Design of Track-Based Climbing Robots Using Dry Adhesives

Proceedings of the ASME 2017 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC2017 August 6-9, 2017, Cleveland, Ohio, USA

DETC2017-67999

DESIGN OF TRACK-BASED CLIMBING ROBOTS USING DRY ADHESIVES

Matthew W. Powelson Stephen L. Canfield Tennessee Technological University Tennessee Technological University Dept. of Mechanical Engineering Dept. of Mechanical Engineering Cookeville, Tennessee, 38505 Cookeville, Tennessee, 38505 United States of America United States of America [email protected] [email protected]

ABSTRACT ability to climb on surfaces of varying curvature using dry This paper focuses on the design of track-type climbing adhesives and a linkage based leg design [9]. Tracked based robots using dry adhesives to generate tractive forces between designs, while less common, have also proven to be effective the robot and climbing surface to maintain equilibrium while in utilizing dry adhesives. Tankbot demonstrated the ability to motion. When considering the design of these climbing robots, climb rough and smooth surfaces while traversing obstacles but there are two primary elements of focus: the adhesive required the use of a tail to maintain adhesion [10]. MaTBot mechanisms at the track-surface interface and the distribution utilized a belt system combining dry adhesives with magnets to of these forces over the full contact surface (the tracks). This climb glass substrates at high angles as well as fully vertical paper will present an approach to integrate a generic adhesion ferrous substrates [2]. model and a track suspension system into a complete model that can be used to design general climbing robot systems While legged robots are more common, tracked vehicles utilizing a broad range of dry adhesive technologies. exhibit several advantages. They are intuitive kinematically and allow the application of off the shelf path planning algorithms. Further, tracked vehicles utilize a continuous contact patch in 1. INTRODUCTION motion relative to the robot. This means that the forces on an There are a variety of means incorporated to generate the adhesive material will be continuous, eliminating the possibility adhering forces needed for climbing, which include magnetic, of impact loading that could result from discrete legs in the suction, micro-gripping, electro-statics and adhesives. Magnetic event of an adhesive failure. Likewise, a tracked vehicle has adhesion provides a widely available adhering mechanism but many stable and marginally stable climbing positions [1] that is not suitable for climbing on nonferrous materials [1, 2]. allow the possibility for a robot to recover from an adhesion Microspines have been demonstrated in robotics both for failure without falling whereas a robot with discrete contact climbing robots [3] and perching of aerial robots [4, 5]. While patches exhibit significantly fewer stable climbing these have been shown to be a reliable source of very high configurations. Due to the larger contact area, tracked vehicles adhesive forces [6], they have been demonstrated to be are able to carry larger payloads [10] making them more readily ineffective for smooth surfaces [3]. This paper will instead scalable. focus on dry adhesive adhering approaches. While tracked vehicles for climbing have been previously In recent years, many robots utilizing dry adhesives for studied [1, 2, 10], the literature shows no models that integrate climbing have been developed with legged robots being the properties unique to dry adhesives with models for track design most common. Waalbot is one such robot that utilizes a set of 3 that distribute the climbing load. This paper will present an footed wheels coated in a dry adhesive material to climb on approach to integrate models for dry adhesives and track both smooth and nonsmooth surfaces [7]. Geckobot uses a suspension systems into a complete model that can be used to climbing gate similar to a gecko to climb with a set of adhesive design general climbing robot systems. footpads with active peeling mechanisms [8]. The RiSE platform demonstrates the ability to climb using both microspines and dry adhesives [3]. AnyClimb demonstrates the

1 Copyright © 2017 by ASME 2. DESIGN PROCEDURE FOR TRACKED CLIMBING ROBOTS Another consideration is effect of peeling on the adhesion 2.1 Overview of Design Procedure strength. Whether considering patterned or unpatterned An overview of the robot design procedure is now adhesives, the observed adhesion force is the result of the sum presented. First, the design considerations specific to dry of many small areas of contact. As such, the force required to adhesives are discussed. Second, a model is adapted to describe remove the adhesive is much larger when the load is distributed the distribution of climbing forces at the interface of the robot across an entire contact patch compared to when the load is and the climbing surface by taking into account these unique concentrated at the edge of the contact patch, as is the case considerations. The paper then demonstrates the use of these during peeling [11]. For this reason, it is important that track- models to design a specific climbing vehicle platform with a based climbing robots utilize a force distribution system representative dry adhesive. Design charts are created and their thereby avoiding the concentration of loading seen in track- use is demonstrated. Finally, a physical prototype of the based climbing robots using a tail [10]. climbing robot as designed using the proposed strategy is constructed and tested to evaluate basic operational 2.3 Suspension Model performance. A design approach is now developed to incorporate the adhesion considerations discussed above into a model that 2.2 Adhesive Considerations defines stable climbing for the tracked robot system. This Dry adhesives are typically considered to achieve their approach assumes that the tracked robot contains a suspension adhesive properties primarily through intermolecular forces system that distributes the climbing forces along the length of such as van der Waals forces and hydrogen bonding [11]. They the track. Here, the track length considers the region of an achieve a high degree of contact by conforming to surface endless track that is in contact with the climbing surface. asperities either through micropatterning or through the Further, the climbing forces considered are those in a direction elasticity of the adhesive. Regardless of the technique used to normal to the climbing surface and orthogonal to gravity. The achieve contact, dry adhesives exhibit unique characteristics approach is based on developing a generalized model for that must be considered when utilizing them in climbing determining forces needed for stable climbing and selecting applications. Most significantly is their loading specific nature. appropriate adhesive members using this model. While some adhesives have been developed such that increased shear loads, 휏, allow for higher normal loads to be applied [12] When considered in a kinetostatic sense, equilibrium [13], the most common dependence is that of the maximum equations are used to define the forces occurring at the normal adhesion pressure, 푤 , to the normal preloading boundary between the track and surface for climbing robots. 퐴 Stability occurs when the forces required do not exceed the pressure, 푤푃 – i.e. the relation of the magnitude of the negative pressure that can be sustained before adhesion failure occurs to allowable adhesive load provided by the adhesive material. the magnitude of the positive pressure with which the dry Therefore, a model to predict the forces as a function of adhesive is applied to the surface. Further, this relation is often location along the track surface is proposed for evaluation and nonlinear as the adhesion is typically driven by material design of track-type climbing robots. This model is based on a deformation at the microscopic level where adhesive geometry generalization of the tracked-type robot climbing model and surface asperities produce a nonlinear relationship between presented in [1] and will be called the PK model. A brief force applied and new contact area achieved. Additionally, as summary of the PK model is first presented. the conformity to the climbing surface generally depends on the asperity size, maximum adhesion is dependent upon surface roughness, R [11, 14]. Finally due to their viscoelastic nature, dry adhesives allow for the possibility of time dependent Adhesive Elements responses such as a dependency on preloading time, 푡푃 [11]. As such, the maximum adhesion pressure that a dry adhesive can sustain can be expressed as an equation of the general form,

푤퐴 = 푓(푤푃, 휏, 푡푃, 푅). (1)

It can then be assumed that if the robot is travelling over a small range of velocities, the time variability can be neglected. Further, on a uniform surface RMS roughness can be Suspension Springs approximated as being constant. Since the shear loading would Load Transfer Guides be constant in kinetostatic equilibrium, the maximum adhesion is therefore considered to be a known function of the preloading condition only. FIGURE 1 – MODEL OF A TRACK BASED CLIMBING ROBOT UTILIZING PK SUSPENSION AND DISCRETE TRACK ELEMENTS [1]

2 Copyright © 2017 by ASME The PK model assumes that the robot contains a track running through a suspension that is able to distribute forces normal to and away from the climbing surface along the length of track in contact with the climbing surface (see Fig. 1). The PK model is applied to a single track and assumes that the robot mass and loads are uniformly distributed among all tracks on the robot. The climbing surface is assumed to be uniform along lines orthogonal to the direction of travel permitting a planar model of the suspension. This model further assumes that the local surface curvature is small relative to the length of the suspension such that individual suspension links undergo small changes in orientation relative to the local frame. Finally, the mass of the entire robot system (adhering members, track, suspension system, chassis, payload) will be included in the external loads Px, and Py and are not locally distributed.

The PK model is based on a matrix-structural evaluation of the track suspension where the suspension links are treated as elastic beams connected with revolute joints, the springs are linear elastic axial elements, and the chassis is a frame member FIGURE 2 – FORCE PROFILE GENERATED BY PK MODEL with relatively high stiffness. Further, the track is modeled as a A generalized suspension model is now developed from chain carrying tension loads only and running in parallel with these results. A schematic of the climbing robot is shown in Fig. the suspension. The tension in the chain carries the loads that 3a while the generalized load distribution along the track is lie tangent to the climbing surface. The tension is evaluated shown in Fig. 3b. The model assumes a uniform load from a piecewise step function that distributes the climbing distribution in each of the four regions as a simplified load among the adhering members in a manner proportional to representation of the loading conditions shown in Fig. 2. their maximal friction force ability under a Coulomb friction Further, this model assumes that each of the regions represents model. The model is constrained through its connection to the a distinct portion of the track such that, climbing surface through the adhering members. The formulation of this model results in a nonlinear system to be 퐿 = ∑4 푙 (2) solved, since the surface normal force in the adhering members 푛 푛 is required in calculated the chain tension loads. Therefore, the solution is derived through an iterative process to converge on a consistent value of the normal force in the adhering members. w Kumar et al. [1] present a representative application of this 1 w model with comparison against a physical prototype with load 2 l1 distribution over the track as shown in Fig. 2FIGURE 2. This figure represents the loading perpendicular to the climbing surface at each point along the track for a robot in a vertical l 2 climbing configuration, with positive forces representing L w compression and negative forces representing tension. From 3 this result, the suspension behavior is characterized into four w l distinct regions of the track for a robot in motion; Region 1: 4 3 track makes contact with the surface generating compression forces to place the adhering members. Region 2: suspension l pulls on track resulting in tensile forces on the adhering 4 members. Region 3: suspension pushes on track to maintain 푥푐푚 equilibrium resulting in compression forces on adhering members, and finally, Region 4 (not shown in PK model but FIGURE 3A FIGURE 3B present during motion): the suspension pulls on the track to SCHEMATIC MODEL OF CLIMBING ROBOT WITH PRESSURE remove the adhering members. This corresponds to the findings REGIONS DEFINED AND LOAD DISTRIBUTION SHOWN of Unver and Sitti [10]. This uniform loading condition can then be adapted to the case of distinct track elements. Considering that these track elements may not continuously cover the length 푙푛 but actually consist of smaller elements separated by gaps of known length,

3 Copyright © 2017 by ASME it can be assumed that the actual length covered by adhesive is The adhesive mechanism can now be considered. As ′ some smaller length 푙푛 such that discussed in Section 2.2, the maximum adhesive pressure is generally a function of the preload pressure, 푤1. Thus for the ′ 푙푛 = 휂푙푛 (3) robot to successfully maintain kinetostatic equilibrium, it must also satisfy the adhesive equations. In the most simplistic case, For track elements small with respect to the total length of parameter 푤4 is assumed to be the max pulloff pressure the robot, it can therefore be assumed that this adhesive is calculated from the adhesion model, but one could incorporate 푙푛 a peeling model as well if appropriate for the robot geometry centered at . Loads 푤1 – 푤4 are shown as pressures with 푏 2 considered. Equation 1 therefore simplifies to being the width of the track. Thus, the total adhesive force on region 1 is 푤 푙′ 푏 acting at the center of the region. 1 1 푤 = 푓(푤 ) (8) 4 1

Equations of equilibrium for the climbing robot are now A valid climbing condition is therefore the intersecting of constructed to solve for the distributed load terms, 푤 − 푤 . 1 4 these two curves, where the maximum pulloff pressure of the Considering a summation of forces perpendicular to the adhesive corresponds to the necessary pressure 푤 to achieve climbing surface and the summation of moments about the 4 kinetostatic equilibrium for a given preload, 푤 . This is lowest point of contact of the track to the climbing surface, the 1 illustrated in Fig. 4 for the adhesive and robot of the type following equation must be satisfied for the robot to exist in described in Sections 3.1 and 4 respectively. kinetostatic equilibrium,

푤 푙′ −푙′ 푙′ −푙′ 1 1 2 3 4 푤 [ 푙 푙 푙 푙 ] [ 2] ′ 1 ′ 2 ′ 3 ′ 4 푤 −푙1 ( + 푙2 + 푙3 + 푙4) 푙2 ( + 푙3 + 푙4) −푙3 ( + 푙4) 푙4 ( ) 3 2 2 2 2 푤4 0 = [푚푔푥푐푚] (4) 푏

An additional constraint is then imposed on 푤2. Under normal operation 푤2 is typically a constant parameter dictated by the spring constant of the suspension. For design however, 푤2 is assumed to be the max pulloff pressure divided by a Factor of Safety (FoS) for climbing such that,

푤 푤 = 4 . (5) 2 퐹표푆

This yields an under constrained system of equations FIGURE 4 – INTERSECTION OF ADHESION MODEL WITH ROBOT dependent only on the robot configuration, MODEL FOR DESIGN

′ ′ ′ ′ 푙1 −푙2 푙3 푙4 푤1 From Fig. 4 it can be seen that these equations will have 푙 푙 푙 푙 −푙′ ( 1 + 푙 + 푙 + 푙 ) 푙′ ( 2 + 푙 + 푙 ) −푙′ ( 3 + 푙 ) 푙′ ( 4) 푤2 more than one solution in the general case. It is important to 1 2 2 3 4 2 2 3 4 3 2 4 4 2 [ ] 푤3 1 note that this is due to the condition imposed for design in Eq. 5 0 1 0 − 푤 [ 퐹표푆 ] 4 and does not indicate that the robot could exist in two stable 0 푚푔푥 climbing conditions during operation. This will be further = [ 푐푚] (6) 푏 addressed in Section 3.5. 0

Solving for the adhesion pressures and eliminating 푤2 and 3. MODEL APPLICATION 푤3, this system can be reduced to a single equation for 푤4 as a linear function of 푤 and the constant robot parameters, 1 3.1 Adhesive Selection

′ ′ ′ The robot model described in Section 2 is by design 퐹표푆(2푚푔푥+푏푙1푙1푤1+2푏푙2푙1푤1+푏푙3푙1푤1) 푤4 = ′ ′ ′ (7) independent of adhesive selection. However, the model does 푏(푙2푙2+푙3푙2−퐹표푆∗푙3푙4−퐹표푆∗푙4푙4′) assume that the adhesive characteristics have been quantified. This equation represents the set of adhesion pressures that The adhesive should have a predictable maximum adhesion will result in the robot existing in kinetostatic equilibrium. pressure given a loading/preloading condition and should be time independent on the time scale of one cycle (i.e. the time it takes for the adhesive to go through all four pressure regions

4 Copyright © 2017 by ASME described above). As an example, the authors selected microsuction tape to demonstrate the efficacy of the robot model. Known as Regabond-S [14], this tape is an acrylic foam patterned with microscopic voids that allow a combination of van der Waals forces as well as suction forces to generate adhesion. It is commercially available off the shelf and is effective on surfaces such as acrylics, smooth metals, and glass.

FIGURE 6 – EQUILIBRIUM SOLUTIONS FOR A ROBOT OF VARYING MASS UTILIZING SUCTION CUP TAPE ON ACRYLIC

3.3 Suspension Design This section will consider the effect of suspension parameters on overall system performance. In this case, the suspension design parameters are assumed to be the relative lengths of the pressure regions (Fig. 3b) 푙 – 푙 . Fixed FIGURE 5 – REGABOND-S MODEL AND CURVE FIT USED AS 1 4 EXAMPLE IN THIS PAPER parameters in this case are the robot mass, factor of safety, η, total track length, and track width. For effective climbing, it is In order to be utilized in robot design, the suction cup tape assumed that any dry adhesive will have an optimal loading was characterized through empirical testing and a model of condition that can be found using Eq. 1. Since the shear loading maximum adhesion as a function of preload was developed for is assumed constant, the designer should design the suspension the climbing surface to be considered, acrylic. This model is such that 푤1 is in a favorable preload region by changing the demonstrated on a plot of empirical test data in Fig. 5 from proportional length of each pressure region. For suction cup which it can be observed that the adhesion is nonlinear with tape, it is desirable that the adhesive be in the more reliable respect to preload. While this model will not be described in higher preload region of its response, but it should not be detail, similar models for other dry adhesives can be found in loaded so heavily that the adhesive is compressed to the point the literature [11]. of permanent damage. This region is approximately between 20 and 70 kPa for this case but could be much lower for adhesives 3.2 Integrating Models that primarily rely on shearing forces and require normal The suspension and adhesion models will now be preloading only to insure sufficient contact. combined into an integrated system that can be applied to aid in climbing robot design. This system is evaluated over a range of Considering the scalable pressure profile described above, conditions and organized into sections that consider elements the lengths of the pressure regions 푙1 – 푙4 are related to the associated with the suspension as well as the track. The model overall length 퐿 by the proportionality constants 푟1 – 푟4 is formed from a system of nonlinear equations that yield valid (푙푛 = 퐿 ∗ 푟푛). Thus 푟1 – 푟4 must sum to 1. Further, considering a solutions over a bounded region of operating conditions. This symmetrical robot the pressure regions 푟1 and 푟4will be equal. This allows for two of the four to be manipulated to adjust the can be shown by graphing the pressures, 푤1 – 푤4, with respect to changing payload, 푚. Figure 6 demonstrates this for a robot pressure response. Figure 7 shows the resultant preload utilizing suction cup tape climbing on acrylic with a track pressure 푤1 for a track length of 17.5cm, a combined track length of 17.5cm, combined track width of 9cm, center of mass width of 9cm, a robot mass of 1.25kg, center of mass 4cm from 4cm from surface, and a factor of safety of 2. Pressure region surface, and a factor of safety of 2. The dotted lines indicate the preferred workspace. For a suspension point load to support 푤 lengths 푙1-푙4 were 15%, 55%, 15% and 15% of the total track 3 length respectively, and 휂 was selected as 0.375. From Fig. 4 (such as a rolling caster), the designer would pick a value on and Fig. 6 a series of design tables and curves can be generated the right end of one of the 푟1 curves where 푟3 would approach that define the allowable workspace of configurations. These 0. For robot designs that use adhesive pads on discrete tracks, are demonstrated in the following sections. 푟1 can be estimated using the length of a discrete track element in relation to the length of the entire track. It can be noted that

FIGURE 8 – TRACK DESIGN CHART – MAXIMUM ALLOWABLE PAYLOAD VS TRACK WIDTH

FIGURE 7 – SUSPENSION DESIGN CHART – ADHESIVE PRELOAD 3.5 Robot Operating Conditions PRESSURE VS r2 RATIO The previous sections provided tools to choose robot parameters to aid in the design of a tracked climbing robot. This 3.4 Track Design section considers the condition of the robot during operation. Once a suspension design has been selected, the robot track During design, it is useful to relate the target suspension parameters are now considered. Fig. 8 shows the maximum pressure, 푤2, to the maximum pull off pressure, 푤4, by a fixed allowable payload for a given track length and width. This is proportion, 퐹표푆, as shown in Eq. 5. This allows the designer to tabulated for pressure regions of the same proportion of total select the physical mechanism needed to apply the appropriate length as given for Fig. 7, center of mass 4cm from surface, and pressure. However, during operation on a flat surface, the a factor of safety of 2. While this chart can be used to illustrate suspension pressure will actually be a constant dictated by the the maximum allowable payload, it should be noted that the stiffness and pretensioning of the suspension. Therefor Eq. 7 adhesion pressures at these payloads are not considered. Thus, will not generally hold during operation. Instead, allowing 푤2 while the chart may indicate much higher payloads than the to be a constant and solving for 푤4 in terms of 푤1 yields robot would require, when compared to Figs. 6 and 7 it becomes apparent that it is sometimes advantageous to operate 2푚푔푥 푤 (푙 푙′ + 2푙 푙′ + 푙 푙′ ) + − 푙 푙′ 푤 − 푙 푙′ 푤 at a payload significantly less than the theoretical design 1 1 1 2 1 3 1 푏 3 2 2 2 2 2 푤4 = − ′ maximum to avoid extreme preload forces as discussed in 푙4(푙3 + 푙4) Section 3.3. (9)

Similar to Eq. 7, this equation represents the adhesion pressures that will result in the robot existing in kinetostatic equilibrium. It can be noted from this equation that its slope is always negative. This corresponds to the expectations that it should cross the adhesion model line only once. Once the robot configuration has been set (ie, 푚, 푏, 퐿, 푟푛, 휂, and 푤2 have been set), changes in the robot parameters will shift the operating point as shown in Fig. 9. Increasing 푚 will shift the solution along the adhesion model curve to the left, as will decreasing 푏, 퐿, or 휂. This is important as it shows, for example, that a change in mass during operation will not generally result in an unstable climbing condition or a discontinuous “snap” to another solution. The solution will simply shift continuously to another solution along the adhesion model profile until the two curves no longer intersect; Eq. 5 will just not be satisfied.

6 Copyright © 2017 by ASME With these steps are completed, a full set of robot track size, material type and suspension parameters are defined. In our case, these values are defined above. To illustrate the practical implementation of these, a prototype robot was constructed based on this design. The robot was modeled in CAD and then constructed using an FDM fabrication tool. The robot is constructed primarily using PLA plastic (the density of Increasing m PLA is 1.25 g/cm3 for a total system mass of approximately Decreasing b, L, 휼 1.25 kg), and 2 inch Habasit snap on 1843T conveyor chain [16] was used as the track. The resulting robot is shown in Fig. 10, while the details of the track and suspension for one side of the prototype robot are shown in Fig. 11.

The robot underwent cursory testing to evaluate the physical system against the design. The early results show reasonable agreement between its performance and that predicted. The robot is able to climb approximately one body length before manual reapplication of some or all of the adhesive elements is necessary. The prototype in practice

FIGURE 9 – INTERSECTION OF ADHESION MODEL WITH ROBOT introduced some additional variables that limited full contact of MODEL FOR DESIGN AND OPERATION SHOWING DIRECTION OF the adhesive with the climbing surface that reduced the MOTION FOR CHANGING ROBOT PARAMETERS effective adhesion strength and was not fully included in the model through the Factor of Safety. The most significant of these problems was the non-constant pitch nature of the chain 4. DESIGN EXAMPLE based track. As the chain left the front sprocket and entered the This application will demonstrate the use of the integrated straight portion of the suspension, the gap between the adhesive adhesion/suspension model for a specific robot design. First the elements at the climbing surface changed length (this can be adhesive material and climbing surface are chosen and observed from Fig. 11), introducing relative sliding and identified. In this case, suction cup tape on an acrylic climbing preventing adequate preloading. This was limited by applying surface was selected allowing the use of the model discussed in the adhesive to only a small portion of the physical track as Section 3.1. Next, an initial tread size is approximated to begin seen in Fig. 10. In future versions of the robot, this could be the design evaluation. In this example, the approximate tread solved by adding a forward idler such that contact occurs at a size is 17.5cm by 4.5cm on each side for a two tracked vehicle small angle to the climbing surface, minimizing the change in which allows Fig. 7 to be used to choose a suspension design. pitch at the adhesive element surface. Further, smaller track Next, the preload range and initial suspension sizes are elements relative to the total length of the robot would allow for selected, in this case a preload value between 20 and 70 kPa more adhesive elements to fail before robot equilibrium is no longer sustained. was selected and 푟 and 푟 were chosen to be 0.15 based on the 1 4 relation of the distinct track elements to the overall length selected above (Fig. 7 – purple line). The ratio, 푟2, is chosen to be 0.55, positioning the preload pressure within the allowable range and making 푟3 be equal to 푟1 and 푟4 while allowing the possibility of adding a discrete caster support at a later time (shifting 푟2 to 0.70).

The next step is to check the overall track lengths and widths selected above. For this robot, it is desired that the payload be at least 1.25 kg with an estimated center of mass at 4cm. It can be seen from Fig. 8 that there are multiple valid solutions and that the dimensions assumed above will provide an adequate working range. It can now be seen that 푙1 will be 2.6 cm. If discrete tracks are used, it can be assumed that preload will occur across one track element at a time. Thus, a track element should be approximately 2.6 cm.

A specific dry adhesive, suction cup tape, is then selected as a representative example, and design charts are created to aid in track and suspension design based on the general principles developed. The bounds of the design space are considered and the allowable operating conditions of the robot are discussed.

Finally, the method is demonstrated through the design of a lightweight, tracked climbing robot using suction cup tape. A prototype of this climber is manufactured using PLA plastic and FDM additive manufacturing techniques. It incorporates a simple suspension based on a series of constant force springs and shows reasonable agreement with the performance predicted by the design model. Its performance is stated and future improvements are discussed.

FIGURE 10 – PROTOTYPE CLIMBING ROBOT DESIGNED USING The model predicts some solutions that would likely not be ROBOT MODEL AND CONSTRUCTED USING FDM MANUFACTURING practical on a physical platform. One such solution is for a case METHODS where the solution is based on a very small preload pressure. According to models that are based on empirical testing in idealized test conditions, the adhesives do satisfy the equilibrium requirements for climbing and would theoretically function in the robot models. However, in practice, at the low preload conditions, small geometric tolerances can prevent full adhesion of the material onto the climbing surface. These geometric tolerances have a much lesser effect at higher preload values. For example, an abnormality in the track geometry could recess the adhesive surface, requiring a higher preload pressure to deform the material to the climbing surface. For these cases, the robot configuration should be adjusted to allow solutions that correspond to more reliable conditions. 푙1 푙2 푙3 푙4 ACKNOWLEDGMENTS FIGURE 11 – PROTOTYPE CLIMBING ROBOT – SIDE VIEW TO This work was supported in part through NSF IIP, Award SHOW SUSPENSION DESIGN No. 1548009. The authors also appreciate work of Micah Hardyman in manufacturing the robots for the experimental section of the paper. 5. CONCLUSIONS This paper has presented a general design approach for REFERENCES track-type climbing robots based on dry adhesives. This design [1] P. Kumar, T. W. Hill, D. A. Bryant and S. L. Canfield, "Modeling approach has considered a model for the distribution of the and Design of a Linkage-Based Suspension for Tracked-Type adhering forces when integrating a generic dry adhesive model into a track-type robot. This model considers tracked machines Climbing Mobile Robotic Systems," ASME 2011 International with suspension elements but could also apply to tracked Design Engineering Technical Conferences and Computers and machines without suspensions by including the counteracting Information in Engineering Conference, pp. 827-834, 2011. force mechanism as another suspension component. [2] M. Fremerey, S. Gorb, L. Heepe, D. Kasper and H. Witte, "MaTBot: A Magnetoadhesive track robot for the inspection of The paper considers the characteristics unique to dry artificial smooth substrates," International Symposium on adhesives and presents a set of simplifying assumptions for Adaptive Motion of Animals and Machines, pp. 19-20, 2011. their utilization in tracked robot design. It then presents a [3] A. T. Asbeck, S. Kim, M. R. Cutkosky, W. R. Provancher and M. generalized suspension model considering a continuous track Lanzetta, "Scaling hard vertical surfaces with compliant suspension and describes how that model can be integrated with microspine arrays," The International Journal of Robotics a dry adhesive model for design. The nonlinear nature of this Research, vol. 25, no. 12, pp. 1165-1179, 2006.

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