solution. Since power consumption is critical in planetary exploration missions, the minimization of this variable is chosen as the criteria in finding a solution. For systems actuated by DC motors using pulse-width-modulated amplifiers (as in this case), the power consumed can be estimated by the power dissipation in the motors’ resistances (Dubowsky et al., 1995). Therefore, power consumption in the wheels is a function of the square of the motor current (see Equation B-38). P R i 2 = å × k (B-38) k

Page 54 where R is the motor resistance and ik the current through the motor k. The motor current ik is defined by Equation (B-39).

tmotor ,k (B-39) i = k k motor

where tmotor,k is the torque applied by the motor and kmotor is the motor constant. The quantity

tmotor,k is related to the output motor torque by the gear ratio r (see Equation (B-40)).

tk (B-40) t = motor ,k r

where r is the gear ratio of motor k. The power consumption can be deduced from (B-38), (B- 39) and (B-40) and is given by: 2 R 2 R ×rad 2 (B-41) P T = 2 å×tk = 2 å× k r ×k motor k r ×k motor k

In other words P can be written as a second order function of T1 andT2. The function P is an elliptic paraboloid. Since P is a second order polynomial, it has a unique global extremum. Moreover, since P is always greater than or equal to zero, that extremum is a minimum (if it were a maximum, then the branches of the paraboloid would tend to negative infinity): P is monotonically increasing away from the minimum point. The solution that minimizes power consumption can now be found. To do this, the system of equations (B-42) must be solved. ì ¶P (B-42) = 0 ï ¶T min( P) Þ 1 í ¶P = 0 ï T î ¶ 2 Since P is second order, Equation (B-42) is a linear system of equations which is solved numerically. only. If the computed minimum value does not violate any constraint, it is the solution. If it does, the optimum lies on one of the violated constraints (because P is monotonous). The following steps are used to compute the optimum: 1) The constraints that are violated by the minimum are set aside. They are defined as the active constraints (see Figure B.9). 2) If only one of these constraints is violated, the solution is taken as the closest point to the minimum that lies along the line equation of the constraint. The equation specific to that geometric problem can be found in (Anton, 1984). This is not necessarily the optimum solution but it can be found rapidly. The algorithm ends. 3) If more than one constraint is active, it is not possible to use the step 2) method the closest point to the minimum on any active constraint is not guaranteed to satisfy all the conditions. Therefore, the easiest and fastest way to find a solution is to look at the intersection of the

Page 55 constraints lines. The algorithm calculates the intersection of the active constraints with all the other constraints (the intersections between non-active constraints are not interesting since the optimum should lie on an active constraint). The active intersections set A is defined as the set of the intersections that do not violate any constraint. If A is void, there are no solutions. If not, the solution is taken as the active intersection that has the minimum power. This configuration is presented in Figure B.9.

Figure B.9: Force Analysis Solution Search Method. Of course, this solution does not always provide the optimum solution, because the constraints intersections are not always the optimum. But it is sufficient to determine if a suitable solution can be found.

B.4 Calculation of Important Parameters It is necessary to define and compute some measures that give an indication of how well the rover is performing. The factors considered here are: static stability, power consumption, actuator saturation, wheel slip and distance traveled. The definitions and computation of these measures are presented below. For reasons of robustness, they are represented as non- dimensional ratios. Some errors in the model or ground representation are likely to alter the real value of that ratio.

Page 56 B.4.1 Stability Margin There are different ways to determine the stability of a vehicle. If dynamics is important one measure of stability is the energy required to tip over the vehicle (Ghasempoor et al., 1995; Messuri et al., 1985). However, in the case of the LSR, dynamics are negligible. Consequently, stability margin is defined as a function of the location of the center of mass with respect to the wheels’ contact points. A means to evaluate this stability is to project the center of mass on the horizontal plane of the wheel footprint polygon projection (see Figure B.10). The distance from the center of mass to the border of the stability polygon defines the system stability. Therefore, the stability margin can be defined as: d (B-43) S = min d 0 min

where dmin is the minimum distance between the center of mass and the stability polygon, and d 0 min is the nominal minimum distance evaluated when the rover is at its most stable position, i.e. on an horizontal surface (see Figure B.10).

Figure B.10: Stability Margin Definition. th Let Pi(xi, yi) be the coordinates of the i contact point between the wheel and the ground in Rground. The origin of Rground is translated to the center of mass of the system. Here, the stability polygon’s vertices are ordered from 1 to 6 (the sides are [PiPi+1] ). Let vi be the normalized vector orthogonal to PiPi+1 pointing towards the center of the polygon. Let di be the distance between [PiPi+1] and the center of mass. The quantity di is deduced with the following formulae : y y é -( i 1 - i )ù 1 (B-44) v = + × i x x 2 2 ê i 1 - i ú y y x x ë + û ( i +1 - i ) + ( i +1 - i ) x ×( y - y ) - y ×( x - x ) P O v i i +1 i i i+1 i (B-45) di = i · i = (y y )2 ( x x )2 i+1 - i + i+1 - i

If $ i /di<0, then the center of mass is out of the stability polygon. dmin=0. Else, dmin=min(di),= i=1...6. This method gives a good representation of the stability of the vehicle. However, it does not consider top heaviness: using this method, if the center of mass has the same projection on the contact polygon, its altitude does not affect the stability. In reality, it does, because a small

Page 57 perturbation on the rover would destabilize the rover more easily if the center of mass is high (see Figure B.11).

Figure B.11: Top Heaviness. Another method considers top heaviness in a more accurate way (Papadopoulos et al., 1996).

Let Li be the line joining the wheel contact points Pi and Pi+1. Let hi be the angle between the vertical direction and the line that is orthogonal to Li and contains the center of mass of the system (see Figure B.12). The stability margin S is then defined as: æ (B-46) S min ç hi ö = nom ÷ i è hi ø

nom where hi is the angle measured when hi the rover is standing on a horizontal surface.

Figure B.12: Stability Margin that considers Top-Heaviness.

Page 58 B.4.2 Actuator characteristics

It is important to determine how the wheel torques are close to saturation (tsat). The torque saturation ratio measure is important in determining if the rover can move over obstacles. The torque saturation ratio is defined by Equation (B-47). t (B-47) t = i ratio , i t sat

B.4.3 Slip ratio th The slip ratio determines how close a wheel is from slipping. The i wheel slip ratio Si is defined as : T i (B-48) N S = i i m i

where mi is the local coefficient of friction under wheel i. The slip ratio can be seen as the ratio between the coefficient of friction at which the wheel would slip and the actual coefficient of friction.

B.4.4 Power and Distance The distance traveled by the rover across the terrain is also calculated. Power consumption is a crucial element. Its computation is detailed in Section 0. It is felt that these measures are useful evaluation tools. Different designs can be implemented in the simulation and the influence of the kinematic parameters can be investigated.

B.5 Graphical Simulation A graphical representation of the system is also beneficial to enhance the understanding of the system and to verify the veracity of the model. The simulation includes a graphical interface. It originated from Mechanical System Visualizer (MSV), a 3-D graphical software (Torres, 1993). The original version has been upgraded to meet the requirements of the simulation (Cassenti, 1997). Specifically, it was upgraded to enable the representation of a meshed surface for the terrain, and to create a user interface window. The rover is displayed as it moves and interacts with its environment. Figure B.13 shows a typical instance of the graphical interface.

Page 59 Stablity Margin Wheel 1l Wheel 2l Wheel 3l Rover Top View Control Panel Window Torque Time : 330.7 s Slip Ratio Distance traveled : 428.2 cm

Simulation Speed

Torque Slip Ratio Energy Consumed

Simulation Window

Figure B.13: Graphical Simulation. Additional features are included. First, it is possible to display the ground reaction forces. This makes it possible to check the load is distribution on the wheels. Other features are displayed in another “Control Panel” window. This window displays the measures defined in Section B.4, and updates them as the rover moves. This was created using a C-code library, called the Forms library, a graphical user interface toolkit for Silicon Graphics Workstations (Overmars, 1995). More details on how the simulation and the graphics work can be found in (Hacot, 1998). Stability margin is displayed on the left corner of the “Control Panel” window. Also, a rover top view is displayed and torque saturation and slip ratios are shown for each wheel. Finally, energy consumption is represented in a graph that is updated in real time.

Page 60 There are also buttons that allow a user interface with the simulation. These buttons allow the user to stop, pause, step forward or backwards, at any desired speed. These capabilities proved useful in evaluating rover performance.

B.6 Conclusion This chapter has presented the rover force analysis and simulation. The analysis is performed using a quasi-static model. The input force to the system can be arbitrarily chosen and can reflect the manipulator’s interactions with the ground. The analysis shows that the actuator redundancy can be used to affect the load distribution on the wheel. A method has been developed that finds a solution to the under-determined system of equations for static equilibrium. A graphical interface has been developed that enhances the understanding of the physics of the system and displays different useful evaluation parameters. The analysis is not specific to a single configuration of the rocker-bogie mechanism. The kinematic parameters can be varied and their influence to the mechanics of the system can be studied.

Page 61 Appendix C Modular Design This appendix describes the modular design problem for field robots and the application of a hierarchical selection process to solve this problem. Sections C.1 and C.2 present an analysis of the size of the modular design search space. Section C.3 describes the theory of a hierarchical approach to the modular design problem. Section C.4 contains a description of this approach to designing modular field robotics. In Sections C.5, the approach is applied to example tasks.

C.1 The Modular Design Problem The goal of modular design is to select the best assembly of modules from a prefabricated inventory for a given task. The assumption of a modular approach is that useful designs can be created for a reasonable amount of tasks with a reasonably sized inventory. This is the first assumption as presented. If a large inventory can only produce designs for a few tasks, it is probably more effective to independently create specific designs for each task. However, if a reasonably sized inventory can create reasonable designs for a reasonable number of tasks, the advantage of a modular approach can be realized. A design that is independently created for a specific task can be optimized for that task. Such a design will, most likely, be sub-optimal and may not even be sufficient for another task. To create an individual design for every task is time consuming and costly. Conversely a design produced using a modular approach will, most likely, be sub-optimal for a specific task. However, the modular design may prove sufficient. Also, a modular design can be quickly and cost effectively reconfigured to produce a second sufficient design for a second task. In a modular approach, optimality is sacrificed to create a sufficient, cost-effective, rapid design.

C.1.1 Conventional Design versus Modular Design In important ways, the design of a modular system can be simpler than the design of a conventional system. In conventional design the design variables are, in general, continuous, and the number of possible solutions is infinite. In modular design the design space is discrete. This places an upper bound on the size of the modular design space. Theoretically, this space could be enumerated and every possible design evaluated. As shown later, the number of possible solutions in this discrete space, however, grows very rapidly with the number of available modules. For any real problem an exhaustive evaluation of these solutions is not practical. Also, modular designs are composed of pre-existing components. All characteristics of the components are known a priori.

C.2 A Study of the Modular Robot Design Space To gain insight into the design process, the size and growth of the modular design space is studied. For a group of modules, the number of possible assemblies can be computed. To do this, a set of common sense rules dictating how a robot can be assembled and what constitutes a robot assembly is defined. The rules used in this study are: 1) All robot assemblies must contain a power/control module.

Page 62 2) Limbs are groups of modules connected in a serial chain. 3) Limbs can be attached to ports on the power/control module. 4) Each limb must terminate in a module classified as an end effector. 5) All modules in the inventory do not need to be used in producing an assembly. 6) The power module is not completely symmetric. (e.g. the center of gravity does not lie at the geometric center)

C.2.1 A Simple Inventory

The design space is enumerated for a simple inventory shown in Table C-1. Here, np, njoints and nfeet represent the total number of power/control modules, joints and feet in the inventory respectively. Also, Nports represents the number of locations on the power module that limbs can be attached. These locations are called ports. Table C-1: A Simple Inventory Name Quantity

Power / Control np = 1

Module Nports = 14

Joint njoints = 4

Foot nfeet = 2

The number of possible designs, D, can be qualitatively thought of as a product of two factors: the number of limbs that can be created and where these limbs can be placed on the power module. This is indicated in Equation (C - 1). D = [(moving limbs amongst the ports) ´ (number of possible limbs)] (C - 1) = D D ports ´ limbs

Where Dports is the number of possible permutations of moving the limbs amongst the ports, and Dlimbs is the number of limbs that can be created. The number of limbs that can be created using a given number of modules (the second factor in Equation (C - 1)), is given by: (j + i - 1)! (C - 2) D limbs = j!(i - 1)! where j represents the total number of joints used in the limbs and i represents the total number of limbs created. Since each limb must terminate in an end effector, the number of limbs in this assembly is equal to the number of end effectors used.

Page 63 The number of assemblies that can be created using i limbs (the first factor in Equation (C - 1)), is given by: N ! ports (C - 3) D = ports i! N i ! ( ports - ) The derivation of this equation is given in Appendix A. These different robots result from

moving the i limbs to different ports on the power control module.

Substituting Equation (C - 2) and (C - 3) into Equation (C - 1) gives the number of assemblies that can be created using j joints and i limbs. This product can be summed over i (where i varies from 0 to nfeet.) and j (where j varies from 0 to njoints) to determine the total number of possible designs.

n feet n (C - 4) é æ N ! ö æ jo int s j i 1 ! ù ports ç ( + - ) ö D = 1 + åê ç ÷ å ÷ ú i 1 i! N i ! è j =0 j! i - 1 ! ø = ë è ( ports - )ø ( ) û Note a one is added to represent the robot that contains only the power module.

Using Equation (C - 4) the search space using the small inventory of Table C-1 contains 2800 possible robots. The size of the search space for inventories that contain various numbers of joints and end effectors is shown in Table C-2. It can be seen that the size of the modular design space, even for such a simple inventory, grows very rapidly with the number available modules. Table C-2: Number of Robot Assemblies

nfeet 1 2 3 4 5 6 4 70 2800 7.9x104 106 106 108 5 6 8 9 njoints 6 98 5194 1.4x10 10 10 10 8 104 8316 3.6x105 107 108 109

C.2.2 A More Realistic Inventory The growth of the search space becomes even more dramatic using a more realistic inventory. Since the inventory of Table C-1 only contained 4 joints, it could not produce a wide variety of useful robots. More joints are added so that more mobile robots can be produced. Also a gripper is added so the robots may be capable of manipulation. Connecting links are also included to change the lengths of limbs. This inventory is shown in Table C-3. Table C-3: A Larger Inventory Number Name Quantity

Page 64 1 Electrical n1 = 1

Power/Control Nports = 14 Module

2 Lower Torque n2 = 10 Electric Joint

3 Higher Torque n3 = 4 Electric Joint

4 Short Link n4 = 8

5 Foot n5 = 6

6 Electric gripper / n6 = 1 foot 7) Joints can be attached in 2 distinct configurations. These joint attachment configurations are shown in Figure C-1.

a) vertical b) horizontal Figure C-1: Joint Attachment Configurations The ability to attach joints in two configurations greatly increases the number of kinematic configurations that can be produced. All these factors allow this larger inventory to produce more realistic robots. Equation (C - 5) can be modified to describe this new inventory and assembly rule. Factors of 2K and 2j must be included to account for the fact that joints can be attached in 2 distinct ways. Also, a factor of: min( i,n ) (C - 5) 5 æ i! ö å ç k max( 0,i n ) è k! (i -1)! ø = - 6 must be included, where n5 is the total number of feet, n6 is the total number of grippers and i is the total number of limbs in the assembly. This factor accounts for the location of gripper. It is needed now that there are two different end effectors, a foot and a gripper. The number of assemblies is increased by this factor to account for placement of the gripper on the various limbs.

Page 65 The equation for the total number of possible robot assemblies then becomes:

( n + n ) é ì N ! n n n ü min( i , n ) ù (C - 6) 5 6 ports 2 3 k j 4 æ ( j + k + s + i - 1 )!ö 5 æ i! ö D = 1 + å ê í å å 2 2 å ý å ú i!( N i)! è j! k ! s!(i 1)! ø è k ! (i 1)!ø i = 1 ê - j = 0 k = 0 s = 0 - k = max( 0, i - n ) - ú ë î ports þ 6 û where: ns = the total number of module of type s available Nports = the total number of ports on the power/control module D = total number of possible robot designs The inventory shown in Table C-3 can be assembled into over 1020 different designs. A series of tests were conducted to study how the size of the design space can be reduced by placing restrictions on the types of robots that can be built. In each test an additional restriction was placed on the assemblies that can be produced. Using Equation (C - 6), the size of the design space was computed. The restrictions used are shown in Table C-4. The restrictions are cumulative. As additional restrictions are applied the previous restrictions are also used. For example, as restriction #4 is applied, restrictions #3, #2 and #1 are still enforced. The results of these test can be seen in Table C-5 and Figure C-2. Table C-4: Inventory Test Series Restriction # Restriction on Assemblies 1 Each robot/kit must have a power supply 2 Each robot/kit must have limbs that end in an end effector 3 Static Stability requires at least 3 limbs 4 Manipulation is required, a gripper must be included 5 Basic mobility analysis requires at least 3 joints per limb (to allow body to move in 6 DOF)

6 Limbs on the top ports are not useful (Nports = 11)

7 Limbs on the bottom ports are not useful (Nports = 8)

8 Limbs on the front/rear ports are not useful (Nports = 6)

9 Using only 4 ports (Nports = 4) Table C-5 shows the size of the design space after each restriction was applied. It also shows the number of designs eliminated by the restriction and the percentage of designs that remain after the restriction is applied. For example, restriction #6 reduces the design space by 24% as compared to the size of the space after restriction #5. Table C-5: Test Results restriction # Number of Reduction in % reduction Designs Designs in Designs 2 7.73E+20 3 7.73E+20 -4.96E+14 100% 4 7.70E+20 -1.25E+17 98%

Page 66 5 7.70E+20 -6.43E+14 100% 6 1.79E+20 -5.19E+18 24% 7 2.20E+19 -1.41E+18 13% 8 2.45E+18 -1.86E+17 13% 9 4.39E+17 -2.10E+16 22%

As expected, these additional assembly rules reduce the number of possible assemblies. Each additional restriction further limits the number of possible designs, as seen in Figure C-2. As each additional restriction is applied, huge numbers of possible assemblies are removed from consideration. For instance, when restriction #7 is applied, over 1018 designs are eliminated and the design space is reduced by nearly a factor of 10. However, even with these fairly tight restrictions (such as Stipulation #9: only using 4 ports on the power/control module) and the elimination of the huge number of assemblies, the number of possible assemblies for this relatively simple inventory is still on the order of 1017. These tests suggest that it is difficult to effectively reduce the inventory in this manner.

1.00E+22

1.00E+20

1.00E+18

1.00E+16

1.00E+14

1.00E+12

1.00E+10

1.00E+08 Number of Assembiles 1.00E+06

1.00E+04

1.00E+02

1.00E+00 0 1 2 3 4 5 6 7 8

Restriction Number Figure C-2: Results of Restrictions on Number of Assemblies The tests in Table C-4 were then repeated using an additional assembly rule. The new rule requires that each assembly must include all modules in the inventory. This changes Equation (C - 6) by replacing all summation variables with the maximum limit of the summation. The results of this second series of tests are shown in Figure C-3.

Page 67 1.00E+20

1.00E+18

1.00E+16

1.00E+14

1.00E+12

1.00E+10

1.00E+08

1.00E+06

1.00E+04 Number of Assemblies

1.00E+02

1.00E+00 0 1 2 3 4 5 6

Restriction Number Figure C-3: Restrictions Applied with New Assembly Rule Again, this additional restriction further reduces the number of possible assemblies. However, even with this highly restrictive restriction the number of possible assemblies for this relatively simple inventory is still very large ( 1012).

C.2.3 An Inventory with Higher-Level Modules Another way to reduce the size of the search space is to consider the level of modularity used in the inventory. If the components of the inventory were limbs instead of individual modules, the nature of the design space would be quite different. This inventory would have a “higher-level modules.” Such an inventory is shown in Table C-6:

Page 68 Table C-6: An Inventory with Higher-Level Modules Number Name Quantity

1 Electrical n1 = 1

Power/Control Nports = 14 Module

2 Limb A n2 = 6

3 Limb B n3 = 6

Equation (C - 7) now describes the number of possible assemblies that can be created in using this inventory.

n1 n 2 æ N ! (C - 7) ports ö D = ç ÷ åå i! j! N i j ! i=0 j=0 è ( ports - - )ø The effect of using an inventory with higher-level modules can be seen in Equation (C - 1). Here, the total number of assemblies is the product of two factors: the number of limbs that can be created (Dlimbs), and where these limbs can be placed on the power module (Dports). By using higher-level modules, the factor that pertains to the number of limbs that can be created (Dlimbs) is reduced. This is illustrated in Figure C-4. Using these higher-level modules, or “sub- assemblies” in the inventory greatly reduces the number of possible designs that need to be considered.

Page 69 Lower-Level Modules ) limbs

. Permutations of limbs (D

Permutations of limb location (D ports ) Higher-Level Modules ) limbs

Permutations of limb location (D ports ) Power Module limb 1 limb 2 no limb Permutations of limbs (D (14 ports) Figure C-4: Effect of High-Level Modules The number of possible designs that can be produced with the inventory of Table C-6 is 3.34x107. This number is small compared to the 1020 designs that can be constructed from the inventories using low-level modules. However, this is still a large design space for such a simple inventory (only two higher-level modules). It is too large to be exhaustively searched. This is because only one axis of the design space has been reduced, see Figure C-4. There are still many combinations of attachment points for the limbs, and with this high-level inventory it is possible to construct a robot with up to 12 limbs. If robot assemblies are limited to 7 limbs, as with the low-level inventory of Table C-3, there are just over 700,000 possible designs. Therefore the high-level action modules inventory can create 105 robots as compared to the 1020 possible robots of the inventory in Table C-3. This represents a reduction of the inventory by a faction of 1015. This study of the high-level module inventory shows the importance of evaluating designs on the sub-assembly level. This observation is utilized in the hierarchical design approach presented below.

C.3 The Hierarchical Design Approach The key to a practical search lies in reducing the design space to a computationally feasible size. The study of the search space presented above gives some clues as to how this might be accomplished. These ideas are incorporated into a hierarchical selection process presented here.

Page 70 This process is based on the observation that simple physically based design rules can eliminate large sections of the design space (Farritor et al., 1996-2; Rutman, 1995). The selection process is hierarchical because it considers the design at various levels. The process consists of tests and filters applied at varying levels: first to modules, then groups of modules (or kits), then to assemblies of modules (or sub-assemblies), and finally to entire robot assemblies. It attempts to eliminate entire sub-trees of solutions from further consideration. The tests and filters exploit the physical nature of the system, their tasks, and their environments. The method achieves effectiveness by recognizing that some performance characteristics of these systems are much simpler and computationally efficient to predict than others (Rutman, 1995; Shiller and Dubowsky, 1991). For example, if an individual module can be removed early in the design process, it will eliminate a vast number of sub-assemblies and an even larger number of robot assemblies. Hence, filters at the early stages are very effective in reducing the size of the design space later in the process. At a second level of complexity a group of unassembled modules, called a kit, can be considered. For example, a kit that contains no joint modules can never produce a useful robot. Such a kit is shown in the left branch of Figure C-5. Therefore, this entire branch of solutions can be eliminated from consideration.

Figure C-5: Hierarchical Selection Process Only the successful candidates need to be considered by the later, more computationally complex

tests. For instance, if the total weight of a module exceeds the maximum weight constraint, it

can be eliminated from further consideration early in the process. Hence complex performance

Page 71 parameters, such as power usage or dynamic characteristics, of all the robots that could constructed using this module do not have to be evaluated.

C.3.1 The Assumptions of the Hierarchical Selection Process To design a robot for a task there must exist some method of determining if the robot is “good” or “bad” at performing the task. The obvious method would be to construct the robot and attempt to perform the task while monitoring its performance. This is not practical. A second method would be to simulate the robot performing the task. It will be shown in this thesis that this is also not practical. The proposed methodology assumes that computationally simple tests can help distinguish between “good” and “bad” robot designs. This is the second assumption of the approach as presented. These simple tests are used to reduce the design space to a manageable size, then more complex tests can be applied to this greatly reduced design space. The methodology also assumes that, to a useful extent, a robot's design can be developed without precise knowledge of how the robot will execute the task. "Good" robots can be designed, or “bad” robots can be eliminated, without knowing exactly how they will be used. This third assumption basically states that the design and planning problems can be decoupled. However, the final stages of the design process may required some iteration between selecting a design and developing the action plan. Due to these assumptions it cannot be guaranteed that the selection process will produce an optimal design. Only an exhaustive search could guarantee optimality. Instead, the search process is simplified so that a sufficient design can be developed in a reasonable amount of time.

C.4 The Modular Robot Design Process The structure of the modular robot design process is shown in Figure C-6. It is based on a given inventory of modular components. Obviously, a single inventory cannot create useful robots for every task. It is designed to create robots for tasks chosen from a stated class of tasks. The inventory description and task definition are considered inputs to the process. This procedure is explained in the following sections.

Page 72 Inventory Description

Hierarchical Selection Process

Large Module Simple Design Filters/Rules Tests Space Class of Task Tasks Description/ Sub-Assembly Task Primitives Filters/Evaluation

Assembly Filters/Rules

GA GA Fitness

Candidate Designs Complex Small Tests Design Simulation Space

Final Design Figure C-6: The Modular Robot Design Structure

C.4.1 Task Description To design a robot for a specific task, a description of the task is required. To do this a group of task primitives is developed. It is assumed that the task is a combination of these task primitives. Then the task description becomes a matter of identifying the relevant task primitives. These task primitives can be used to develop the tests and filters of the selection process. For example, a task primitive might require a robot to climb a step. This task primitive might lead to tests that deal with limb length and limb strength. Also, there might be external constraints added to the task description. An example of an external constraint might be that the robot needs to weigh less than 10 pounds so it can be easily carried to the deployment area. The task primitives can also be used to identify the class of tasks. The class may be defined as all tasks that can be represented as an assembly of task primitives.

C.4.2 Module-Level Evaluation The process begins by applying module filters to all the available modules. These module filters are derived from the task description. They eliminate modules from the inventory that are not appropriate for the task. For example, if a robot needs to pass through a small opening, all modules that are larger than this opening can be eliminated. As discussed above, eliminating modules at this early stage greatly reduces the number of assemblies to be evaluated later.

Page 73 As discussed in Section C.1.1, a complete description of the modules is available to the designer a priori. An example of this description is shown in Figure C-7.

JOINT MODULE SPECIFICATIONS: Stall Torque = 42 [oz.-in.] Weight = 1.5 [oz.] Cost = $70 Gear Ratio = 56:1 Motor Inductance = 126 [mh] Torque Constant = 536 [oz.-in./amp] Range of motion = {-95°

JOINT KINEMATIC MODEL: é cos( q) -sin( q) 0 a + b sin( q)ù z i ê sin( q) cos( q) 0 b sin( q) ú z i +1 i+1 T = b i ê 0 0 1 d ú y y i i+1 ú ëê 0 0 0 1 û

xi+1 xi a d a = 1.50” b = 1.00” d = 0.00” Figure C-7: Joint Module Description With this knowledge, some determinations can be made as to the usefulness of this module in producing robot designs. For instance, the weight, size and cost can be compared against the task requirements.

C.4.3 Sub-Assembly-Level Evaluation Next, the design can be analyzed on the sub-assembly level. At this stage simple filters and tests can be applied to the development and evaluation of robot sub-assemblies. First, entire sub-assemblies and groups of sub-assemblies can be eliminated from consideration. Again, a sub-assembly whose cost or weight exceeds the task requirements can be eliminated. Also, it might be decided that sub-assemblies that do not contain joints, or sub-assemblies that contain more then five joints, will not be useful in producing useful robots. Finally, sub-assembly groups can be evaluated. For example. A sub-assembly that contains three joints is shown in Figure C-8. This kinematic configuration may represent many different sub-assemblies of modules. WORKSPACE:

KINEMATIC CONFIGURATION:

Page 74 3 Joints (Z-Y-Y) z z 1 z reach y

x x P 2 3

A B C D

x reach

y y reach

x

Figure C-8: Kinematic Sub-Assembly Useful conclusions can be drawn about all sub-assemblies of this kinematic configuration such as the size of the workspace.

As the sub-assembly evaluation proceeds, more complex tests can be feasibly applied. For a given configuration, very detailed information about the sub-assembly can be quickly computed. For instance, from the module information (Figure C-7) a sub-assembly Jacobian, for sub- assemblies of the form shown in Figure C-8, can be developed. This is shown in Figure C-9. FORCE/POWER/VELOCITY:

z 3 JACOBIAN: Bs Cc s Dc s Cs c Ds c Ds c y é - 1 - 2 1 - 23 1 - 2 1 - 23 1 - 23 1 ù x J = ê -Bc 1 - Cc 2 c 1 - Dc 23 c1 -Cs 2 s1 - Ds 23 s1 -Ds 23s 1 ú

ê 0 Cc 2 Dc 23 Dc 23 ú 2 ë - û

1 Applicable Force P F Figure C-9: Sub-Assembly Evaluation Important information such as the maximum applied force, nominal power consumption per unit applied force or the average velocity a sub-assembly could move can then be computed. The evaluation of sub-assemblies can be viewed as the development of an inventory of high- level components. If a sub-assembly scores well it can be viewed as a single component in a higher-level inventory. By evaluating the designs at the sub-assembly level this advantage is exploited.

Page 75 C.4.4 Assembly-Level Evaluation Finally, the design process considers an entire robot assembly. First, assemblies may be eliminated by extremely simple filters and tests such as cost and weight. Also, if the minimum dimension of an assembly is larger than the smallest dimension passage a robot has to traverse this assembly can be eliminated with computationally efficient tests. At this stage, information obtained from the pervious levels of the design process can be used. For instance, the assembly can be viewed as an assembly of sub-assemblies, and the maximum payload for a robot could be estimated by the sum of the maximum forces that can be applied by all the sub-assemblies. Examples of assembly evaluations can be seen in Figure C-10.

y reach x reach Stability Reach

W

Fend

F F 2 F4 1 F3 Force / Power Figure C-10: Assembly-Level Evaluation With the design space substantially reduced, but still large, a genetic algorithm is used to search for the best designs (Goldberg, 1989). The genetic algorithm (GA) represents the robot assemblies with a tree structure, or chromosome. This representation is shown in Figure C-11. The discrete nature of the genetic chromosome makes a very natural mapping between modular design and genetic algorithms. The genetic algorithm begins with a number of random robot assemblies, called a generation. The algorithm combines some attributes (modules in this case) from one assembly with those of another, thus creating a new generation of robots. This process is called crossover. Robots are chosen for crossover using a fitness function and the well documented genetic algorithm methodology to make "better" robots more likely to appear in the next generation. The algorithm may also add new characteristics (modules) that were not present in the previous generation. This process is called mutation.

Page 76 Power Module

Gripper

Joint

Link

Foot Robot Assembly Tree Chromosome Representation Figure C-11: Genetic Representation The genetic algorithm uses the simple physically based rules, or tests, to produce a fitness value for a given robot configuration. The fitness value is used to compare one assembly to another. Simple tests make estimates of assembly performance as shown in Figure C-10, such as power consumption, applicable forces, static stability, and mobility. As an example, mobility is estimated based on the average leg length of the robot with respect to the size of steps the robot might need to climb during a task. The implementation of this approach is further demonstrated on examples where example fitness functions are given. Using the techniques of crossover and mutation robot configurations, or candidate designs, are evolved. Again, full description of genetic algorithms can be found in (Goldberg, 1989).

C.4.5 Advanced Tests: Simulation The candidate designs can then be evaluated using more complex analyses. Here, a computer simulation is used in the final analysis of a robot design. This simulation performs a very detailed analysis of the robot assembly such as considering constraints such as actuator saturation, static stability, energy consumption, kinematic constraints, obstacle avoidance, etc.

C.5 A Class of Tasks: Conduits As shown in Figure C-6, the modular design process can be defined for a specific modular inventory and class of tasks. Here, a class of tasks and a corresponding inventory is defined. Then the hierarchical selection process is defined for this class of tasks. Both the U.S.S. Constitution inspection task and the duct inspection task belong to this class of tasks.

C.5.1 Class Definition/Description Many mobile robot applications require the robot to travel to a location where it is impossible or dangerous for humans to access. One example is conduit networks. This class would include all types of pipe and duct networks, as well as small enclosed rooms or channels. Instances of such tasks can be found in the telecommunication industry, city infrastructure and large buildings.

Page 77 To formalize the description of the conduit class of tasks, the class has been broken down into sub-tasks, or task primitives. These primitives provide a basis to develop the tests and filters used in the hierarchical selection process. Not all task primitives may be relevant to a specific task. The task primitive inventory used for the conduit class of tasks is shown in Figure C-12.

F

1) Max. Force 2) Smallest Passage 3) Tallest Step

5) Max. Payload 6) Max. Traverse 4) Widest gap

7) Max. Grade 8) Min. Turn 9) Scale

10) Max. Reach Figure C-12: Task Primitive Inventory

C.5.2 Inventory Description As stated earlier, the inventory of modules available for the design are fully characterized before the process begins. The inventory used for the conduit class of tasks is shown in Table C-7, Table C-8, Table C-9, Table C-10 and Table C-11. All robots constructed from this inventory will consist of a main body from which serial sub-assemblies, or limbs, can be attached. Table C-7 shows the power/control modules (body) available. These modules contain on-board computers used to control the robot and energy to power it. They provide energy of two types, electric and pneumatic, and all modules are classified as one of these two types. Modules of one energy type are not compatible with modules of another. Table C-7: Power/Control Modules ID Type Quantit Weigh Dimensi Available Cost Notes # y t on Energy ($) (oz.) (in.)

Page 78 00 Electric 1 8x4x4 10 AA 3750 14 limb attach 1 48 Alkaline points 2750 mA-hr full computation and control 00 Electric 1 16 3x4x4 10-C 50 4 additional 2 Alkaline attach points 7800 mA-hr power only 00 Electric 1 16 3x4x4 10-C 50 4 additional 3 Alkaline attach points 7800 mA-hr power only 00 Pneuma 1 60 16x8x8 tethered 4000 16 limb attach 4 tic points full computation and control All robots must contain either a Module #001 or Module #004, as these are the modules that contain on-board control computers. Modules #002 and #003 can be attached to the rear of #001 to provide additional electrical energy, see Figure C-13. Module #004 is tethered to a pneumatic power source while Module #001 can operate independently. All of these modules provide ports where additional modules can be attached. The ports provide a mechanical and an energy connection.

Module #001 Module #001 with #002 Module #001 with #002 & #003 Figure C-13: Electrical Power/Control Module Configurations Table C-8 shows the articulated active joints available. Linear and rotary joints are available of various sizes, strengths and speeds. Table C-8: Joint Modules ID Type Quanti Weig Dimensio Power Cost Notes # ty ht n Consumpti ($) (oz.) (in.) on (watts) 10 small 6 1.5 2.25x1.5x .593 70 42 oz-in 1 electric 1 stall 10 medium 6 3.3 2.25x1x1 .585 110 92 oz-in 2 electric stall 10 large 6 2.8 2.5x1.3x1. .54 240 200 oz-in 3 electric 8 stall

Page 79 10 non- 5 backdriva 4 2.8 2.5x1.3x1. .54 240 300 oz-in ble 8 stall electric 15 small 6 5.5 1x3x1 tethered 125 200 oz.-in. 1 pneumatic stall 15 medium 6 6.2 1.5x4x2 tethered 125 325 oz-in 2 pneumatic stall 15 large 6 8.0 2x6x3 tethered 180 580 oz-in 3 pneumatic stall Joint modules can be attached in two unique ways. Figure C-14 shows a rotary joint in each of the two attachment configurations. The difference between the two configurations is the 90 degree rotation of the joint axis.

a) vertical b) horizontal Figure C-14: Joint Attachment Configurations Table C-9 shows the available end effector modules. All limbs must end in an end effector module. Wheels, feet, and grippers are included in the end effector inventory. A wheel and a gripper can be used like a foot. The ability to make robots that walk and roll creates greater diversity in the robots designs and expands the number of tasks that can be performed. Table C-9: End Effector Modules ID# Type Quantity Weigh Dimension Power Cost Notes t (in.) (watts) ($) (oz.) 301 rubber foot 8 .25 1x1x1 0 5 302 magnetic 8 .65 1x1x1 .75 35 16 oz. break-away foot force (electric) 303 suction cup 8 .25 1x1x1 0 5 10 oz. break-away force 304 wheel 6 3.5 2.5x2.5x1 .54 180 150 oz.-in. stall

Dwheel = 2” 305 track 4 15.0 2.5x2.5x4 1.2 250 150 oz.-in. stall 306 electric 1 1.5 1.5x1x2 .8 210 .6 lbf grip gripper 307 pneumatic 1 18.0 2x2x3 tethered 150 6 lbf grip

Page 80 gripper Table C-10 shows the sensors available. These sensors are used for both hazard avoidance and navigation. Certain sensors may be required for specific tasks, such as cameras for inspection tasks. Table C-10: Sensor Modules ID# Type Quantit Weigh Dimension Cost Notes y t (in.) ($) (oz.) 405 camera 1 3 1.8x1.8x.8 450 w/ transmitter 406 laser range 1 4.5 .5’-4’ range finder .4” resolution 407 acoustic 1 4.0 1x1x1 80 30 beam width range 1’-15’ range sensor 6” resolution 408 roll & pitch 1 3.6 1.5x2x2 229 0.5 resolution sensor .6 sec settling time 409 gyroscope 1 2.5 1x.5x.5 350 3 /min. drift 410 compass 1 3.0 1.5x2x.8 500 2.3 sec. settling time 411 touch/ 4 .5 .5x.5x.5 15 contact 412 6 axis force 1 4x3x4 1100 torque Table C-11 show the available connecting link modules. These links change the dimension of sub-assemblies. They can be connected to modules of either energy type. Table C-11: Connecting Link Modules ID# Type Quantity Weight Dimension Cost (oz.) (in.) ($) 201 small 12 .5 1x1x1 10 202 medium 12 1.0 1.5x1x1 10 203 large 12 2.0 2x1x1 10

C.5.3 Hierarchical Selection Process for the Conduit Class of Tasks The first step in the hierarchical selection process is to develop the simple tests used to reduce the size of the inventory. Table C-12 shows how these simple tests, used to estimate robot performance, can be derived from the relevant task primitives shown in Figure C-12. Table C-12: Example Simple Tests Task Requirement Example Simple Test 1) Max. Applied Force Fendpoint 2) Smallest Passage X, Y, Z size 3) Tallest Step limb length limb strength 4) Widest gap limb length limb strength

Page 81 5) Max. Payload Fendpoint all limbs 6) Max. Traverse available energy 7) Max. Grade limb strength coefficient of friction 8) Min. Turn X, Y, Z size 9) Max. Reach maximum limb length 10) Scale limb strength coefficient of friction Time to complete task velocity w.r.t max. traverse Each stage of the hierarchical selection process requires that relevant simple tests and filters, used to reduce the design space, be created. Table C-13, Table C-14 and Table C-15 show the simple tests used in the design for the conduit class of tasks. In Table C-13 the module-level filters and tests are shown. External constraints on the weight and cost of a robot are part of the task description. If a module exceeds these constraints it is eliminated. Geometric constraints, derived from the task primitives, can also be used to eliminate modules. Also, if a module cannot accomplish a certain function (such as grip the required object, for example) it can be eliminated. Finally, all modules that do not match the energy type of the other remaining modules can be removed from consideration. Table C-13: Module Filters and Tests External Module Filters a) module weight < Wmax b) module cost < Cmax Geometric Module Filters c) module size < lmax d) gripper span > dobject Function Module Filters e) gripper force > Wobject Module Energy Domain Filters f) discard all modules without appropriate power sources g) discard all power sources without appropriate modules Similar constraints, such as weight and cost, are placed on sub-assemblies of modules. More complex tests, such as those shown in Figure C-8 and Figure C-9, are applied. Such tests can reveal a great deal about robots made from these sub-assemblies. Information such as average robot velocity, maximum payload and average power consumption, are related to these sub- assembly tests. The tests used to determine the value of sub-assemblies are given in Table C-14. Table C-14: Sub-Assembly Filters and Tests Filters a) all sub-assemblies must end with an end effector b) cost < Cmax c) weight < Wmax d) maximum of 3 joints per limb (15 kinematic possibilities) Kinematic Analysis

Page 82 e) x reach f) y reach g) z reach h) DOF/dimension of workspace (1-D, planer, spatial) i) Fmax = [Fx ; Fy ; Fz] Power Analysis j) average power consumed Mobility Analysis k) Power / (Velocity*Weight) Finally, assembly tests are used. Much of the information, such as reach or static stability, can be easily estimated using information obtained during the sub-assembly-level analysis. Kinematic analysis, power analysis and mobility analysis are all part of the assembly-level evaluation. Table C-15: Assembly Filters and Tests Filters a) cost < Cmax b) weight < Wmax Kinematic Analysis a) static stability a) x reach b) y reach c) z reach d) Fmax = [Fx ; Fy ; Fz] Power Analysis e) average power consumed f) peek power constraints g) power to move h) operating time Mobility Analysis i) DOF analysis j) velocity analysis k) Power / (Velocity*Weight) l) max. distance that can be traveled These module, sub-assembly and assembly-level tests are used to develop candidate designs for the field tasks studied.

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