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  • Articulated Wheeled Vehicles:Back to the Future?

    Xiaobo Zhou, Aliakbar Alamdari and Venkat Krovi

    Abstract Articulated Wheeled Vehicles (AWVs) are a class of wheeled locomo-tion systems where the chassis is connected to a set of ground-contact wheels viaactively- or passively-controlled articulations, which can regulate wheel placementwith respect to chassis during locomotion. The ensuing leg-wheeled systems exploitthe reconfigurability and redundancy to realize significant benefits (improved sta-bility, obstacle surmounting capability, enhanced robustness) over both traditionalwheeled-and/or legged-systems in a range of uneven-terrain locomotion applica-tions. This article examines the history of such articulated-wheeled-vehicles leadingup to the current day, while placing in context the pioneering and seminal contribu-tions of Professor Kenneth Waldron and his students. Subsequently, we outline ourown research efforts on variants of AWVs, including the creation of a systematiccomputational screw-theoretic framework to model, analyze, optimize and controlsuch systems.

    1 Introduction

    We seek to investigate the design, modeling, analysis and implementation of multi-ple variants/exemplars from the broad class of locomotion systems termed Articu-lated Wheeled Vehicles (AWVs), originally explored by Professor Kenneth Waldronand his students [32, 33].

    The characteristic feature is the attachment of the multiple wheels to a commonchassis via articulated chains, which facilitates (active or passive) repositioning ofthe wheels with respect to chassis during locomotion. Such AWVs can provide sig-nificantly superior locomotion performance (such as uneven-terrain obstacle sur-mounting capability and improved suspension characteristics). Equally importantly,

    Xiaobo Zhou, Aliakbar Alamdari and Venkat KroviDepartment of Mechanical and Aerospace Engineering, State University of New York at Buffalo,Buffalo, NY 14260, e-mail: [email protected]

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  • 2 Xiaobo Zhou, Aliakbar Alamdari and Venkat Krovi

    the reconfigurability and redundancy inherent in such systems can be exploited toenhance vehicle performance characteristics (such as efficiency, stability, traction).The combination of these benefits is extremely valuable in a variety of applicationsettings from material handling on the shop floor to challenging uneven-terrain ex-ploration.

    However, articulated wheeled vehicles are highly-constrained systems subjectedto both holonomic constraints (due to the multiple closed-loops) and non-holonomicconstraints (due to wheel/ground contacts). Violation of these constraints e.g. typ-ically in terms of slipping and skidding at the ground-wheel contacts, results bothin energy-dissipation and estimation-uncertainty. Hence considerable research hasfocused on both enhanced-suspension-design (kinematic and kinetostatic), to avoidconstraint violation without either sacrificing payload capacity or increasing power-consumption; and active-coordinated-control for enhancing mobility, stability andtraction.

    In this article we will first present some background on such articulated-wheeled-robots followed by an abbreviated history of literature leading up to the currentday. Subsequently, we highlight aspects of our own work, inspired by and build-ing upon the contributions of the Waldron group. We focus in on the computa-tional/algorithmic implementation of screw-theoretic framework, that aids the mod-eling, analysis, refinement and control of such systems. Finally, we conclude with adiscussion of the promise and potential of Articulated-Wheeled-Vehicle paradigm,which we are seeking to systematically exploit by various design- and control-related research efforts.

    2 Background

    Wheeled Mobile Platforms/Vehicles, comprise of a platform supported by multi-ple wheels which allow for relative motions between the platform and the ground.Wheeled vehicles have traditionally offered simplicity of mechanical constructionand control, very favorable payload-to-weight ratio, excellent load and tractive-forcedistribution, enhanced stability and energy-efficiency, making them the architectureof choice for most man-made terrestrial locomotion systems.

    However, despite their incredible versatility, disk wheels impose severe con-straints on the design and control of the wheeled vehicle to which they may beattached. Multiple disk-wheels cannot be arbitrarily attached to a single commonplatform/chassis without over-constraining the system. Kinematic overconstraint(as often seen in various machinery) occurs due to the lack of compatibility be-tween the instantaneous motions of all moving parts. However, unlike in traditionalmachines, the violation of the wheel-ground contact-constraints (enforced only byforce-closure) is possible and gives rise to undesirable kinematic wheel-slip (skid-ding/slipping/scrubbing) seen in poorly-designed wheeled vehicles. Such wheel-slipis deleterious both from the perspective of reduced efficiency (power is wasted by

  • Articulated Wheeled Vehicles: Back to the Future? 3

    scrubbing) and poor performance (degraded odometric localization, uncontrollableand unpredictable stick-slip behavior).

    Kinematic overconstraint has traditionally been relieved by the addition of me-chanical compliance (in the form of bushings and couplings) in order to mitigate theundesired stick-slip behavior at the wheel-ground contact. A case can be made forthe systematic and careful introduction of additional mechanical compliance in theform of small articulated subchains with passive (springs/dampers) or semi-active(adjustable spring-dampers) or active (motorized) actuation. The resulting articu-lated leg-wheel systems form multiple closed-kinematic loops with the ground thatserve to constrain and redirect the effective forces and motions on the chassis.

    Thus, viewing wheeled vehicles as yet another class of a parallel-kinematicchains (with multiple articulated leg-wheel branches attached to a common chas-sis) allows the systematic application of the rich theory of articulated multibodysystems to design, analyze, simulate and control of the ensuing systems. The natureand number of both the added wheels, together with the intermediate articulations,has a significant influence on the mobility, maneuverability, controllability, stabilityand efficiency of the wheeled vehicle.

    From a design perspective, there is enormous diversity at various levels within se-lection of: (i) the individual components, like the wheels (disk wheels vs Mecanumwheels) and the articulations (lower-pair revolutes/prismatics vs higher-pair camjoints); (ii) the topology/number of joints of each subchain; and (iii) the numberof sub-chains/type-of-attachment to the chassis. The suitable selection of topology,dimensions and actuation of the individual sub-chains together with the selectionof the number and attachment location to the common chassis creates enormouschoice.

    From the control perspective, the control and reconfiguration of the collaborat-ing leg-wheel subsystems to regulate the mobility and maneuverability of the chas-sis offers other challenges. System configurations must be chosen in order to: (i)minimize singular configurations of the system; (ii) enhance mutual cooperation(motions and forces) during task performance; and (iii) improve robustness to lo-cal controller lapses and environmental disturbances. Significant freedom for im-plementation is also available by virtue of the reconfigurability and the ability totrade-off passive-equilibration versus active-actuation.

    A systematic design, analysis and control framework that builds upon individualcomponent capability to examine system-level behavior is desirable. We are cur-rently examining one such computational differential-geometry framework [18, 19]that builds upon the rich articulated multibody literature and provides the tools tocharacterize, analyze, and validate seemingly disparate articulated-wheeled loco-motion systems in a unified manner.

  • 4 Xiaobo Zhou, Aliakbar Alamdari and Venkat Krovi

    3 Literature

    3.1 Planar Locomotion/ Payload Transport

    Traditionally, wheeled mobile robots were considered to operate on planar surfaces,allowing the wheels to be modeled as thin disk-wheels with a holonomic rolling-without-slip constraint in the forward direction and offering the non-holonomic noside-slip constraint in the lateral direction. Alternate designs of wheels (such asthe Ball Wheel [34] or the Swedish Mecanum wheel) or tracks avoid limitationsimposed by the non-holonomic constraints, but possess other design and controllimitations.

    Thus, multi-disc-wheel platforms have many advantages but arbitrarily attachingand actuating these disk-wheels to a common chassis creates challenges. The overallchassis/platform motion-constraints are the union of all the individual constraintsfrom each wheel/ground contact and hence further articulations (passive/active) arerequired to ensure compatibility.

    In the plane, the rigid body constraint takes the form of requirement of all themoving-elements to have a common instantaneous center of rotation (ICR) whichcan also be visualized easily. A number of authors have surveyed the various planar-wheeled platform systems and their kinematic motion analysis in the plane [11,8]. Kinematic compatibility is established, evaluated and maintained in terms ofmatching of the Instantaneous Center of Rotations (ICR) of the disk-wheels and thechassis/platform, as illustrated in Fig. 1.

    (a) (b) (c)

    Fig. 1 Planar ICR based analysis for (a) differential drive; (b) tricycle; and (c) Ackerman steering.

    Campion et al. [13] present a systematic, general and unifying approach forderivation of kinematic- and dynamic-models of planar wheeled vehicle, with ar-bitrary number of various types of planar articulated-leg-wheel chains attached toa common chassis. They classified the ensuing planar composite-wheeled-vehiclesystems into five generic model-classes; and for each model-class systematicallyaddress performance-related questions on system-level mobility and maneuverabil-ity, model-reducibility and controllability, and selective actuation.

  • Articulated Wheeled Vehicles: Back to the Future? 5

    In a variant on this theme, many researchers have contemplated means for cou-pling together multiple differentially-driven wheeled bases with rigid axles to formcomposite Multi-Degree-of-Freedom (MDOF) Vehicles [11]. Even operating on aperfect plane, two mobile robots with such rigid axles, cannot be rigidly coupledto each other without losing some or all of their mobility. The research challengesentailed include: passively relieving the kinematic-constraints between the multipleself-contained individual modules so as to permit arbitrarily long trains of such ve-hicles to be created; and coordinating the multiple degrees of freedom within thislarge assemblage to realize enhanced performance. Hence examples of such com-posite systems always feature some sort of passive-compliant-linkage examplesinclude designs like the OmniMate/CLAPPER where differentially-driven mobilerobots are attached to each other by a compliant link; or appropriately designedcoupling within modular snake-robot systems like ACM-III [24].

    In our own work, we examine the potential for further generalizing and extend-ing this work to create planar Composite Wheeled Vehicles that exploit active-orpassive-articulated subchains for relaxing the rigid body constraints between thevarious axles by introducing further articulations. The resulting articulations en-dow the composite vehicle with: (i) ability to accommodate changes in the relativeconfiguration; (ii) redundant sensing for localizing the modules; and (iii) redundantactuation method for moving the common object to compensate for disturbances inthe motions of the base [8, 10, 31, 18, 25, 30, 36, 37, 38, 29].

    Fig. 2 Cooperative payload transport by mobile robot collectives in the ARMLAB [1].

    3.2 Transitioning to the Spatial Case

    The three-dimensional nature of the robot-motion with the varied ground-wheel-contact, creates many challenges. Various authors had noted that proper vehi-cle kinematic design, with adequate and appropriate inter-vehicle reconfigurationdegrees-of-freedom, is required to permit adaptation to uneven surfaces, and allowfor slip-free rolling of the wheels. Srinivasan and Nanua [27] demonstrated that a

  • 6 Xiaobo Zhou, Aliakbar Alamdari and Venkat Krovi

    Variable Length Axle (a prismatic joint connecting two wheels joined on an axle)could accommodate the varying wheel/ground contact points wheeled vehicle sys-tems moving on uneven terrain and help eliminate kinematic slip. From an imple-mentation perspective, Choi and Sreenivasan [15] explored creation of Vehicles withSlip-free Motion Capability (VSMC) that facilitates passive-accommodation of thevaried ground-wheel contact within the articulated chassis. Alternately, Chakrabortyand Ghosal [14] introduced a Passive Variable Camber (PVC) an extra degree offreedom (DOF) at the wheel/axle joint that permits the wheel to tilt laterally relativeto the axle and thereby allowing for the effective wheel/ground contact points tochange without any prismatic joints. Auchter et al. [9] examined the performance(reduced-wheel slip and improved adaptation) of a 3-wheeled vehicle equipped witha Passive Variable Camber rear-axle to uneven terrain in simulation.

    For rougher terrain applications, significantly more freedom becomes necessarybetween the chassis and ground contact. Hence numerous groups have examinedcreating hybrid-articulated leg-wheel subsystem-designs for terrestrial wheeled-locomotion systems to aid operation on rough unprepared surfaces. The leg-wheelsubsystem designs consist of articulated linkages with multiple lower pair joints(revolute/prismatic) between the wheel and the chassis. This addition of individual-articulations (or even small articular-sub-systems) increases the degrees-of-freedomand provides for greater redundancy and reconfigurability. However, it also cre-ates a need for controlling these additional degrees of freedom either passively viasprings/dampers or actively with actuation. Numerous variants of such designs arepossible depending upon the type, number, sequencing and nature of actuation (ac-tive/passive) of the joints. Examples range from the Mars Rover [21] and Shrimp[26] with rocker bogie suspensions, the WAAV [28] and Nomad [35] with articu-lated frames; to systems like the WorkPartner [22] and ALDURO [23] with pow-ered legs and active/passive wheels. Such systems have found numerous applica-tions in a wide variety of arenas such as exploration of extra-terrestrial [16, 21], ex-treme terrestrial [22, 35], and disaster environments. While high mobility, obstacle-surmounting capability and maneuverability are the obvious major requirements,additional criteria such as robustness, reliability and efficiency are also extremelydesirable.

    4 Our Work

    4.1 Analysis Framework

    From an analysis and control perspective, it must be noted that much of the ICRbased analysis-framework begins to break down even in the presence of the slightestnotion of the ground-planarity, small-ruts and obstacles or the wheel-circularity as-sumptions (as may be expected in an industrial setting). In addition, the treatment oftruly spatial wheeled-systems for traversing the uneven terrain required the model-

  • Articulated Wheeled Vehicles: Back to the Future? 7

    (a) (b) (c)

    (d) (e) (f)

    Fig. 3 Examples of leg-wheel systems: (a) ATHLETE [2]; (b) Shrimp [3]; (c) WorkPartner [4]; (d)ALDURO [5]; (e) Nomad [6]; (f) SRR [7].

    ing and analysis of spatial-chains. Thus an extension of the planar ICR theory to theinstantaneous-screw-axes (ISA) theory proves critical for treatment of spatial casesbut there is relatively limited work in this regard [12, 27]. Sreenivasan and Nanua[27] explored first- and second-order kinematic characteristics of wheeled vehicleson uneven terrain in order to determine vehicle mobility using screw-theory. Bruyn-inckx and Schutter [12] examined a description of the statics and velocity kine-matics of serial, parallel and mobile robots based on the fundamental concepts oftwists/wrenches and reciprocity and proposed a unified treatment of serial, paralleland mobile robot kinematics.

    Inspired by these efforts, in our work we examined a systematic and symbolicrapid computational formulation of kinematic models for the general class of AWV.

    Fig. 4 Computational/algorithmic implementation ofscrew-theoretic modeling approach [19].

    Further, automating this pro-cess by using the symbolictoolbox in MATLAB, facili-tates the rapid modeling andanalysis of any given designof an AWV [19]. Twist- andwrench-based approaches hadpreviously been used to ana-lyze motion and force capabil-ities of in-parallel articulated-mechanical-systems (such asparallel manipulators or multi-fingered grasping) but never

  • 8 Xiaobo Zhou, Aliakbar Alamdari and Venkat Krovi

    for articulated-systems with rolling wheel-ground contacts. Our contribution layin extending the twist- and wrench-based modeling framework to such articulatedwheeled robotic systems (and subsuming the extant specialized approaches for or-dinary wheeled robots [12]). Automating this process by use of symbolic analysismethods facilitates the rapid analysis of various AWV designs. The resulting mod-eling and analysis framework is well suited for both the design and control of suchAWVs.

    4.2 Passive Articulated Wheeled Vehicle Systems

    The main advantages of passive AWVs are in terms of power consumption, pay-load capacity, and controller design. In almost all these cases, it is the addition ofarticulated mechanical suspension design that endows them with their superior lo-comotion capabilities. For example, the JPL planetary rovers [21] and the Shrimprover [16] have shown enhanced terrain adaptability changing their configuration tomatch the varying terrain topology by virtue of their rocker-bogie or four-bar basedsuspensions. The suspension-designs typically feature multiple-closed kinematic-loops, are designed to have few degrees of freedom, and exploit structural equilibra-tion to passively support the weight of the system. However, in almost all cases nosystematic effort to design the articulated leg-wheel system is ever considered otherthan to perform multiple parametric-studies with high-fidelity simulation runs.

    In general, any such design process must take into account innumerable, oftenequally important and competing considerations such as the loss of stability, tip-overstability and ground traction for the task of locomotion on uneven terrain. However,in our work, we will specifically focus our attention on two major complemen-tary/conflicting design criteria large-workspace and stiff-suspension with minimal-actuation in evaluating candidate designs for such articulated leg-wheel systems.Our emphasis was on realizing the ability to surmount relatively-large obstaclesusing minimal joint actuation within the subsystems while locomoting on uneventerrain. Suitable selection of various kinematic parameters, such as the link-lengthsand initial configuration, as well as static parameters such as spring constants andtheir preloads was critical. A novel kinetostatic design-customization framework isemployed for matching of desired kinematic and static specifications. Significant re-ductions in overall actuation requirements were achieved by judicious combinationof structural-equilibration, spring-assists and actuation [25].

    4.3 Fully Actuated Articulated Wheeled Systems

    Fully-actuated articulated wheeled systems possess significant potential for recon-figurability (principally due to the absence of closed-loops of passive AWVs). Fur-ther, the redundant-actuation endows the system capability to optimize secondary

  • Articulated Wheeled Vehicles: Back to the Future? 9

    Fig. 5 Kinetostatic design of articulated leg-wheel system [25].

    performance indices (such as stability or traction) in addition to realizing the pri-mary locomotion tasks. On the other hand, more actuators add extra weight andcontrol complexity necessary to resolve the redundancy in actuation. Thus the re-configurability and redundancy of fully-actuated AWVs needs to be unlocked bycareful modeling, analysis and control [20, 28].

    In our own work, we examined a similar over-actuated AWV design calledthe Reconfigurable Omnidirectional Articulated Mobile Robot [17, 18, 19]. Mul-tiple variants of kinematic control schemes were developed to ensure kinematic-constraint consistency and resolving the redundancies inherent in such articulatedwheeled robots. Two generations of hardware-in-the-loop prototypes were devel-oped and simulations and real-time experiments varied out to validate localizationdynamic control, and reconfiguration planning algorithms. Planned future work in-cludes expanding our modeling framework and control scheme into 3D AWVs mov-ing on uneven terrain.

    Fig. 6 The Reconfigurable Omnidirectional Articulated Mobile Robot (ROAMeR) [19].

  • 10 Xiaobo Zhou, Aliakbar Alamdari and Venkat Krovi

    5 Discussion

    The Articulated-Wheeled-Vehicle paradigm offers remarkable and diverse opportu-nities for creation of very mobile and maneuverable terrestrial locomotion systems.However, the capabilities of articulated-wheeled locomotion systems to manipulatethe chassis/payload (to improve obstacle surmounting capabilities and reduce actua-tion requirements) needs to be carefully unlocked by both design and control. Froma design perspective, the selection of the topology, dimensions and finally configura-tion of the highly reconfigurable leg-wheel system plays a critical role in determin-ing the performance. The subsequent selection of the type and number of such indi-vidual modules, together with the location and nature of attachment to the commonpayload determines the topology and parameters of the overall system. From thecontrol perspective, the control and reconfiguration of the collaborating leg-wheelsubsystems to regulate the mobility and maneuverability of the chassis offers op-portunities and challenges. Significant freedom for implementation is also availableby virtue of the reconfigurability and the ability to trade-off passive-equilibrationversus active-actuation.

    A systematic design, analysis and control framework that builds upon individualcomponent capability to examine system-level behavior is desirable. We are cur-rently examining one such screw-theoretic framework, built upon a theoreticallysound articulated multibody background and implementation within an algorith-mic/computational differential geometric formulation. It allows for flexible, mod-ular and reconfigurable interchanges of component- and system-level constraints,while permitting integration into an operational framework. Quantitative measuresof system-level cooperation (such as system manipulability, load-distribution andstability) aid the design-refinement, control and evaluation efforts. The ability to de-sign, analyze and deploy under-actuated, exactly-actuated and redundantly-actuatedarticulated-wheeled systems using this framework can now be systematically ex-ploited to enhance locomotion capabilities of such systems.

    Acknowledgements This work was supported in part by the National Science Foundation AwardCNS-1135660.

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