MULTI-LIMBED ROVER FOR SURFACE EXPLORATION USING STATIC LOCOMOTION Marco Chacin and Kazuya Yoshida Department of Aeronautics and Space Engineering, Tohoku University Aoba 6 - 6 - 01, Sendai, 980-8579, JAPAN {mchacin, yoshida}@astro.mech.tohoku.ac.jp

ABSTRACT For the coming mission of a minor body explo- ration, a smart design of a robotic system that will This paper presents the design and preliminary anal- allow scientists more accurate positioning on the mi- ysis of a mobile robot for asteroid exploration. The crogravity surface condition is expected. One of mis- basic requirement for the robot is to achieve scientific sion scenarios may include scientific on site observa- investigation of the asteroid surface at arbitrary lo- tion of a tiny crater hole that could be created when cations with fine positioning capability after a large the main spacecraft would attempt impact sampling stride movement. A preliminary discussion and sim- [4]. The rover will be deployed over the surface just ulation on the dynamic behavior of a multi-legged before the sampling and then it would crawl to the robot in microgravity is addressed. This paper con- pinpoint location of the fresh crash-hole after the siders the principle of the motion using 3D computer sampling. simulation, prototype design, feasible mission scenar- To comply with the previous requirements, in this ios, grasping and control which is focused on the gen- paper, a limbed ambulatory locomotion system is de- eration of statically stable gaits so the robot advances veloped inspired by clever solutions exhibited by bio- with a desired speed and direction. logical systems and modeled as a free-falling manipu- lator which does not have a fixed-point but interacts with the ground. The main goal is to enable the 1. INTRODUCTION rover to move using the natural features of the envi- ronment and the friction of the surface for forward With the recent success of the MER Missions [1], progress in any direction having contact only in the there is an increasing interest in robotic exploration limb end-points. This type of locomotion has the ca- to small celestial bodies characterized by a medium pacity to provoke minimum reactions on the asteroid to low gravitational environment such as , as- surface that could push the robot into space, or even teroids and . Such interest, especially in aster- to grab the surface when some legs are controlled oids and comets, is due to their status as the remnant co-coordinately. debris from the inner solar system formation process. There are several issues to be addressed before real The community has spent consid- robots can really interact in such a hostile environ- erable effort and has significant interest in the devel- opment of mechanical mobility systems that could ment; this paper considers the principle of the motion using 3D computer simulation, prototype design, fea- be capable of supporting long-range scientific explo- sible mission scenarios, grasping and control which is ration of such bodies, and so revealing their interest- ing nature, but the best method to achieve mobility focused on the generation of statically stable gaits. on these planetary bodies is still the subject of dis- 2. BACKGROUND RESEARCH cussion. As an alternative, hopping systems for planetary 2.1 exploration were first proposed and used in the Asteroids are metallic, rocky bodies without at- MUSES-C mission; a robotic device named Minerva mospheres that orbit the sun but are too small to will be deployed on the target asteroid [3]. It will be classified as planets. Known as “minor planets,” use an internal reaction wheel to obtain a thrusting tens of thousands of asteroids congregate in the main force in order to move on the surface. Even with : a vast, ring located between the orbits this idea, the motion of the rover will be hopping of Mars and Jupiter 2.1 AU1 to 3.2 AU from the and bouncing on the asteroid, therefore the location sun. Gaspra and Ida are main belt asteroids, and of the robot when the bounds are finally damped out are most probably the remains of the process that is very difficult to predict or control. 1 AU stands for astronomical unit and is based on the mean distance from Earth to the Sun, 9.3×10 7 miles (1.5×10 8 km).

Proc. of 'The 8th International Symposium on Artifical Intelligence, Robotics and Automation in Space - iSAIRAS’, Munich, Germany. 5-8 September 2005, (ESA SP-603, August 2005) dezvous (NEAR) mission to (Fig.1), these missions were very successful in terms of fulfilling sci- entific and technological goals, having achieved im- portant scientific firsts like making a close flyby of an asteroid (Gaspra), discovering a satellite of an asteroid (Ida’s satellite Dactyl) and surviving a low- velocity, low-gravity impact landing on an asteroid. Yet recently, the exploration of an asteroid by a robot has just begun to be considered, ergo rover designs are being proposed for such task. The NANO Rover [5] was studied as a candidate for the rover to be deployed in the MUSES-C as- teroid mission. However, its cancellation was an- nounced by NASA in November 2000. The NANO Rover had four wheels; each one is attached at the end of a swing able strut. The wheel itself will not work on micro-gravity surface because no traction force is generated without any normal force to push the wheel on the surface. However, the wheel may work with dynamic forces when it is swung down by the strut, and the rover will hop to a certain direc- tion. Figure 1 . Mosaic of Eros’ northern hemisphere. The hopping action could be generated by a sim- c Applied Physics Lab. Johns Hopkins University pler mechanism. MINERVA [3] uses a single reaction wheel inside the robot to produce the inertial reac- formed the inner planets, including the Earth. tion. In both designs, however, the location of the Although the relationship between asteroids and robot when the bounds are finally damped out is very remains a puzzle, it is believed that as- opportunistic and difficult to predict or control. teroids are the sources of most meteorites that have Finally, while a snake-like articulated body that struck the Earth’s surface. The most common mete- can tie around a rocky edge or push both lateral orites are composed of small grains of and ap- sides in a narrow ditch, is an interesting idea [6]; if pear to be relatively unchanged since the solar sys- the robot has limbs with a gripper, it can walk on tem formed. Since many of these meteorites have al- the surface like a rock climber [7], or a spider. This ready been subjected to detailed chemical and phys- is a very promising idea, but the development of a ical analyses, the very next step is to identify if cer- reliable gripper becomes an issue [8]. tain asteroids are the sources of those well-studied meteorites, thus its detailed composition and struc- 2.3 Our Next Mission Scenario ture will provide important information on the chem- A rover will be located during the space trip in ical mixture, and conditions from which the Earth the main spacecraft that will be deployed on the formed several billion years ago when the building asteroid surface to touch down on a boulder. For blocks of life may have been brought to the Earth soft touch-down, the deployment should be done not via asteroid and impacts. Therefore the study from a high altitude of orbit, but from the spacecraft of asteroids is not only important for studying the hovering at the height of about 10-100 meters. The primordial chemical mixture from which the Earth specific values depend on the gravity of the target formed, but also they may hold the key as to how asteroid; although, if the size of target is equivalent the building blocks of life were delivered to the early to the target of MUSES-C (several hundred meters Earth. in a mean diameter,) the touch-down velocity will Many questions remain about asteroids, because be 1-10 [cm/s] after the free fall from the height of we have never been able to study them closely. 10-100 [m]. One issue for the control policy is how to know the 2.2 Past and Current Asteroid Missions exact position of the rover on the surface asteroid. In the past, several missions to asteroids and One solution could be to map the asteroid surface comets have been done, some of the most important in advance from the spacecraft and then using star ones are the Galileo Mission to Jupiter via asteroids sensors the exact location of the rover could be es- Gaspra and Ida, and the Near Earth Asteroid Ren- timated on the asteroid surface represented by the numerical grid. Crawling Mode: In this scenario, power, communication, and other to be used to move toward a location within house-keeping functions must be all contained within small distances from the actual position. the rover. If the spacecraft goes back to the orbit after the deployment of the rover, it will be helpful to relay communication between the Earth and the The Large Stride Mode is already implemented in spacecraft. the MINERVA rover, so its performance is to be im- Also for scientific purposes pictures of the aster- proved and the new idea of this project is to give the oid’s surface, boulders and cracks could be taken as rover the second mobility mode, the crawling one, the rover moves. Mineral composition analysis could which will allow the robot to move small distances also be conducted using on site mass (alpha/gamma- in a matter of millimeters or centimeters. ray) spectrometry. Moreover, seismometers can be carried and set on designated points of the asteroid’s 4. THE ROVER DESIGN surface. The sub-surface studies have in this case a great 4.1 Biomimetic Approach importance. Space shows a huge influ- ence in asteroid surfaces. The elements located in the Biomimetics is a scientific and technical discipline surface of the asteroid can experience some chemical that finds inspiration in biological systems to define alterations by exposure to , so the infor- new engineering solutions. It’s a multi-disciplinary mation about the original materials is simply lost. field that involves a wide diversity of other areas In the same way, small impacts by like electronics, informatics, medicine, biology, chem- modify in a certain degree the composition, and not istry, physics, mathematics, and many others. Cur- only the shape, of the asteroid surface. We assume rently this type of mechanisms’ research is aimed at that the environment faced by the rover proposed in developing robots that might exhibit a much greater this project will be similar to the asteroid Itokawa level of robustness in performance in un-structured [9], the target of the present mission. environments, through the replication of some form of walking, with 2 legs or more. The possible advan- 3. DESIGN GOALS tages of ambulatory locomotion are a robust response There are several issues to be addressed in a pos- to obstacles, the ability to position the body with a sible mission scenario as noted in the previous sec- high degree of accuracy, and rapid movement over tions. In order to achieve the desired level of success complex and unpredictable terrain. Wheeled vehi- in such a case, a substantial amount of research and cles are obviously superior when the terrain is rel- work must be done in some areas in order to develop atively smooth, but have difficulties when encoun- a feasible limbed rover for asteroid exploration. This tering naturally uneven terrains with many obsta- section describes some of the goals and challenges cles. Legged animals can traverse such environments involved. rapidly; therefore the study of legged vehicles is in- The main design points that have driven this teresting. project are indicated below: The most challenging parts of a walking robot are the legs. The leg design presented on this research • To explore a different mobility paradigm which provides 3 DOF (Degrees of Freedom). We feel con- may present advantages over conventional wheel fident that 3 DOF is the minimum needed in a flex- locomotion in microgravity environment. ible outdoor capable walking robot, for example it provides the possibility to walk in any direction in • Power, communication and science instruments narrow environments. The leg consists of a thoracic functions must be all contained in the rover. joint for protraction and retraction, a basilar joint The Surface Science Package (SSP) will consist for elevation and depression and a distal joint for of the Science Payload for on site analysis and extension and flexion of the leg. for sub-surface exploration. There are two main types of legged locomotion: • Improve the mission performance of MINERVA dynamic and static. Dynamic locomotion means implementing two mobility modes: that the walker changes from one unstable position to another. In such a situation, the center of gravity Large Stride Mode: is not always right over the point (or area) where the used to cover large distances by hopping, foot has contact with the ground. In static locomo- using an inner gimbals joint system as a tion, the walker remains constantly well balanced, at reaction wheel for thrusting. every instant of time. with the operation of higher level ones. At the same time they take advantage of the competences pro- vided by lower level processes, sometimes governing their workings by providing specific inputs to them. Also the presented control approach combines two biological control principles, the Central Pattern Generator (CPG) and reflex. Whereas a Central Pat- tern Generator is able to produce rhythmic motion without the need of sensory feedback, reflexes are Figure 2. Prototype Gripper based on the sensor-motor-feedback. It is assumed that the CPGs produced motion patterns are not 4.2 Gripper Prototype learned or adapted by the animal but represent a set In order to get the sticking force required to grasp of low-level locomotion mechanisms specific for the the asteroid a gripper prototype (shown in Fig.2) is species. Applied to a robotic system this implies, currently being developed. A miniature servo motor that is possible to define a set of Motion Patterns commonly used for RC cars or planes was used as ac- a-priori, which can be produced without the need of tuator. The developed gripper works to hold on the sensory feedback. surface of a natural stone, even in 1G environment. This control strategy fulfills the requirements that will make the rover eligible for a mission in a micro- 4.3 Control gravity surface environment: Given that with an appropriate control of move- Mobility: ments, a legged robot could climb boulders, cross As it will be shown in the results of the sim- ditches, and walk on extremely rough terrain to a de- ulation, the rover is able to move itself over a sired position, this type of rover has previously been surface in a microgravity environment. At this proposed for space exploration in order to overcome state of the project this is the main point that the limited movement of wheeled vehicles on rugged the simulation intends to prove. terrain and the lack of friction force for the wheels Redundancy: to work appropriately; but as a counterpart, there Although it is acknowledged that the configura- is a much higher complexity involved in the control tion of the rover involves several actuators, as it of several actuators. This complexity is due in no is seen in Fig.3, many legs and the fact that each small part by the two legged locomotion intercon- one has 3 DOF makes the robot very movable nected subsystems: the stance control and the swing and versatile [11]. This will also minimize the control. Stance Control positions the centre of mass possibility of mission failure due to the amount of the robot and reacts to external disturbances and of contact and grasping points to the asteroid. Swing Control cycles the legs periodically. Many approaches to control already exist, most 5. SIMULATION STUDY of them being biologically inspired. When designing 5.1 Modeling the rover the control of the locomotion of a legged robot there are many aspects that have to be dealt with simulta- The rover (see Fig.3) moves in a 3D environment. neously and whose actions interfere with each other. It consists of six identical limbs meeting at the body. For example, movements of legs must be carefully Each limb has three links and three actuated revo- coordinated in order to advance the body without lute joints. Self-collision between limbs is ignored, causing feet slippage; at each step, an appropriate meaning links are allowed to cross each other. For foothold has to be found, avoiding invalid ground simulation purposes equal mass and length L is as- patches for placing a foot and keeping a sufficient sumed for all eighteen links, and that the joints are range of leg mobility for future motion; body at- limited by internal mechanical stops. A inertia coor- titude must be set according to the terrain profile dinate system Oxyz is embedded in the World, with to avoid collisions with obstacles, keep stability, etc. gravity pointing in the negative direction of the z- To deal with such a complexity we basically have axis. Any configuration of the robot can be defined followed the behavior-based approach [10] in which by a set of parameters, the coordinates and orienta- the control process is broken down into hierarchically tion (xb, yb, zb, rb, pb, yb) of the body and the joint organized modules running simultaneously, each one angles (θ1, θ2, θ3) of each limb. providing a specific competence that solves some as- In the implementation of the different parts of the pect of the control task. In this approach, processes robot in the computer code, all of them are consid- of a given level perform their actions unconcerned ered like rigid bodies, with defining dynamical pa- {Σb}

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1:;< ; θ3 {Σo} (QQV : 1:;< :

Figure 3. The design of the asteroid surface robot discussed in this paper

rameters as the mass and the inertia. The robot is 5.3 Dynamics of the Robot considered as a free-falling manipulator which does To produce an accurate representation of the sim- not have a fixed point but has interaction with the ulated rover, a dynamics simulation model of a free ground. First the dynamics of a free-falling manipu- falling manipulator was obtained from an expansion lator are formulated in the next section by introduc- of the general manipulator simulator scheme. Then ing the variables representing position and posture of the global motion dynamics can be expressed as fol- the base link (the body), and then the formulation lows: of the reaction forces from the ground at end tip of the limbs. H(x)¨x + b(x, x˙)=u + K(x)fext (1) 5.2 Kinematics of the Robot b(x, x˙)=C(x, x˙)˙x + g(x) (2) T T T T T T The considered 3D structure is formed by a cen- Here, x =[pb ,q ], u =[fb ,τ ], and the other tral body, with a hexagonal shape and six legs [12]. parameters are: The legs are similar and symmetrically distributed around the body. Each leg is composed by two links pb : position of the base link and three rotational joints. Two of these joints are q : joint angles located in the junction of the leg with the central H(x) : inertia matrix body. The third joint is located at the knee, con- fb : base force necting the upper and lower link. Therefore each leg has 3 DOF. Considering six legs and the additional 6 τ : actuators torque DOF for central body translation and rotation, the C(x, x˙) : centrifugal and coriolis effects system has a total of 24 DOFs. g(x) : gravity The described robot legs are similar to sim- K(x) : states forces transformation matrix ple manipulator with 3 DOF; therefore the The fext : external forces Denavit-Hartenberg method can be used to compute the transformation matrices between the referential In order to simulate the above dynamics, we in- frames. The derived transformation matrices are tegrate equation (2) aboutx ¨ numerically, and after presented in [17]. solving equation (2) for the accelerations given x,˙x, The six legs and the central body must be inte- and the input uT =[0T ,τT ]. H(x) and b(x, x˙) can be grated to solve the global kinematics problem. obtained by inverse dynamics calculation using the UGE

UGE

Figure 4 . NEAR Shoemaker’s picture of asteroid Eros taken from a range of 250 meters used for the UGE simulation surface. c Applied Physics Lab. Johns Hopkins University

Newton-Euler formulation, that is, given x,˙x andx ¨ solve for u. In fact H(x) can be calculated by solving the in- UGE verse dynamics, setting x to the current state,x ¨ = j, and ignoring the centrifugal and coriolis forces, the Figure 5 . The rover on the simulated Eros surface model gravity effect and the external forces. Here j means a unit vector with its jth element equal to 1 and oth- prevent ground chatter or bounce while still simulat- ers are 0. The solution about u corresponds to the ing a stiff ground. jth column of H. The biasing vector b(x, x˙) can also In z direction, the non-linear force in the normal be computed by settingx ¨ =0. to the contact plane is defined by the following equa- tion: 5.4 Ground Contact Model z − zp The relationship between fingered manipulators Fz = −kz − Bzz˙ (3) and legged locomotion has been established before Lnom +(z − zp) [13]. Such relation states that any motion of a legged where, robot is similar to re-grasping an object by changing the position of the fingers, so while a robot hand Fz : normal component of the end tip grasps an object, a legged robot “grasps” the sur- kz : spring elastic constant face. z : position in z of the end tip In the simulation, a “grasp” is achieved if the robot is able remain attached to the surface while resisting z˙ : velocity in z of the end tip forces (and torques) applied to it from any direction zp : penetration in z of the end tip [14]. Algorithms for computing grasps of given ob- Lnom : nominal length of the spring jects are described in [15]-[16]. Bz : viscous constant Surfaces of asteroids show the characteristics of fragmental debris () and not bare rock, boul- It is observed that as the stiffness is lowered, ders are everywhere, there are patches devoid of greater penetration in the ground occurs. The lower craters; it seems likely that they have been filed in by the damping constants are, the longer the vibrations loose material (Fig.4). Other patches appear bright; occur. However, a very high increment in stiffness it seems likely to be freshly uncovered regolith. or in damping constants can produce instabilities in The ground is modeled as a linear spring damper the simulation due to numerical issues. Here the in the x and y directions and a non-linear spring- ground parameters have been tuned experimentally damper in the z direction. Using a non-linear (hard- until an acceptable ground penetration and bounce ening) spring in the z direction is a standard way to was achieved. 5.5 Movement of the rover on the surface 6 If we consider that while no contact points of the rover are in touch with the ground, the trajectory of 4 the rover is a ballistic one, so it is possible to realize that an analogy should exist between the behavior in 2 normal gravity (1G) and the behavior in micrograv- Roll [deg] 0 ity (μG) conditions. 2 4 6 8 10 − The ballistic trajectory is defined in the x z plane time [s] as follows: 0.0 -0.1 x = Voxt (4) -0.2 1 2 z = zo + Vozt + (−g)t (5) -0.3

2 Pitch [deg] When the rover touches the ground again after -0.4 performing the leap, z =0: 2 4 6 8 10 time [s] gT Voz = (6) 0.0 2 -0.5 where T is the flight time between two leaps. -1.0 On the other hand, -1.5

mgT Yaw [deg] -2 fΔt = mVo ⇒ f = (7) -2.0x10 2Δt 2 4 6 8 10 considering, time [s] Δt : time in contact with the ground Figure 6 . Roll-Pitch-Yaw motion of the body during m : total mass of the robot 2 2 the landing sequence Vo = Vox + Voy and approximating Vox ≈ 0, the expression of the 5.6 Simulation Results force in microgravity becomes A six legged hexapod was created using simula- mgT tion software that emulates physically based dynam- f = (8) 2Δt ics. The microgravity simulations were performed to while in normal gravity: verify the achieved rover model. Preliminary simula- tions showed that the robot was capable of perform- mGT ing the landing sequence on a uneven surface in 10−2 F = (9) 2ΔT gravity. The simulator was able to measure the posi- Keeping the flight times almost constant, the rela- tion and velocity of the hexapod’s body, also the an- tion between the forces applied in microgravity and gle and angular velocity of all joints was outputted. in normal gravity becomes: The position of each foot and the information stating whether it was contacting the ground was also pro- f gΔT = (10) vided all these variables are mentioned because they F GΔt were used in the control algorithm. Since the rover Δt : contact with the ground in μG is actually in the developmental stage, appropriate ΔT : contact with the ground in 1G sensor technology will be employed to obtain this in- m : total mass of the robot formation. Such sensors might include gyroscopes, accelerators, and foot switches. T : flight time between two leaps In each simulation case (Fig.6), minimal motion f : reaction with the grounds in μG in the roll and pitch direction is desired. Although F : reaction with the grounds in 1G during the landing sequence the rover stands on a From the last equation, it can be deduced that boulder on the surface (which makes the roll angle to rover behavior in microgravity should be analogous change undesirably) the position of the body in these to the one observed in 1G. This deduction will pave directions should be stable at zero during walking the way for the policy that is followed during the (crawling mode). simulation process. After running the first simulations it could be ob- served that flexibility (in terms of low stiffness and [7] K. Yoshida, T. Maruki and H. Yano; “A Novel Strategy high damping ratio) of the legs might help to improve for Asteroid Exploration with a Surface Robot,” In Proc. the movement, but this improvement has to be done of the 3rd International Conference on Field and Service Robotics, Finland, 281-286, June, 2002. so that the locomotion should be maintained contin- uously without tipping over. [8] K. Yoshida, Y. Nishimaki, T. Kubota, T. Maruki and H. Yano; “Sampling and Surface Exploration Strategies in 6. CONCLUSIONS MUSES-C and Future Asteroid Missions,” In Proc. 2002 IEEE Int. Conf. on Robotics and Automation, pages This paper has described a new design for a mobile 3155-3160, 2003. rover for future asteroid exploration with the capabil- [9] D. Scheeres, “Dynamical Environment About Asteroid ity of large stride and fine crawling locomotion. The ,” University of Michigan, Department of proposed rover is to touch the ground in five points Aerospace Engineering, USA. and to perform the crawling mode only moving the [10] R. Brooks, “A Robust Layered Control System for a Mo- five that are making contact at the same time. bile Robot,” In IEEE Journal of Robotics and Automa- A dynamic simulation model for the proposed tion, Vol. RA-2, No.1, 1986 pages 14-23. rover was developed and used for the simulation of [11] Mure, K. Inoue, Y. Mae, T. Arai, N. Koyachi, “Sensor- the rover over different gravity conditions. So far the based Walking of Limb Mechanism on Rough Terrain”, results show that static locomotion is possible on the In 5th International Conference on Climbing and Walk- microgravity surface with an appropriate scale of the ing Robots(CLAWAR) leg motion and control forces, assuming that a grasp- [12] K. Inoue, T. Arai, Y. Mae, Y. Takahashi, H. Yoshida, ing force to the surface has been achieved. N. Koyachi: “Mobile Manipulation of Limbed Robots - Proposal on Mechanism and Control-”, In Preprints of 7. FUTURE WORK IFAC Workshop on Mobile Robot Technology, pages 104- 109, 2001.

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