1、Auton Robot (2006) 21:227242DOI 10.1007/s10514-005-9717-9A kinematically compatible framework for cooperative payloadtransport by nonholonomic mobile manipulatorsM. Abou-Samah C. P. Tang R. M. Bhatt V. K r o v iReceived: 5 August 2005 / Revised: 25 May 2006 / Accepted: 30 May 2006 / Published online
2、: 5 September 2006CSpringer Science + Business Media, LLC 2006Abstract In this paper, we examine the development ofa kinematically compatible control framework for a mod-ular system of wheeled mobile manipulators that can teamup to cooperatively transport a common payload. Each in-dividually autonom
3、ous mobile manipulator consists of adifferentially-driven Wheeled Mobile Robot (WMR) witha mounted two degree-of-freedom (d.o.f) revolute-jointed,planar and passive manipulator arm. The composite wheeledvehicle, formed by placing a payload at the end-effectors oftwo (or more) such mobile manipulator
4、s, has the capabilityto accommodate, detect and correct both instantaneous andfinite relative configuration errors.The kinematically-compatible motion-planning/controlframework developed here is intended to facilitate main-tenance of all kinematic (holonomic and nonholonomic)constraints within such
5、systems. Given an arbitrary end-effector trajectory, each individual mobile-manipulators bi-level hierarchical controller first generates a kinematically-feasible desired trajectory for the WMR base, which isthen tracked by a suitable lower-level posture stabilizingcontroller. Two variants of system
6、-level cooperative con-trol schemesleader-follower and decentralized controlM. Abou-SamahMSC Software Corporation,Ann Arbor, MI 48105, USAe-mail: C. P. Tang R. M. Bhatt V. K r ov i (envelopeback)Mechanical and Aerospace Engineering, State University ofNew York at Buffalo, Buffalo, NY 14260, USAe-mai
7、l: vkrovieng.buffalo.eduC. P. Tange-mail: chintangeng.buffalo.eduR. M. Bhatte-mail: rmbhatteng.buffalo.eduare then created based on the individual mobile-manipulatorcontrol scheme. Both methods are evaluated within an imple-mentation framework that emphasizes both virtual prototyp-ing (VP) and hardw
8、are-in-the-loop (HIL) experimentation.Simulation and experimental results of an example of a two-module system are used to highlight the capabilities of areal-time local sensor-based controller for accommodation,detection and corection of relative formation errors.Keywords Composite system.Hardware-
9、in-the-loop.Mobile manipulator.Physical cooperation.Redundancyresolution.Virtual prototyping1 IntroductionCooperation has been the key to success of most humanendeavors and the similar incorporation of cooperation inrobotic systems is critical to realize the next generation ofsystems and application
10、s. Interest in cooperating systemsarises when the tasks are inherently too complex for a singlesystem to accomplish; or when building and using severalsimple systems can be more flexible, fault-tolerant or cheaperthan using a single large system.Our guiding vision is to create and evaluate an overal
11、lframework for cooperative payload transport using a fleetof semi-autonomous wheeled mobile manipulator modules.Within this framework we examine coupling of various mod-ules to create a larger variable-topology composite-wheeledsystem, with inherent internal reconfigurability to accommo-date disturb
12、ances and enhance payload manipulation capa-bilities. The proposed application arena ranges from indus-trial applications, where suitable numbers of such modulescan be tasked to manipulate variable-sized payloads, to extra-terrestrial applications, where individual rover modules senton separate miss
13、ions can cooperate to support planetarySpringer228 Auton Robot (2006) 21:227242colonization efforts (Adams et al., 1996; Juberts, 2001;Schenker et al., 2000).In our system, each basic module consists of a passive,planar, two degree-of-freedom (d.o.f.) revolute-jointed ma-nipulator mounted on a diffe
14、rentially-driven Wheeled Mo-bile Robot (WMR), as shown in Fig. 1(a) and (c). An ef-fective articulated compliant linkage between the wheeledbases is created when a common payload is placed on theend-effectors of multiple adjacent modules, as shown inFig. 1(b) and (d). The resulting composite vehicle
15、 now pos-sesses: (a) the ability to accommodate changes in the rela-tive configuration (by virtue of the compliant linkage); (b) amechanism for detecting such changes (using sensed articu-lations); and (c) means to compensate for such disturbances(using the redundant actuation of the bases), while p
16、erform-ing the payload transport task.1.1 BackgroundOver the millennia, wheeled platform designs (with multiplesets of disc wheels attached to a common chassis) have re-mained popular in payload transport applications since theypermit the load and traction forces to be distributed betweenthe multipl
17、e wheels. However, the mobility, steerability, andcontrollability of the overall wheeled system depend largelyupon the type, nature and locations of the attached wheels.The process of selecting and attaching the set of wheels ina multiple-wheeled system creates various kinematic (holo-nomic/nonholon
18、omic) compatibility constraints. Arbitrarilyactuating such wheels can precipitate violation of the con-straints and result in degradation in overall system perfor-mance (Campion et al., 1996). Hence, the design and controlof such vehicles need to first explicitly take into accountthe maintenance of
19、the kinematic compatibility conditions(before dynamic and/or contact conditions can even be con-sidered).Most design approaches consider the addition of activeor passive articulations between the wheels and chassis toensure kinematic compatibility. This is pertinent since weconsider formation of lar
20、ger composite wheeled systems bycoupling together multiple individual WMRs with an ar-ticulated compliant linkage. This allows such systems toaccommodate momentary controller errors without transfer-ring any interaction forces between the WMRs. Examplesinclude the CLAPPER and the OMNIMATE (Borenstei
21、net al., 1996), which feature compliant linkages with twopassive revolute joints and one passive prismatic joint. How-ever, the biggest limitation of the CLAPPER/OMNIMATEdesigns comes from the fact that the two WMRs have to stayassembled together because of the compliant linkage.Fig. 1 CAD models of
22、 the (a)individual module (b) compositewheeled system with theircorresponding physicalprototypes below in (c) and (d)respectivelySpringerAuton Robot (2006) 21:227242 229Hence, we propose the alternate development of a com-posite wheeled system with a modular formation of the artic-ulated compliant l
23、inkage between the wheeled bases. Whilewe will focus the discussion around a 2-module/payloadcomposite system for the rest of the paper, we would like tomake some general observations. First, our selection of thetopology of the individual mobile manipulator modules isguided by the requirement for mo
24、dularity (in terms of easyattachment/detachment of multiple such modules to a com-mon payload while maintaining at least three d.o.f. withineach sub-chain). In this light, we note that a passive planarfour-bar mechanism is formed when two such modules at-tach to a payloadand this articulated linkage
25、 introducesmore than the minimum (three) required d.o.f. between thebases. However, such excess mobility within the articulatedsuperstructure is eliminated when the more general case ofthree or more modules is considered. Second, we assumethat the second link (shown as a “flat support” in Fig. 1(a)i
26、s rigidly attached to the payload. It is worth noting that avariety of other joints may be formed by relaxing this rigidattachment requirement; a discussion of these alternatives,however, is beyond the scope of this paper.1.2 Research issuesWe see that while the articulated compliant linkage resolve
27、sthe issue of maintenance of compatibility conditions, it intro-duces a variety of other challenges. First, it creates holonomic(loop closure) constraints that limit the d.o.f. Hence, carefulselection of the type and number of joints within the linkageas well as the configuration parameters (link le
28、ngths and ini-tial pose) is critical and these aspects are examined elsewhere(Abou-Samah and Krovi, 2002; Tang, 2004). Further, the re-striction in d.o.f. due to the holonomic constraints translatesinto the fact that not all joints need to be actuated. The se-lection of the location of active and pa
29、ssive joints within thecompliant linkage is yet another design choice that plays animportant role in determining the payload transport perfor-mance (Tang and Krovi, 2004).The unique contributions of this paper come from thedevelopment and evaluation of control schemes for the com-posite wheeled vehi
30、cle that facilitate maintenance of allkinematic (holonomic and nonholonomic) constraints withinsuch systems. Given an arbitrary end-effector trajectory,each individual mobile-manipulators bi-level hierarchicalcontroller first generates a kinematically-feasible desiredtrajectory for the WMR base, whi
31、ch is then tracked bya suitable lower-level posture stabilizing controller. Whilethe mechanical articulated structure facilitates accommoda-tion of disturbances within the mobile manipulators, sucha controller ensures the maintenance of relative configura-tion while tracking the desired end-effector
32、 trajectory. Thecomposite wheeled vehicle controllers, built up from theseindividual mobile-manipulator controllers, now allow for ac-commodation, detection and correction of relative formationerrors and help maintain desired formations. These system-level controllers are also well-suited for online
33、 implemen-tation from the viewpoint of both ease of incorporation oflocal sensor data and computational efficiency.The rest of the paper is organized as follows: Sec-tion 2 provides a brief summary of the pertinent lit-erature. In Section 3, we present the development ofthe kinematically-compatible
34、controllers for the individualmobile-manipulators that can help maintain a desired config-uration while tracking a given end-effector motion trajectory.In Section 4, we derive two variants of system-level cooper-ative control schemesleader-follower and decentralized based on the controllers develope
35、d for the individual mobilemanipulator. Section 5 describes the hardware and softwareimplementation framework of our system with experimentalresults presented in Section 6. Section 7 concludes the paperwith a discussion.2 Literature surveyMobile manipulator systems are typically composed of aWMR pla
36、tform with one (or more) mounted manipulators(Honzik, 2000; Seraji, 1998; Yamamoto, 1994; Yamamotoand Yun, 1994). While track-, gantry- or manipulator-basesmay be modeled and analyzed easily, WMR bases offerspecial challenges. WMRs cannot be stabilized to a singleequilibrium point by a continuous (s
37、mooth) time-invariantpure state feedback law, due to the violation of Brockettscondition (Brockett, 1981). Hence, the motion planning andcontrol of such WMRs requires special treatment (Canudasde Witt et al., 1996; Latombe, 1991; Li and Canny, 1993;Murray and Sastry, 1993). Concomitantly the class o
38、f non-holonomic mobile manipulator with such bases requirescareful handing.Further, combining the mobility of the base platform andthe mounted manipulator creates redundancy (Seraji, 1998;Yamamoto and Yun, 1994). The determination of the actu-ator rates for a given end-effector motion of a redundant
39、manipulator is typically an under-constrained problem butessential for motion planning/control of such systems. Mostof the redundancy resolution methods available in the lit-erature have a principal underlying theme of optimizing ameasure of performance based on kinematics (or in somecases the dynam
40、ics) of the system. See Nakamura (1991)fora review of these methods.Several of these results have been extended and ap-plied to mobile manipulators. Serajis (1998) extension ofWhitneys (1969) approach to kinematic redundancy reso-lution of mobile manipulators hinges on a fully actuatedmanipulator co
41、nfiguration. This makes it difficult to adaptSpringer230 Auton Robot (2006) 21:227242this approach to our case, since our mobile manipulator pos-sesses a mixture of active and passive joints. Alternatively,Yamamoto and Yun (1994) decompose the motion of the mo-bile manipulator into decoupled WMR-bas
42、e and manipulatorsubsystems. The WMR is then controlled so as to bring themanipulator to a preferred configuration (using criteria suchas the manipulability measure) as the end-effector performs avariety of unknown manipulation tasks. This approach lendsitself better to decentralized planning and co
43、ntrol, and we de-velop our controllers in this paper building on this approach.Our situation is one where the agents physically interactwith each otherlesser literature exists but with consider-able variety in their proposed approaches. Some approachesemphasize cooperative physical manipulation by t
44、eams ofrelatively simple pushing mobile robots (Donald et al., 1997;Kube and Zhang, 1997; Spletzer et al., 2001; Stilwell andBay, 1993; Wang et al., 1994). Khatib et al. (1996)useda decentralized control structure for cooperative tasks withmobile manipulation systems, but with holonomic bases andful
45、ly actuated manipulators. Others have considered devel-opment of optimal motion-planning/control schemes (Desaiand Kumar, 1999) and control schemes for nonholonomiccooperating mobile manipulators grasping and transportingpayload (Adams et al., 1996), including the effects of flexi-bility (Tanner et
46、al., 1998) but only from a centralized per-spective. Furthermore, in almost all cases, the focus is ona fully actuated manipulator, without any passive or semi-passive joints, which is a dominant feature in our system.Relatively limited literature discusses design/control modi-fications intended to
47、aid the decentralization of cooperationtask, including approaches of selective locking/unlocking ofjoints (Kosuge et al., 1998) and/or special mechanical de-signs of the couplings between the multiple manipulators(Humberstone and Smith, 2000).3 Kinematic controlIn this section, we present the develo
48、pment of a bi-level hier-archical control implementation that enforces the kinematiccompatibility condition for the individual mobile manipu-lator. The implementation combines an upper-level designof the kinematically-compatible desired trajectories for theWMRs which are then tracked using a lower-l
49、evel posturestabilization controller.3.1 Modeling of the individual mobile manipulatorsFigure 2 depicts a differentially-driven WMR with the baseof an RRR-manipulator1mounted at the midpoint of the1R indicates revolute joint. RRR indicates serial linkages connected bythree revolute joints.Fig. 2 Schematic diagram of a 3-link mobile manipulatorwheel axle. The frame M is rigidly attached to the WMRwith the X-axis oriented in the direction of the forward travel.Frames 1, 2 and 3 are rigidly attached at the proximalends of the first, second an
