Preliminary Design And Kinematic Analysis Of A Mobility .
Preliminary Design and Kinematic Analysis of a MobilityPlatform with Two Actuated Spoke WheelsDennis HongDoug LaneyMechanical Engineering DepartmentVirginia Polytechnic Institute and State UniversityBlacksburg, VA, 24061, USAMechanical Engineering DepartmentVirginia Polytechnic Institute and State UniversityBlacksburg, VA, 24061, USAdhong@vt.edudlaney@vt.eduAbstract – IMPASS (Intelligent Mobility Platform withActive Spoke System) is a novel locomotion system concept thatutili zes rimless wheels with individually actuated spokes toprovide the ability to step over large obstacles like legs, adaptto uneven surfaces like tracks, yet retaining the speed andsimplicity of wheels. Since it lacks the complexity of legs andhas a large effective (wheel) diameter, this highly adaptivesystem can move over extreme terrain with ease whilemaintaining respectable travel speeds. This paper presents theconcept, preliminary kinematic analyses and design of anIMPASS based robot with two actuated spoke wheels and anarticulated tail. The actuated spoke wheel concept allowsmultiple modes of motion, which give it the ability to assume astable stance using three contact points per wheel, walk withstatic stability with two contact points per wheel, or stridequickly using one contact point per wheel. Straight-line motionand considerations for turning are discussed for the one- andtwo-point contact schemes followed by the preliminary designand recommendations for future study.(Intelligent Mobility Platform with Active Spoke System) is anovel locomotion system concept that utilizes rimless wheelswith individually actuated spokes to provide the ability to stepover large obstacles like legs, adapt to uneven surfaces liketracks, yet retaining the speed and simplicity of wheels (Fig.1.) Since this system lacks the complexity of legs and has alarge effective (wheel) diameter, this highly adaptive systemcan move over extreme terrain with ease while maintainingrespectable travel speeds, making this novel system anexcellent candidate for unstructured environment applications.Index Terms – IMPASS, rimless wheel, actuated spokewheel, mobility, locomotion.I. I NTRODUCTIONIntelligent mobility platforms which can handle extremeterrain have many important application areas: scientificexploration, environmental monitoring and protection, antiterror response, and search-and-rescue missions are someexamples where the use of such robots is a necessity [1]. In areport [2] prepared for the Office of the Secretary of DefenseJoint Robotics Program on the lessons learned from the robotassisted search and rescue efforts at Ground Zero following the9/11 World Trade Center tragedy, robot mobility is noted asthe major limitation of current robotic technology andrecommends that other alternative locomotion strategies whichare more effective must be further investigated.Legged vehicles can provide greater mobility than wheelsor tracks by enabling discontinuous contact with the surface.In the past decade, there have been several legged vehiclesdeveloped for unstructured environment applications [3, 4].However, the problem of legged vehicles is that they are tooslow and mechanically too complex. In this paper, we presentthe concept, preliminary design and the kinematic analysis of anovel high-mobility locomotion platform for unmannedsystems in unstructured environments which incorporates thebenefits of tracked, wheeled, and legged systems. IMPASSFig. 1 Some examples of the mobility and terrain adaptability of IMPASS.II. LOCOMOTION STRATEGIES FOR ROUGH TERRAINA. Alternate Robot Locomotion StrategiesBesides using wheels, tracks, or legs, there are severalclever ideas currently under development for alternative robotlocomotion strategies for unstructured environments. Mobileplatforms that use spoked wheels or similar mechanismsinclude the Scout [5, 6], RHex [7], Whegs [8, 9], and theexpanding wheel vehicle [10]. Scout [5] is a small cylindricalrolling robot designed to be operated over relatively evensurfaces. To improve its limited mobility, one prototype ofthe Scout has a single degree of freedom umbrella likemechanism to increase the diameter of the wheel [6] to increasethe clearance between the robot body and the ground. RHex [7]is a compliant-legged hexapod with a simple clock-drivenopen-loop tripod gait. RHex is different from other leggedrobots in the sense that its legs rotate a full circle acting as asingle spoked wheel. The Wheg series of robots [8, 9] is
another derivation of the spoked wheel concept utilizingcompliant appendages. The Wheg II is a robot [8] with sixWhegs developed from abstracted cockroach locomotionprinciples. The smaller version, Mini-Wheg [9], is a robotwith four Whegs using an alternating diagonal gait. Theexpanding wheel vehicle [10] has four wheels that can expandbased on polyhedral single degree-of-freedom expandingstructures using prismatic joints. This adds navigationalcapabilities by allowing the wheels to expand according to therequirements of the terrain. Other interesting approaches to dealwith highly variable, rough terrain include the JPL SampleReturn Rover (SRR) [11, 12] for planetary exploration and theShrimp rover [13]. The SRR can actively modify its kinematicconfiguration to improve its rough terrain mobility while theShrimp rover uses a passive structure approach with a uniquemechanism using an articulated fork and two lateral bogieswith six wheels.B. The IMPASS ConceptAll of the mobile platforms shown above share somesimilar aspects with the IMPASS concept: the idea of spokedwheels, the use of compliant legs, the ability to reconfigure itsstructural kinematic configuration, leg-wheel hybridlocomotion, and variable diameter wheels, to name a few.However, while IMPASS shares some of the characteristicsand the resulting benefits of these systems, IMPASS isfundamentally different from all of them.The key to the concept of IMPASS is its ability toactuate individual spokes with intelligence. While currentsystems that use some flavor of spoked wheels have only onedegree-of-freedom to change its effective diameter [6, 10] orrely on passive compliance [7, 8], the system of activelyactuated spokes enables IMPASS to have extreme mobilityover rough terrain. As illustrated in Fig. 1, the spokes can actas active legs to pull and push the robot body for climbing,enable the robot to change or maintain its angle (pitch androll) relative to the ground, adapt to uneven surfaces and act asactive suspensions, or increase the clearance between the bodyand the ground for obstacle avoidance. Fig. 2 shows a sequenceof pictures illustrating the ability of an IMPASS concept withtwo actuated spoke wheels and an actuated tail to climb over awall four times its nominal height.Fig. 2 A two actuated spoke wheel IMPASS climbing over a wall.Though empirically stable, the spokes can also allow therobot to have additional contacts with the ground and to changethe kinematic configuration of its structure for added stabilityduring manipulation tasks if needed. Due to the additionalactuators required for the spokes, IMPASS is more complexthan RHex and Whegs based robots, but its mobility andversatility can be comparable to, or even surpass those oflegged vehicles while maintaining simplicity in mechanicalstructure and control. Since the spokes pass through the hub ofthe "wheel" unit, only three actuators are required to actuate thesix spokes. The ability to change its effective diameter alsoenables it to move faster than other spoked wheel based robotsthat have equal nominal diameter.1) Fixed stroke locomotion: On relatively even terrain,IMPASS can operate with the stroke of each spoke fixed andmove simply utilizing the compliance of their shanks likeWheg based robots, or implement gaits similar to those ofRHex controlling only the rotation of each wheel unit toconserve power. Even in this mode, the motion of IMPASSwould be relatively smooth since it has a large number ofspokes (six spokes per wheel unit, compared to three forWhegs and only one for RHex).2) Simple gait motion: If a smoother ride is needed, thethree actuators can control the six spokes of each wheel unitfollowing a simple predetermined coordinated spoke motionsequence with no terrain sensing or actively controlledadaptation, thus acting as treads moving over flat terrain.However, the real benefit of IMPASS lies in its ability toactively actuate the individual spokes with intelligence to adaptto the terrain and to use the spokes as legs for climbing overobstacles.3) Motion planning for optimum internal configuration:At a certain stance of the vehicle over the terrain, IMPASS hasthe ability to change its internal kinematic configuration byadjusting the stroke of its spokes. Though empirically stableon even terrain, by adapting its internal configurationIMPASS can move over hills with steeper angles and increaseits stability. Given the positions of the foot contact points onthe ground, one task for the motion planner is to generate theoptimal joint variables (stroke for the spokes and angularrotation for the wheel) for maximizing its stability, groundclearance, or traction.4) Active coordination of spokes for uneven terrainadaptation: Whether the vehicle is autonomous or remotelycontrolled by an operator, the actuation of each individualspoke must be autonomous based on data obtained from theon-board sensors and/or the geometric terrain information.Depending on the number of foot contact points, the clearancebetween the ground and the body, and the constraints forinternal configuration, a strategy for coordinating the motionof the spokes can be formulated based on the terrain profilegeometry by modeling it as a closed kinematic chain withchanging topology. If the geometry of the terrain becomes
extreme or the robot needs to climb over a large obstacle, wemust use a different strategy as explained next.5) Motion planning of spokes for extreme terrain or forclimbing: When IMPASS needs to move over extreme terrainor encounters a large obstacle that it cannot handle with theuneven terrain adaptation method, the motion planner must usethe extreme terrain method. IMPASS can theoretically climbover obstacles 4 times its nominal height (Fig. 2); however,generating the necessary motion sequences for the spokes is achallenging task. First of all, unlike legs with multi degreesof-freedom, the wheel unit of IMPASS has very limitedchoices of positions for placing its feet on the ground thuseach motion of the spokes must be carefully planned tomaximize its ability to cope with the extreme terrain. Second,since the spokes are being used as legs, collision andinterference with the obstacles and the spokes now becomes animportant factor to be considered. We are currently developingalgorithms to plan and coordinate the spoke motion in order toovercome the large obstacles or extreme terrain it must goover, and to do so in a stable fashion.6) Steering: Skid steering, or using differential rotationsof the left and right wheel units, is not desirable for spokedwheel systems since this creates bending moments on thespokes and drags the foot at the end of the spoke in contactwith the surface. Utilizing its ability to change its effectivediameter, preliminary analysis of the novel steering methodssuch as having different effective diameters on the left and theright is presented in this paper.At this stage, the overall concept of IMPASS is not yetcomplete. In this paper, we present our on going research on arobot utilizing the IMPASS concept with two actuated spokewheels and an articulated tail.III.PRELIMINARY KINEMATIC ANALYSISA. Kinematic Model and ConfigurationThe development of the kinematic models for the actuatedspoke wheel is based on a rimless wheel with three linearlyactuated spokes that pass through the axis of the wheel inparallel planes. The angle between the spokes, β , is fixed at60 as shown in Fig. 3. Three spokes per wheel were chosenas a balance between the requirements for acceptable mobilityand the increasing mechanical complexity that comes withadding additional spokes. Having the spokes pass through theaxis of the wheel allows the number of actuators for thespokes to be reduced, as only three actuators are necessary forthe independent motion of the spokes. The two actuated spokewheels considered in this analysis are driven by a single axle,so that the two actuated spoke wheels always rotate in phase.Thus not including the articulated tail with the caster wheel forthe robot shown in Fig. 2, only a total of seven motors arerequired for the locomotion of the robot.Fig. 3 Two actuated spoke wheels with a single axle.1) Coordinate systemThe coordinate system for the model is defined based onthe SAE J670e convention in which the x-axis is defined inthe direction of positive travel, and the z-axis is oriented suchthat forces from the spokes to the ground are positive, asshown in Fig. 3. The robot configuration consists of a robotthat has two actuated spoke wheels, spaced apart of a width ofw, and point G at the center of the axle. Since the actuatedspoke wheels considered here are driven by a solid axle, theyare always in phase (θR θL θ).The ground is represented by the inertially fixed referenceframe N{xN , yN , zN}. The robot travels along a path frame,P{xP, yP , zP}, that is rotated from the N-frame by a yaw angleφ about the zN axis. A body fixed frame, B{xb, yb , zb}, iscreated by choosing different left and right side spoke lengths,which will cause the robot to roll through an angle ψ aboutthe xP axis. Finally, a wheel fixed frame, W{xw, yw , zw}, iscreated by the actuated spoke wheel pitching through an angle,θ, relative to the body about the yb axis.2) Degrees of freedomThe preliminary analyses presented here will considermotion over flat terrain only and the articulated tail with thecaster wheel will not be included in the analysis. Since each ofthe three spokes in a wheel can be independently actuated, itbecomes clear that it would be possible for the actuated spokewheel to have one, two, or three contact points with theground, with each of these modes of locomotion havingdifferent mobility characteristics. With the assumption of animposed no-slip condition at each contact point with theground, this contact point is modelled as a revolute jointbetween the ground and the actuated spoke wheel. Equation (1)gives Grubler’s equation [14] to calculate the planar mobilityof a single actuated spoke wheel in different modes.M 3(n "1) " 2 f1 " f 2(1)Where M is the mobility, n is the number of links, f1 is thenumber of 1 degree of freedom (DOF) joints, and f2 is thenumber of !2 DOF joints. As shown in the kinematic diagramin Fig. 4 (a), an actuated spoke wheel with a single contactpoint with the ground has two degrees of freedom, as the angle
and length of the spoke in contact with the ground can beindependently controlled. For the two-point contact case, thedegrees of freedom for a single actuated spoke wheel is one,and for the three-point contact case, the degrees of freedom fora single actuated spoke wheel is zero, as shown in Fig.s 4 (b)and (c) respectively. This will give each mode a differentmobility characteristic and will require different strategies formotion as will be presented next. Note that as the actuatedspoke wheel advances, the spokes will make and break contactwith the ground changing the topology of the mechanism.change of the wheel angle . From the mobility analysis, theconstraint equations are given asr AR r AL(4)(5)Using a vertical speed uz and a longitudinal speed ux to specifythe motion along the current heading angle, the resulting inputequations are!z uz(6)(7)(a) One point contact(b) Two point contact(c) Three point contactFig. 4 Kinematic diagram of a single actuated spoke wheel and itsdegrees of freedom for different modes.B. Straight Line Motion1) One-Point Contact ModeThe kinematic velocity equations are derived by findingthe velocity of point G relative to a fixed point in the N-frame.Choosing the ground contact of the right wheel, AR as thefixed point in the inertial frame, the position of point G isthen(2)and taking the time derivative of this position vector gives! theequations for the velocity of the center of the axle.Recognizing that the pitch angle, ψ , is a function of the leglengths r AR and rAL through the relationship r #r '" sin#1& AL AR )% w ((3)allows one to substitute to remove ψ from these velocityequations. The constraints caused by the no-slip conditions atthe two ground !contact points (one for each wheel) ensure thatthe left and right side spokes in contact with the ground actuateat the same rate and that the velocity of the robot isconstrained to the current heading angle. These constraintslimit the motion of the actuated spoke wheel to a plane overthe course of a step. A set of differential kinematic equationscan be derived using the three equations that result from takingthe time derivative of (2) and the equations that result from theconstraints above [15]. The resulting complete kinematicdifferential equations are too long to list here, but interestedreaders are encouraged to contact the authors for moreinformation. In summary, there are seven states given by thethree translational velocities of point G, , , and , twolinear velocities of the legs,and, and two rotationalvelocities given by the change in heading angle, φ , and theThese equations allow the motion of the robot to bedetermined for a given! set of input speeds uz and ux . Thisarbitrary nature of the result highlights the flexibility of thelocomotion of the actuated spoke wheel.Since it is possible to independently actuate the spokesused for the current step and those to be used in the next step,it is possible to select the wheel angle at which the robot willswitch contact points. The optimal angle at which to switchcontact points is 30 since the required rotational velocity ofthe axle needs to be discontinuous from one step to the nextfor all switching angles other than 30 . This represents theinstant during the step at which switching would occur whenthe legs form an isosceles triangle. Using this switchingangle, choosing a height at which to keep the robot willenforce a step length. The robot in this configuration would beable to maintain a constant height of any positive value up to3l /2 , at which point the legs are fully extended and the robotwould be taking a step of length l.Moving at a constant height is a beneficial motionscheme since energy is not wasted by raising and lowering thecenter of mass, but this is only one of many motions possibleby the one-point contact mode, as the inputs uz and ux arearbitrary. The ability of the robot to adjust its height, andthereby adjust its step length, allows it to move in a mannerbest suited to fit the situation. This analysis could bereproduced for other motion schemes better suited to othertasks.2) Two-Point and Three-Point Contact ModeIn the two-point contact mode, with a no-slip condition atboth contact points for each wheel, the distance between thetwo contacts is fixed. Since the angle between the spokes incontact with the ground is constant (β), it is possible toexpress the position of the axle of the robot as a function ofthe wheel angle, θ , using the law of sines. It can be shownthat the relationships for the length from the rear contact pointA to the axle, rA , and for the length from the forward contactpoint B to the axle, r B , are given by(8)(9)
where t is the ratio of the step distance AB , to the total lengthof the spoke l. The flexibility of the design allows for t to bechosen from for any positive value up to 3 /2 , at which! during the step. Once a steppoint the spoke is fully extendedlength is chosen, the robot will move along a specified path asa function of the wheel angle. The prominent feature of this!motion is the repeated arcing pattern of the axle’s path. This isanalogous to the motion of the center of gravity of a passiverimless wheel, which is often used to approximate bipedalhuman walking [16]. While the motion of the actuated spokewheel is not constrained to a circular arc as for the case of thepassive rimless wheel, it does provide a viable scheme forstatically stable walking with as few as two actuated spokewheels.As the mobility analysis of the three-point contact modeshows zero degrees of freedom (Fig. 4 (c)), the three-pointcontact mode is not a scheme for motion. However, the threepoint contact scheme is still of use since this will allow therobot to take a very wide stance on terrain for improvedstability. This statically stable position can be used for bracingat rest which could be useful for the robot performing taskssuch as digging, drilling, or other manipulation tasks. Thisstable position itself is not unique since the spokes of the leftand right wheels can be adjusted independently to brace therobot in a stance best suited for the terrain.C. Turning MotionInstead of turning by differential steering as is common inrobots with two traditional wheels, or Ackerman steering asfound in automobiles, turning for the two actuated spokewheel robot can be implemented by actuating the spokes tohave different spoke lengths between the left and right,changing the effective radii of the two wheels independently.The robot in the one-point contact mode pivots about anaxis in the zN direction at the intersection of the two linesconnecting the left and right ground contact points as shown inFig. 5. When the robot takes steps of equal lengths, thesepivot lines are always parallel, but by making one side’s steplonger than the other, the direction of this line is changed forthe next step. This changes the heading angle, turning therobot in a discrete fashion in an amount related to thedifference in step lengths, as shown in Fig. 5.Each step taken with unequal lengths introduces a changein the heading angle, denoted by Δφ. This relationship is givenby"# i tan 1% t Li t Ri '%t t ' tan 1 Li 1 Ri 1& w (&(w(10)where tR and tL are the step lengths of the right and left actuatedspoke wheels, respectively.In!the two-point contact mode, a similar approach oftaking steps of different lengths with the left and right wheelsmay be applied for turning. However, this cannot occurwithout slipping at some of the ground contact points.Skidding conditions have not been considered at this time, butare listed in the conclusion as a topic for future study.Introducing compliance in the spokes is one way of makingturning in the two-point contact mode possible withoutskidding.Fig. 5 Discrete turning by changing the spokes length for the one-pointcontact mode.IV.PRELIMINARY DESIGNTo evaluate the models and methods developed, and toprovide a test bed for future research, an IMPASS conceptdemonstrator with two actuated spoke wheels is being built atVirginia Tech’s Robotics and Mechanisms laboratory. For thisprototype, we are developing a small, light-class unit under 50Kg with a spoke length of 60 Cm and a body width of 66 Cm.A. Actuation and MechanismThe designing of the active spoke system is an interestingand challenging task in and of itself. To minimize the numberof actuators in a single wheel unit and to maximize the strokeof the spokes, each of the six spokes passes through the hubof the wheel unit; thus there are actually only three spokes andonly three actuators are required. Fig. 6 shows the design of atwo actuated wheel and an articulated tail IMPASS robot underdevelopment. The spokes are actuated using gear head DCmotors (Fig. 7 (a)) with a simple rack and gear mechanism toconvert the rotational motion of the motor output to the linearmotion of the stroke. The spokes consist of a center racksection which engages with the driving mechanism, a shanksection which has compliance to act as passive suspension andfor safety, and a foot connected to the shank with a compliantankle joint to increase the contact area and for a better footholdand to absorb the shock.
C. ControlThe motor control is done by a PC/104 bus 8-axis motioncontroller (Fig. 6 (c)) connected to a PC/104 single boardcomputer (Fig. 6 (d)) with a 850 MHz Pentium III CPUrunning LabView. Nickel-Metal Hydride battery packs providepower to the DC motors through two, four channel servoamplifiers with 7 amps continuous, 10 amps peak capacity.The robot with onboard USB vision cameras will initially beremote controlled via a wireless 802.11b connection to alaptop computer.V. C ONCLUSIONFig. 6 IMPASS with two actuated spoke wheels and an articulated tail.Since the wheel unit needs to be rotated in full, rotatingelectrical connectors such as slip ring assemblies with a"through-shaft" configuration is used for connecting power andfor data communication between the wheel-axle unit and themain body of the robot.B. SensingThe terrain profile information is usually obtained by onboard sensors such as laser rangefinders or stereovisioncameras. For Virginia Tech's DARPA Grand Challengevehicle, we use a pair of Sick Optic laser rangefinders withtwo Eaton VORAD radar units fused together to create a localterrain map. We may implement these types of sensors withIMPASS in the future; however, the first prototype is beingequipped with load cells and simple contact sensors at the tipof each foot to be tested under controlled environments withknown terrain geometry. We are currently developing methodsto generate motion sequences of the spokes to adapt to thechanging terrain without the geometric terrain information byrelying only on simple contact force sensors at the feet todetermine the basic geometric information of the ground incontact (height and surface normal direction) for terrain withvariation less than the nominal radius of the wheel unit. Othersensors may be added to the spokes to measure the bending ofthe shank to detect collisions of the spokes with obstacles.(a) Motor (Pittman GM9236S025)(b) Amplifier (Galil AMP-1940)(c) Controller (Galil DCM-1280)(d) PC/104 CPU (VersaLogic Jaguar)Fig. 6 Electronic components.In this paper, a novel locomotion system concept thatutilizes rimless wheels with individually actuated spokes toprovide the ability to step over large obstacles like legs, adaptto uneven surfaces like tracks, yet retaining the speed andsimplicity of wheels is presented. A robot using two actuatedspoke wheels is analyzed on flat terrain using a one-, two-, andthree-point contact per wheel scheme. These modes areanalyzed to show the possible motions when constrained tonon-slipping contacts with the ground. It is shown that theone-point contact mode has two degrees of freedom where theoutput motion can be arbitrarily selected. This mode wouldallow for moving while maintaining a constant height, whichis analyzed here. The two-point contact mode is shown to haveone degree of freedom, and that by choosing a step length, thepath of the wheel is determined as a function of the wheelangle. This mode of locomotion allows for statically stablewalking with only two wheels, and could be used for carryingheavy payloads. The three-point contact scheme is shown tohave zero degrees of freedom, but would allow for additionalstability during stationary tasks by letting the robot assume awide stance with multiple contacts. Turning for the systemoccurs discretely by changing the heading angle for every stepby taking steps with different spoke lengths for the right andleft wheels.Future work will focus on expanding the understanding ofhow the actuated spoke wheel can be used to provide improvedmobility. Further kinematic analysis needs to be performed tounderstand the general three dimensional motion of the robotas it transitions from one motion scheme to another, to studythe motion over uneven terrain, and to determine thefunctionality of the actuated spoke wheel robot in otherconfigurations, such as allowing the left and right wheels torotate independently. Work will continue into developingalgorithms and strategies for intelligent motion planning andcoordination of the active spokes. Other work will includedynamic analysis, a study of energetics of the various actuatedspoke wheel configurations, and completing the prototype forexperimentations.ACKNOWLEDGMENTThis material is based upon work supported by theNational Science Foundation under Grant No. 0535012. Theauthors would also like to thank Virginia Tech’s Office of the
Provost, the Office of the Vice Provost for Research, and theuniversity’s Central Capital Account for funding this researchthrough the ASPIRES award.REFERENCES[1] Hong, D. W. and Cipra, R. J., “Optimal Force Distribution for ClimbingTethered Mobile Robots in Unstructured Environments,” 27th ASMEMechanisms and Robotics Conference, Montreal, Canada, September30-October 2, 2002.[2] Blackburn, M. R., Everett, H. R., and Laird, R. T., “After Action Reportto the Joint Program Office: Center for the Robotic Assisted Search andRescue (CRASAR) Related Efforts at the World Trade Center,”Technical Document 3141, Space and Naval Warfare Systems Center,San Diego, CA, August 2002.[3] Bares, J. and Wettergreen, D., “Dante II: Technical Description, Resultsand Lessons Learned,” International Journal of Robotics Research, Vol.18, No. 7, July 1999, pp. 621-649.[4] Hirose, S., Yoneda, K., and Tsukagoshi, H., “TITAN VII: Quadrupedwalking and manipulating robot on a steep slope,” Proceedings ofInternational Conference on Robotics and Automation, Albuquerque,New Mexico, 1997, pp. 494-500.[5] Drenner, A., Burt, I., Kratochvil, B., Nelson, B., Papanikolopoulos, N.,and Yesin, K. B., “Communication and Mobility Enhancements to theScout Robot,” Proceedings of the 2003 IEEE/RSJ InternationalConference on Intelligent Robots and Systems, Lausanne, Switzerland,Oct. 2002.[6] Drenner, A., Burt, I., Dahlin, T., Kratochvil, B., McMillen, C., Nelson,B., Papanikolopoulos, N., Rybski, P. E., Stubbs, K., Waletzko, D., Yesin,K. B., “Mobility Enhancements to the Scout Robot Platform,”P
two actuated spoke wheels and an actuated tail to climb over a wall four times its nominal height. Fig. 2 A two actuated spoke wheel IMPASS climbing over a wall. Though empirically stable, the spokes can also allow the robot to have additional contacts with the ground and to change the kinematic configuration of its structure for added stability
limitations, and relationships between kinematic and dynamic reference frames. Kinematic reference frames can be defined quite rigorously. Dynamic reference frames cannot well be bu, definet ard se nonetheleso s very useful. In practice a combination has been generally adopted. Presently we can materialize purely kinematic terrestrial and celestial
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