Behaviors for Physical Cooperation Between Robots for ... - CiteSeerX

Behaviors for Physical Cooperation Between Robots for Mobility Improvement: Hardware Results and Use of Dynamics Ashish Deshpande and Jonathan Luntz Department of Mechanical Engineering The University of Michigan, Ann Arbor, MI USA 48109 [email protected], [email protected]

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Mobile robots are useful for applications such as search and rescue, urban infiltration etc, where the goal is to explore unknown, potentially hazardous terrain. Large teams of small, inexpensive robots have advantages over a few large and expensive robots, such as covering more ground in less time, access to tight spaces, redundancy, and expendability. One of the major challenges in employing small mobile robots is their restricted mobility on rough terrain. The US army is interested in Unmanned Ground Vehicle technologies for the purposes of discreet exploration of enemy areas consisting of rough terrain and complex urban setting. The army has expressed special interest in robots such as PackBots [1] due to two main advantages: sturdy operation on rough terrains and suitability to be carried by a single soldier. The army has currently employed teleoperated PackBots in the war zones in Afghanistan and Iraq where they act as individual units teleoperated by the soldiers to explore dangerous regions. Although fairly successful in their missions, these robots can get stuck on the rough terrain due to their size and power restrictions. We propose to overcome the mobility restrictions by physical cooperation among robots. We are working on designing mechanisms and behaviors for a team of robots that physically cooperate to enhance the team’s overall mobility. The idea is that the robots link up and push or pull on each other to overcome obstacles. We plan to design cooperative teams such that low-cost,

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Abstract— A team of small, low-cost robots instead of a single large, complex robot is useful in operations such as search and rescue, urban exploration etc. However, the performance of such a team is limited due to the restricted mobility of the team members. This paper presents the results obtained toward the goal of enhancing mobility of a team of mobile robots by physical cooperation among the robots with the focus on the development of the low level system components. Recognizing that small robots need to overcome discrete obstacles, we develop specific analytical maneuvers to negotiate each obstacle where a maneuver is built from a sequence of fundamental cooperative behaviors. We have developed a 2-robot hardware system based on our idea of cooperative mobility improvement and guided by the results from the static analysis. We have demonstrated the implementation of basic cooperative behaviors, such as cooperative lift, and by implementing the decentralized control architecture we have demonstrated gap crossing maneuver with the hardware. We have analytically proved that robot dynamics can be used to reduce the friction requirements in the lift behavior and have demonstrated, with simulations, implementation of this idea for the cooperative lifting behavior.

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Fig. 1. A schematic of a semi autonomous team of robots exploring an unknown, rough terrain. Robots are assigned to different regions of the terrain and when obstacles are detected two or more robots hook up to each other, either autonomously or by the operator depending on the sophistication, at which point the operator can switch these robots to autonomous cooperation mode. Robots physically cooperate (A) to climb over rocks, (B) to crossover a ditch, (C) to steering over a slippery surface, and (D) to climb over a steep slope.

simply designed robots can connect to other robots via linkage with minimum or no additional actuation, and cooperation can be achieved with minimum communication between the robots by setting up decentralized control architecture. We believe that based on this physical cooperation idea great many behaviors can be accomplished involving multiple robots and such ideas will work by either retrofitting existing team of robots, such as PackBots, or by designing new teams of low cost robots. Some of these ideas are conceptually demonstrated in Figure 1 which shows robots physically cooperate to (A) climb over rocks, (B) crossover a ditch, (C) steer over a slippery surface, and (D) climb over a steep slope. Each robot

works independently to explore different parts of the terrain, but when faced with difficult obstacles, it physically cooperates with other robots. Currently all the robots employed for reconnaissance and rescue missions are teleoperated which in most cases requires one operator for each robot. We propose semi-autonomous robot teams. We plan to design autonomous cooperative behaviors for negotiating discrete obstacles, thus ridding the operator of controlling intricate cooperative tasks while maintaining control over the overall movement of the robots. One can imagine a single operator controlling a team of robots exploring an unknown terrain as shown in Figure 1. Robots can be assigned to different regions of the terrain and when obstacles are detected, either by robots or by the operator depending on the sophistication, two or more robots can hook up one another. In Figure 1, when faced with a steep slope, robot (A1 ) calls for help and hooks up with robot (A2 ). At this point the operator initiates ‘cooperative step climbing’ mode which can be carried out autonomously. We envision such semi-autonomy as the next pragmatic step toward building smarter robotic teams. Importantly such semi-autonomy is in tune with the US army’s goal of keeping the soldier active in decision making tasks. In this paper we restrict our analysis to the problem of designing cooperative behaviors after the robots have hooked up. A. Related Work and Background Literature There are many of examples of mobile robot teams; we list a few here with brief explanation of the idea and the results. A number of researchers have developed robots and teams of robots for planetary [20] and urban exploration [18] and also for search and rescue purposes [15]. Restricted mobility has been identified as the main impediment and is treated in variety of ways. The marsupial robot team developed by Murphy [15] addresses the mobility problem at two levels: the ‘mother’ robot can cover long distances and the shape changing ‘child’ robots can improve mobility in tighter spaces. This team has been employed to carry out real world missions but limitations of the ‘child’ robots still exist. In the case of the planetary exploration robots [20], mobility is improved with innovative mechanisms, e.g. a ‘rocker’, but this addresses only special situations. Rich et. al. [18] have developed robots with innovative wheeled legs to improve mobility. However, these robots are costly and hence not dispensable. A number of exploration robot teams exist such as the one developed by Parker [16] where, to improve performance, the group members cooperate at information level. However, these robots are not mechanically cooperative so the reach of the group is limited by that of each group member. Physical cooperation among robots to improve performance has been studied by researchers previously. Teams of robots developed by Sugar and Kumar [19] and by Khatib et. al. [12] are examples of such research where the team members cooperate physically to manipulate large objects. Robots developed by the researchers at the Jet Propulsion Lab [17] cooperate to help one robot descend a steep cliff. Among the three robots

cooperating in this design, two are held stationary and are connected to the third robot by tethers. Mobility is improved but for one specific operation namely the cliff descent with specialized hardware for this application. The topic of physical cooperation to improve mobility of robot teams has also been studied by other researchers. Hirose et. al. [9], [10] have developed a mobile robot inspired by snake motion to inspect hazardous areas of a nuclear plant. The robot is constructed by connecting several mobile platforms by actuated prismatic joints which they can use to lift one another. Such design facilitates motion through tight spaces, step climbing and gap spanning. Team of small robots (each around 6 cm long), called Millibots, developed at Carnegie Melon University [6] is another example of physically cooperating robots where step climbing is demonstrated by connecting multiple mobile robot in a chain by actuated revolute joints. Researchers at EPFL, Switzerland, have demonstrated impressive cooperative behaviors with robots (each around 15 cm long) possessing multiple sensors and actuators [13]. Another example is the robot team developed by Asama et. al. [3] which cooperate via a forklift mechanism to climb steps. B. Salient Features of Our Approach Although, these approaches address similar problem i.e. improving mobility via physical cooperation, our approach is inherently different in terms of the design philosophy, analysis and the implementation. Below we list out some of the distinctive features of our approach. • Cost of Cooperation: Simplicity is the underlying principle of our design: cooperation can be achieved with simple, low cost and hence disposable robots, the physical connection between the robots will be a passive, and each robot will control its own state resulting in distributed control architecture requiring simple (possibly nonexistent) communication protocols among the robots. • Ability of Retrofit: We want to design the mechanisms and the behaviors such that they can be implemented with existing mobile robots with minimal modifications. For example, we plan to achieve cooperation using only existing wheel torques to generate the necessary forces thus avoid the need for additional actuators to improve mobility. • Scalability: We want to design behaviors that are scalable with respect to the size as well as number of robots in a cooperative team. Many of the cooperative maneuvers developed by other researchers are feasible only for small sized robots (e.g. step climbing with the Millibots [6]) which involves one robot lifting two other robots up via actuated linkage. As the size of the robots increases, it is harder to implement maneuvers with actuated linkage. The weight of the motor required to actuate lifting mechanism increases by the square of the length of the robots. Thus the fraction of the motor weight increases as the size of the robots increases making it prohibitive to have actuated linkage for medium sized robots such as those used by US army.

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Explicit, Analytically Defined Maneuvers: For small vehicles mobility is defined by their ability to scramble over ‘things’, or more formally, their ability to negotiate discrete obstacles. This is unlike the mobility characterization for large vehicles (such as a truck) where the mobility is assessed by their ability to plow through ‘stuff’ using the criteria such as power required to cover terrain, maximum speed with which terrain can be covered, etc. [4], [2]. For small vehicles, even small objects such as ditches and bushes that large vehicles can plow through are challenging to negotiate. We plan to improve the mobility of team of mobile robots by designing explicit analytical cooperative maneuvers to negotiate discrete obstacles where a maneuver is built from a sequence of fundamental cooperative behaviors. This is a systematic approach to mobility improvement as opposed to making robots hook up and scramble over the obstacles as reported in the literature [6], [13].

C. Explicit Maneuvers for Cooperative Mobility Tasks We plan to improve mobility of a team of mobile robots by designing explicit cooperative maneuvers to negotiate discrete obstacles. We can achieve these maneuvers through a small number of simple cooperative behaviors. Figure 2 shows four examples of cooperative behaviors involving two robots: cooperative lift, cooperative buckle, cooperative climb, and traction sharing. Each of these behaviors is achieved with a simple, un-actuated link connection and combinations of these behaviors can lead to useful cooperative maneuvers, for example a gap crossing maneuver. More complicated mobilityenhancing maneuvers such as climbing steep hills, negotiating slippery patches, and traversing uneven, bumpy, or very soft terrain could also be developed by combinations of simple cooperative behaviors. Since behaviors are simple more robots can be easily added to the maneuvers e.g. gap crossing with a chain of robots can be achieved by adding robots to the lift and buckle behaviors presented in Figure 2.

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(a) Cooperative lift

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(b) Cooperative buckle

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(c) Cooperative climb

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(d) Traction sharing

Fig. 2. Building block behaviors: Maneuvers such as gap crossing can be achieved through these behaviors. Figure shows four examples of cooperative behaviors involving two robots: cooperative lift, cooperative buckle, cooperative climb and traction sharing.

In this paper we focus on design and analysis of the cooperative lifting behavior and extend results to the cooperative buckle behavior since, conceptually, these behaviors

are similar. We start in Section II with the development of the system for cooperative behaviors including the description of the hardware system, and a demonstration of the gap crossing maneuver with the building blocks behaviors. In Section III we propose that the system dynamics can be utilized to reduce the friction requirement. First we prove this conjecture analytically and then give simulation results that demonstrate the implementation of this idea. Finally, we summarize the results and state directions for future research in Section IV. II. S YSTEMS D EVELOPMENT FOR C OOPERATIVE B EHAVIORS We have developed a simple hardware system based on our idea of cooperative mobility improvement and guided by the results of static analysis. In this section we describe steps carried out to demonstrate cooperative behaviors with the hardware platform. A. Description of the Hardware Figure 3 shows the hardware and below is the description of various hardware components. 1) Robots and Connecting Link: We use two toy-sized, remote controlled, treaded tanks as our cooperating robots. Each robot is 45 cm long and weighs about 220 gms. Each robot has two motors, one for each tread and is skid steered. The motors are geared down and the torque to weight ratio is high, which is advantageous for the cooperative behaviors. The two robots are connected by a four-bar linkage made of plexi-glass, the design for which is explained [7]. We have clips for latching and un-latching which are manually activated. The link is un-actuated (no additional motors) and the four bar mechanism allows for change in link configuration by forward/backward movements of the robots. 2) Micro-controller: As mentioned before, each robot has a remote control which sends voltage commands to the motors to control forward speed and steering. Since we want to demonstrate automated gap crossing we have disconnected the inputs to the motor from the RF circuit and installed an OOPic micro-controller on each robot which controls the motor inputs. As the name suggests, an OOPic is an object oriented (easily) programmable IC. We program it on a PC and download the code using a parallel network cable. In the code, we feed in the desired motions for the robots, corresponding to cooperative behaviors, the micro-controller takes in the position and lift angle inputs from the sensors, computes the errors and sends the controlled commands to the motors. 3) Speed and Angle Sensors: We have installed two sensors on each robot one to measure lift angle other to measure position. A potentiometer on the connecting link measures the robot lift angle indirectly and we have photo-electric speed encoders installed on the driving wheel shaft of the robots which give linear position. 4) Control Architecture: We have presented control architecture and controller design in [7]. We have successfully implemented the same architecture with the hardware.

method, described in [11]. The equations have the form: " #" # " #  2 M11 (θ1 ) 0 θ¨1 C11 (θ1 ) 0 θ˙1  + + C21 (θ1 ) 0 d˙2 2 0 M22 (θ1 ) d¨2 # " #" # " B11 (θ1 ) B12 (θ1 ) θ˙1 K1 (θ1 ) + = K2 (θ1 ) B21 (θ1 ) B22 (θ1 ) d˙2 " #" # U11 (θ1 ) U12 (θ1 ) VA U21 (θ1 ) U22 (θ1 )

Fig. 3. Hardware platform built to demonstrate cooperative behaviors. Figure shows two identical robots connected by a four bar link mechanism. This is the cooperative buckling behavior achieved with distributed control such that the front robot controls its position and the rear robot robot controls its lift angle.

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Note that M , C, B, K and U terms are nonlinear functions of θ1 (we do not show the complete equations here due to their length and complexity). The motor models are embedded in the nonlinear system equations and resulting in the damping term, B. VA and VB are the voltages to the motors at the wheels of front and rear robot, respectively. These voltages generate traction forces FA and FB , through the motor dynamics, which in turn move the robots. Terms C are the centripetal terms only (there are no Coriolis effects) dependent only on ˙ We have linearized this non-linear dynamic model so as to θ. design linear controllers. C. Results: Simulation and Hardware Demonstration

Fig. 4. Schematics of two robots cooperating to cross a gap. The maneuver is divided into four stages with three steps in each stage. Wheel torques generate the necessary forces thus avoiding need of additional actuation.

B. Application Example: Gap Crossing Maneuver As discussed earlier, we plan to build useful maneuvers using fundamental cooperative behaviors such as lifting. As an example of improving mobility we implement gap crossing maneuver with two cooperating robots lift and buckle behaviors. The length of a gap that robots can cross is one measure of mobility. For a wheeled robot such length is determined by the size of the wheels and is usually only a small fraction of the length of the robot. For tracked robots it is usually half length of the robots. Figure 4 shows the gap crossing maneuver formed of fundamental cooperative behaviors involving two robots pushing and pulling on each other through an un-actuated link. The gap crossing maneuver can be divided into four stages each involving three cooperative behaviors as shown in the figure. In this paper we present the results from the stage 1 in detail and also show snap shots from other stages of gap crossing maneuver. The two robot cooperative system has two degrees of freedom. We define two generalized coordinates as the front robot angle θ1 and the rear robot position d2 . The equations of motion are derived, analytically, using Kane’s Dynamics

We have designed controllers and presented the tracking performance of the controllers with linearized model as well as with the original nonlinear dynamic system in [7]. We want to control θ1 and d2 such that the cooperative lifting behavior (which is the stage 1 of gap crossing) is completed. In general reference trajectories for a variety of behaviors can be preloaded in the controllers and can be initiated externally, say, by an operator. The coordination of trajectories is time based and either the front robot or a central control system can send signals at the switching instances. Here we present gap crossing with hardware by employing the decentralized control architecture. Figure 5 shows the reference trajectories and response of the hardware system based on the data collected using the robot sensors. This figure shows that in the hardware demonstration we have modified stage 1c. Instead of the rear robot holding its position and the front robot bringing its angle down we move the rear robot forward and hold the front robot position. This change, although resulting in same cooperative maneuver (hence shown as “pseudo” reference in Figure 5(a)), is advantageous because in our hardware controlling positions is easier than controlling angle. Fairly good tracking is achieved but, due to effects of backlash in real system the hardware response does not follow the reference as closely as the simulation response, especially, under the effects of interactions. We have carried out the complete cooperative gap crossing maneuver with two robots with the same control architecture which was designed for the cooperative lifting behaviors but with different reference inputs. Figure 6 shows snap shots from the gap crossing demonstration with hardware. The four pictures correspond to the middle column of maneuver sequence in Figure 4.

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III. E XPLOITING DYNAMICS

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In [7], [8] we have discussed that high ground friction is required to achieve cooperative lifting and we have presented design guidelines to reduce friction requirement. Still high friction requirement is a critical issue. For the simulation system we considered in [7] the friction required for lifting statically is greater than 11 . We propose that the friction requirements can be relaxed if the lifting occurs while the robots accelerate i.e. in a dynamic situation. This hypothesis comes from the fact that a single vehicle can not pop-up its own front wheels statically but can do so if accelerating. For two-robot case, dynamics is introduced by applying unequal opposing wheel torques on robots. In this section we will analyze how dynamics affect front robot lifting.

Fig. 7. Variation of the friction requirements with the front robot lift angle. The friction requirements are determined analytically for the configuration shown in Figure 3. As the lift angle increases the friction requirements go down.

dynamics conditions. The friction requirements depend on the normal forces at wheels in contact with the ground which under the dynamic conditions are functions of the applied forces as well as the generalized coordinates (θ1 , d2 ) and generalized speeds (θ˙1 , d˙2 ). For the sake of simplicity we represent these relationships by the following equations: NA NB

= f3 (θ˙1 , θ1 , FA , FB ) = f4 (θ˙1 , θ1 , FA , FB )

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A. Determination of Friction Requirement

The friction requirement at each wheel in contact is given by taking the ratio of the normal force to the traction force at each wheel. It is interesting to note that the static friction requirements change as the front robot lift angle changes i.e. if we start from a lifted position. Figure 7 shows the variation of µA and µB with front robot lift angle in the static case. As the front robot angle increases less traction force is needed for lifting thus reducing the friction requirements. Thus, it is advantageous to reduce the friction requirement using robot dynamics at the start of front robot lift, and once the robot is lifted it requires less friction to stay up.

To analyze the effects of introducing dynamics we first need to be able to determine the friction requirements under the

B. Effect of Dynamics

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have used Newtonian friction model with a unit-less coefficient of friction. Deep grousers on a soft surface can achieve effective coefficient of friction greater than 1.

For the two-robot case, dynamics are introduced if we apply unequal opposing wheel torques on the robots. We define fr as the ratio of the front robot force to the rear robot force.

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Fig. 8. Effect of applying unequal forces on 2 robots. Analytically computed friction requirements plotted against ratio of front to rear robot wheel forces. Static lifting when fr = 1, otherwise dynamic lifting. Friction requirement µB is high when fr < 1. Friction requirements are low when fr > 1.

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Solving the equations of motion for a fixed value of fr with the condition that θ¨1 , θ˙1 , θ1 are all equal to zero (i.e. the front robot barely starts to lift up) uniquely determines the values of the forces required and thus defines, analytically, the friction requirements. Figure 8 shows the variation of the front and the rear robot friction requirements with fr . The greater of the two µ’s is the dominating one. The two dots on the plot show the friction requirement for fr = 1, i.e. the static lifting case. In case of fr ≫ 1 the rear robot acts like a ballast, free to roll. Predictably, µB is high and µA is low. In case of fr ≪ 1 the rear robot yanks the front robot and lifts it up; µA is high and µB is low. The dominating friction requirement is low for fr > 1 i.e. for lifting with forward acceleration. The friction curves cross and overall requirements are minimum at fr ≈ 2 in this particular case.

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C. Introduction of Dynamics in Cooperative Lifting Now that we have proved the importance of robot dynamics in reducing the friction requirement, we introduce dynamics into the 2-robot system by cleverly designing the reference inputs. Since the forces on the robots are not controlled directly we have to design reference trajectories for the front robot angle and the rear robot position such that the desired force ratio is achieved. Figures 9(a) and 9(b) show the reference trajectories and the responses. The front robot angle reference is such that the front robot is lifted up in 0.5 sec and stays lifted. The rear robot position reference consists of an initial acceleration which corresponds to force ratio fr = 2, followed by a deceleration necessary for stopping. Figure 9(b) also shows the desired and the actual rear robot acceleration. Note that the deceleration is lower in magnitude than the acceleration because if equal deceleration is applied after acceleration the friction requirement reduction achieved by acceleration (fr > 1) is reversed immediately by deceleration

Fig. 9. Simulation of cooperative lifting with the introduction of dynamics: the rear robot is accelerated as the front robot lifts up. The dotted line in Figure 9(b) shows the acceleration profile for the rear robot. Front and rear robot friction requirements are lower under the dynamic lifting condition.

(fr < 1). The deceleration needs to be applied for a longer time interval to bring the robot to rest. Figure 9(c) shows the friction requirement plot. The important aspects of this plot are as follows. As desired, the friction requirement at the start of the lifting (point a), is lower (0.67) than the static lifting case (1.34). Thus the primary goal of reducing the friction requirement at the start is achieved. We analyze the friction requirement over the entire substage 1a. Immediately after lifting (at b) there is a peak in the friction requirement caused by high rotational acceleration of the front robot resulting in a reduction of the normal force on the rear robot. However, this peak at 0.87 is still much smaller than the static lifting friction requirement. The friction requirement then reduces and is lowest at point c due both to the negative

angular acceleration at this point and to the increase in the front robot angle as discussed in Section III-A with Figure 7. At point d there is a sudden rise in the friction requirement due to the switch from acceleration to deceleration although the friction required is still low. From point e there are two factors affecting the friction requirement; the linear deceleration of the rear robot increases it and at the same time the increase in angle of the front robot reduces it. First there is a gradual increase in the friction requirement till f at which point the deceleration stops and the friction requirement drops down. At point g the angle is at the desired value and the deceleration is zero thus the friction requirement reaches a steady state value which is equal to that in case of static lifting at elevated angle. There are a number of factors, such as the rear robot linear acceleration/deceleration, the front robot angle and angular acceleration etc., that affect the maximum friction requirement during the maneuver and one needs to consider them while designing the angle and position references. One should be able to implement cooperative lift involving dynamics with hardware platform by feeding the above mentioned reference trajectories. In our case the limited bandwidth of the OOPic micro-controller prevented us from implementing dynamics behavior with hardware. IV. C ONCLUSIONS This paper presents the results obtained toward the goal of enhancing mobility of a team of mobile robots by physical cooperation among the robots. Our focus is on the development of the low level system components. Recognizing that small robots need to overcome discrete obstacles, we develop specific analytical maneuvers to negotiate each obstacle where a maneuver is built from a sequence of fundamental cooperative behaviors. The overall goal is to design the mechanisms and the behaviors for mobile robot cooperation such that they can be employed on the existing mobile robots with minimal modifications. We have developed a hardware system with two robots based on our idea of cooperative mobility improvement and guided by the results from the static analysis. We have demonstrated the implementation of basic cooperative behaviors, such as cooperative lift, and by implementing the decentralized control architecture we have demonstrated gap crossing maneuver with the hardware. We have analytically proved that robot dynamics can be used to reduce the friction requirements in the lift behavior and have demonstrated, with simulations, implementation of this idea for the cooperative lifting behavior. We want to generalize the ideas of cooperative mobility improvement through a larger class of behaviors to achieve maneuvers such as step climbing, climbing steep slopes, and negotiating slippery, bumpy, or soft terrain involving multiple robots. However, to go through similar analysis for each and every behavior is cumbersome and as the number of robots increases it is impractical due to multi-fold increase in the complexity of the system. To address this problem we are developing a generalized framework to represent multiple cooperating robots by extending and adopting approaches

developed to represent and analyze robots cooperating to manipulate large objects [12], [5]. The idea is that we can treat the robot to be lifted, in case of cooperative lifting, as an object and other robots in the chains as manipulating it. Acknowledgement: This work was supported, in part, by the US Army Automotive Research Center. R EFERENCES [1] www.packbot.com. 2003. [2] D. Ahlvin and P. Haley. NATO reference mobility model edition II, NRMM II user’s guide. In Technical Report Number GL-92-19, US Army Waterways Experiment Station, December, 1992. [3] H. Asama, M. Sato, N. Goto, H. Kaetsu, A. Matsumoto, and I. Endo. Mutual transportation of cooperative mobile robots using forklift mechanisms. In Proceedings of IEEE International Conference on Robotics and Automation, 1996. [4] M. Bekker. Off-the-road locomotion; research and development in terramechanics. University of Michigan Press, 1960. [5] A. Bicchi. Force distribution in multiple whole-limb manipulation. In Proceedings of IEEE International Conference on Robotics and Automation, 1993. [6] H. Brown, M. V. Veghe, C. Bererton, and P. Khosla. M ILLIBOT trains for enhanced mobility. IEEE/ASME Transactions on Mechatronics, 7:452– 461, 2002. [7] A. Deshpande and J. Luntz. Decentralized control for a team of physically cooperating robots. In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2003. [8] A. Deshpande and J. Luntz. Enhancing mobility of a group of mobile robots via physical co-operation among the robots. In Proceedings of SPIE Conference on Unmanned Ground Vehicle Technology V, 2003. [9] E. F. Fukushima, S. Hirose, and T. Hayashi. Basic manipulation considerations for the articulated body mobile robot. In IEEE/RSJ International Conference on Intelligent Robots and Systems, 1998. [10] S. Hirose and A. Morishima. Design and control of a mobile robot with an articulated body. The International Journal of Robotics Research, 9:99–114, 1990. [11] T. Kane. Dynamics Online: Theory and Implementation with AUTOLEV. OnLine Dynamics, Inc., Sunnyvale, CA, 2000. [12] O. Khatib, K. Yokoi, K. Chang, D. Ruspini, E. Holmberg, and A. Casal. Coordination and decentralized cooperation of multiple mobile manipulators. Journal of Robotic Systems, 13:755–764, 1996. [13] F. Mondada, A. Guignard, M. Bonani, D. Bar, M. Lauria, and D. Floreano. Swarm-bot: From concept to implementation. In Proceedings of the 2003 IEEE/RSJ Intl. Conference on Intelligent Robots and Systems, 2003. [14] S. Munkeby, D. Jones, G. Bugg, and K. Smith. Applications for the matilda robotic platform. In Proceedings of SPIE Conference on Unmanned Ground Vehicle Technology IV, 2002. [15] R. Murphy. Marsupial and shape-shifting robots for urban search and rescue. Intelligent Systems, IEEE, 15:14–19, 2000. [16] L. Parker. ALLIANCE: An architecture for fault tolerant multi-robot cooperation. IEEE Transactions on Robotics and Automation, 14:220– 240, 1998. [17] P. Pirjanian, C. Leger, E. Mumm, B. Kennedy, M. Garrett, H. Aghazarian, S. Farritor, and P. Schenker. Distributed control for a modular, reconfigurable cliff robot. In Proceedings of IEEE International Conference on Robotics and Automation, 2002. [18] S. Rich, C. Wood, and J. Keller. ODV mobility enhancement using active height control. In Proceedings of SPIE Conference on Unmanned Ground Vehicle Technology II, volume 4024, 2000. [19] T. Sugar and V. Kumar. Control of cooperating mobile manipulators. IEEE Transactions on Robotics and Automation, 18:94–103, 2002. [20] C. Weisbin, J. Blitch, J. D. Lavery, E. Krotkov, C. Shoemaker, L. Matthies, and G. Rodriguez. Miniature robots for space and military missions. IEEE Robotics and Automation Magazine, 6:9–18, 1999. [21] M. Yim, Y. Zhang, K. Roufas, D. Duff, and C. Eldershaw. Connecting and disconnecting for chain self-reconfiguration with polybot. IEEE/ASME Transactions on mechatronics, special issue on Information Technology in Mechatronics, 7:442–451, 2003.