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 Cooperative Payload Transport by Robot Collectives*

Cooperation has been the key to success of most human endeavor and the similar incorporation of cooperation in robotic systems is critical to realize the next generation of systems and applications. Interest in cooperating systems arises when the tasks may be inherently too complex for a single system to accomplish; or when building and using several simple systems can be more flexible, fault-tolerant or cheaper than using a single large system. The recent explosion of communications capabilities has fostered an increased pace towards systems that can take advantage of spatially and temporally distributed physical and informational resources. The ongoing revolution in computing effectiveness and miniaturization of processors/sensors/actuators has accelerated the pace of implementing cooperation in distributed embedded systems, with numerous emergent applications in plant-automation, consumer electronics, automotive and defense arenas.

Despite advances in state-of-the-art and considerable efforts over past few decades, the incorporation of physical cooperation into distributed robotic systems still remains a challenge. The applicability has been restricted to small sized samples due to the complexity - introduced either by the physical systems under consideration or the sheer numbers. This is particularly the case in robots, whose nature as systems requires integration of physical and information infrastructures and system-based thinking.

Our guiding vision is to create an overall framework for payload transport by a fleet of semi-autonomous wheeled mobile modules, combined together flexibly to create a variable-topology composite system, controlled as a collective while possessing the ability to reconfigure to enhance performance. The emphasis on physical collaboration in such physically-coupled collectives imposes more stringent constraints than encountered in many of the concurrent collective robotics efforts that focus on information collaboration for foraging, map building and reconnaissance. The increased flexibility and robustness, derived from replacing a single large material handling device by a fleet of smaller inexpensive systems achieving equal or better overall performance, is very attractive in many unstructured material-handling application environments. The proposed application arenas range from industrial applications, where suitable numbers of such modules can be tasked to manipulate variable-sized payloads in the absence of gantry systems, to extra-terrestrial applications, where individual rover modules sent on separate missions can cooperate to support planetary colonization efforts.

*This project is funded by the National Science Foundation CAREER Award under Grant IIS-0347653.

   
 Students Involved:
- Rajankumar Bhatt, PhD Candidate, University at Buffalo [Graduated]
- Chin Pei Tang, PhD Candidate, University at Buffalo [Graduated]
- Leng-Feng Lee, PhD Candidate, University at Buffalo [Graduated]

- Glenn D. White, M.S., University at Buffalo [Graduated]

- Waseem A. Khan, M. Eng., McGill University [Graduated]

- Michel Abou-Samah, M. Eng., McGill University [Graduated]

 
 
 Research Issue - Kinematic and Dynamic Control Schemes:
Mobile manipulator systems typically possess more degrees of freedom than required for the task and hence effective redundancy resolution methods become important for the control. Particular attention is paid for the development of kinematic control schemes, which take into account both the nonholonomic constraints of the base and the presence of passive joints in the manipulator system.

The composite multi-degree-of-freedom vehicle, formed by placing a common object on the end-effector of two (or more) such mobile manipulator systems, possesses the ability to change its relative configuration as well as accommodate relative positioning errors of the mobile bases. However, closed kinematic loops are also formed constraining the relative motions of the overall system and requiring a careful treatment. We verify that creating an arbitrary composite cooperative system using an arbitrary number of mobile modules retains its mobility. We verify this by ensuring two requirements: (a) arbitrary desired end-effector motions can be accommodated within the feasible motion distributions of the articulation and the mobile bases, and (b) any developed motion-plans can be actively realized using only a set of restricted active motion-distributions.

Two variants of the control schemes developed for mobile manipulators are adapted for the control of the overall collaborating system of two mobile manipulators carrying a common object along a desired trajectory. The performance of both methods - the Leader-Follower approach and the Decentralized Control approach - is evaluated using virtual prototypes, to test various design and control system alternatives in software, prior to actual implementation on the experimental test-bed. Particular attention is paid to evaluate the ability of the overall collaborating system to accommodate, detect and correct for systematic and non-systematic errors in the relative positioning of the mobile platforms.

We also extended the control schemes to take into account of the dynamic (force) of the system. We introduce a dynamic control routine that allows the manipulator's end-effector and the mobile base to be independently controlled. We show a simultaneous position/force control method for the end-effector and show how the characteristic behavior can be designed. We also introduce a tracking/stabilization control routine for the nonholonomic mobile base that allows it to track moving trajectories as well as stationary points.

 Research Issue - Interactions between Cooperative Modules:

 The nature of individual modules and their interactions can effectively affect the overall cooperative system performance. We examine this aspect in the context of cooperative payload transport by robot collectives wherein the physical nature of the interactions between the various modules creates a tight coupling within the system. In this work, we leverage the rich theoretical background of analysis of constrained mechanical systems to provide a systematic framework for formulation and evaluation of system-level performance on the basis of the individual-module characteristics. The composite multi-degree-of-freedom wheeled vehicle, formed by supporting a common payload on the end-effectors of multiple individual mobile manipulator modules, is treated as an in-parallel mechanical system with articulated serial-chain arms. The system-level model, constructed from the twist- and wrench-based models of the attached serial chains, can be systematically analyzed for performance in terms of mobility and disturbance rejection with the effect of selections of different actuation schemes (active, passive or locked).

 Research Issue - Distributed Dynamics:

The simulation of mathematical models of mechanical systems with closed kinematic chains involves the solution to a system of highly coupled differential-algebraic equations. The numerical stiffness of these systems calls for small time steps in order to insure accuracy. Real-time and interactive forward simulations tend to be difficult to achieve for such systems, especially for large multibody systems with multiple links and many kinematic loops. One way to overcome the time constraint is to distribute the load onto several processors.

The modular formulation of mathematical models is attractive because existing models may be assembled to create different topologies, e.g. cooperative robotic systems. Conversely, a given robotic topology may be broken into smaller topologies with simpler dynamics. Moreover, parallel-kinematics machines bear inherent spatial parallelism. This feature is exploited in this research, in which we examine the formulation of such modular and distributed models and evaluate their performance as applied to mechanical systems with closed kinematic chains. Three general undistributed formulation methods are specialized to cope with distribution and modularity and applied to a three-degree-of-freedom planar parallel manipulator to generate distributed dynamics models.

 Research Issue - Optimal and Decentralized Artificial Potential Field Formation Motion Planning:

 The goal is to develop team-optimal kinematic motion plans for all members of a team of Wheeled Mobile Robots (WMRs) moving in formation. The structure provided by the formation paradigm reduces the problem of simultaneous motion planning for the entire team into a staged motion planning problem.  Motion plans are created first for a single WMR from which all other team members subsequently derive their individual motion plans. There is still considerable freedom, however, in terms of selection of relative positions within the formation which affects the performance of the team as a whole. The principal contributions of this thesis are in: modeling such formations of WMRs forming the team; determining the "best formation" to trace desired planar paths; and concurrently projecting the team-optimal motion plans into individual motion plans for all members of the team.

Specifically, this is achieved by coupling kinematic motion planning methods developed for individual WMRs with creation/evaluation of performance measures developed for the overall formation. The preferred kinematic motion planning method used is the Geometric Motion Planning Strategy (GMPS) wherein each WMR is aligned with an induced vector field. This strategy is extended to the formation by considering a preferred "team-fixed frame" and aligning all WMRs within the team with the corresponding induced helicoidal velocity vector-field. Different relative position of each mobile robot within the formation induces different motion plans for individual WMRs. Special emphasis is placed on developing quantitative measures of formation quality, from appropriate metrics on, that permits subsequent optimization of the relative positions of mobile robots within the formation for given tasks. Case studies for three nonholonomic WMRs maneuvering along certain desired paths are presented. For the cases when analytical expressions are possible, the expressions for the optimal configuration of the formation are derived analytically for comparison with the numerical results.

 

In another work, we evaluate the performance of two candidate formulations for distributed motion planning of robot collectives within an Artificial Potential Field (APF) framework. We exploit the parallel between formulation of motion planning for group of robots coupled by constraints and the forward dynamics simulation of constrained multibody systems to develop the candidate approaches. We compare and contrast these approaches on the basis of ease of formulation, distribution of computation and overall computational accuracy. Traditionally penalty formulations have enjoyed a prominent position in motion planning of robot collectives due to their ease of formulation, decentralization and scalability. However, the instabilities introduced in the form of "formulation stiffness" at the algorithm development stage have the potential to hinder the subsequent control. Representative results from the distributed motion planning for a group of 3 point-mass robots moving in formation to a desired target location are used to highlight the differences.

 
 Research Issue - Manipulability Analysis:

A suitable selection of the topology, dimensions, and configuration of the overall system can significantly influence the overall cooperative performance. In this research, we first develop the velocity-level kinematics of the cooperative system, extending methods developed for treatment parallel-kinematic-chains to handle the presence of nonholonomic constraints and varied inclusion of active/passive joints, characteristic of our cooperative system. Then we examine the applicability of a manipulability measure (Isotropy Index), to quantitatively analyze the performances of the cooperative system with different actuation schemes in representative case-studies.

 

 Movies - Motion and Interaction Force Control of a Nonholonomic Mobile Manipulator:
 
  Part I - Simulation.

1. Motion Tracking

- End-effector and base follow separate sinusoids;

- No interaction Force.

- File Size: 1.17MB [Download]

- View it on  

 

2. Motion Tracking

- End-effector and base follow separate square-waves;

- No interaction force.

- File Size: 1.63MB [Download]

- View it on

 

3. Motion Tracking

- End-effector and base follow infeasible trajectories

- End-effector tracking achieved, Base tracking compromised;

- File Size: 1.26MB [Download]

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4. Motion and Force Tracking

- Environment coincident with desired end-effector trajectory;

- Wall at y=0.5m; Desire force: Sinusoid

- File Size: 676KB [Download]

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5. Motion and Force Tracking

- Environment not coincident with desired end-effector trajectory;

- Wall at y=0.5m; Desire force: Constant 10N; Position gain: high; Force gain: Low

- File Size: 684KB [Download] or

 

6. Motion and Force Tracking

- Environment not coincident with desired end-effector trajectory;

- Wall at y=0.5m; Desire force: Constant 10N; Position gain: Low; Force gain: High

- File Size: 662KB [Download] or

7. Motion and Force Tracking

- Environment not coincident with desired end-effector trajectory;

- Wall at y=0.25m; Desire force: Constant = 0N

- File Size: 1.02MB [Download]

- View it on

     
         

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  Part II - Physical System Demos.

- File Size: 8.27MB [Download]

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- File Size: 4.35MB [Download]

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- File Size: 3.51MB [Download]

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- File Size: 3.75MB [Download]

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- File Size: 3.78MB [Download]

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- Design Explanation part 1.

- View it on

- Design Explanation part 2.

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 Movies - Robot Control:

1. Virtual Robot Algorithm

- Performance testing of Virtual Robot Algorithm for tracing prescribed trajectories (using both virtual prototypes and physical prototypes);

- Trajectory: Straight Line

- File Size: 4.72MB [Download]

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2. Virtual Robot Algorithm

- Performance testing of Virtual Robot Algorithm for tracing prescribed trajectories (using both virtual prototypes and physical prototypes);

- Trajectory: Circle

- File Size: 3.49MB [Download]

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3. Virtual Robot Algorithm

- Performance testing of Virtual Robot Algorithm for tracing prescribed trajectories (using both virtual prototypes and physical prototypes);

- Trajectory: Sine wave

- File Size: 4.58MB [Download]

- View it on

4. Single Module Test: Physical Prototype using Odometry

- Single mobile manipulator module using only odometry for self-localization.

- File Size: 3.05MB  [Download]

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5. Single Module Test: Physical Prototype using Articulation Sensing

- Single mobile manipulator module using articulation for self-localization.

- File Size: 2.90MB [Download]

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6. Leader Follower Collaboration: Physical Prototype using Odometry

- The two collaborating mobile manipulators use only odometry for self-localization. The mobile manipulator on the right moves straight ahead even after the wheels of the robot on the left encounter an obstacle and therefore the desired relative configuration cannot be maintained.

- File Size: 4.69MB [Download]

- View it on

7. Leader Follower Collaboration: Physical Prototype using Articulation-based Control

- The two collaborating mobile manipulators use the relative joint information for self-localization permitting the robots to (a) accommodate; (b) detect; and (c) correct errors in the relative configuration due to environmental disturbances.

- File Size: 4.20MB [Download]

- View it on

8. Decentralized Collaboration : Virtual Environment using Articulation-based Control

- Control algorithm for maintaining a desired configuration being tested on  virtual prototypes.  A disturbance is introduced to cause the left wheel of the mobile robot on the left to slip and simulation shows how the other mobile robot compensates.

- File Size: 2.53MB [Download]

- View it on

9. Decentralized Collaboration : Physical Prototype using Odometry

- The two collaborating mobile manipulators use only odometry for self-localization. The mobile manipulator on the right moves straight ahead even after the wheels of the robot on the left encounter an obstacle and therefore the desired relative configuration cannot be maintained.

- File Size: 3.70MB [Download]

- View it on

10. Decentralized Collaboration : Physical Prototype using Articulation-based Control

- The two collaborating mobile manipulators use the relative joint information for self-localization permitting the robots to (a) accommodate; (b) detect; and (c) correct errors in the relative configuration due to environmental disturbances.

- File Size: 3.80MB [Download]

- View it on

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
 Movies - Artificial Potential Field Approach Motion Planning:
 
  Part I - Visualization.

1. Visualization of Navigation Function

- See how the shape of the potential field created using navigation function of a workspace with 4 obstacles changes as the control value k changes.

- File Size: 344KB [download ]

2. Visualization: Analogy of APF approach-ball rolling down a surface.

- Following the negative gradient of a potential surface, a robot (ball) rolls down the surface.

- File Size: 867KB [download]

3. Visualization: 3 Balls Rolling, without formation constraint

- As 3 balls rolling down a surface without formation constraint, they collide into each other.

- File Size: 897KB [download]

4. Visualization: 3 Balls Rolling, with formation constraint

- With formation constraint, three ball maintained a formation while rolling down the surface.

- FileSize: 1.76MB [download]

5. Visualization: Simulated real workspace-Motion planning of single robot.
- Show motion plan of single robot using potential field method.
- FileSize: 1.49MB [download]

 
   Part II - Single Robot Module Simulation.

1. Single Robot, One Obstacle, FIRAS Function.
- Motion Planning of single robot in workspace with one obstacle, potential created using FIRAS Function.
- FileSize: 4.32MB [download].

2. Single Robot, two obstacles, Ge's new potential.
- Motion Planning of single robot in workspace with two obstacle, potential created using FIRAS Function.

- FileSize: 7.77MB [download]
 

3. Single Robot, four obstacles, Navigation Function.
- Motion Planning of single robot in workspace with two obstacle, potential created using Navigation Function.

- FileSize: 1.46MB [download]
 

4. Single Wheeled Mobile Robot, four obstacles, Navigation Function.
- Motion Planning of single Wheeled Mobile Robot in workspace with four obstacles, potential created using navigation function.

- FileSize: 2.89MB [download]
 

5. Three Robots, No Obstacle, No formation constraint.
- Simulation of three robots in a quadratic potential field without formation constraint.

- FileSize: 2.99MB [download]

6. Three Robots, One Obstacle, No formation constraint.
- Simulation of three robots formation constraint in a workspace with one obstacle, potential field created using navigation function.

- FileSize: 6.36MB [download]

   
   Part III - Robot Collectives Simulation.

1. Case Study 1: 3 Robot in quadratic field, with formation constraint.
- Motion planning solved using Method I: Direct Lagrange Multiplier Elimination Method.

- File Size: 7.5MB [download]

2. Case Study 2: 3 Robot with one obstacle, with formation constraint.
- Motion planning solved using Method II: Penalty Based Formulation.

- File Size: 3.8MB [download]

3. Case Study 3: 3 Robot in quadratic field, with formation expansion.
- Motion Planning solved using Method III: Constrained Manifold Projection Method.

- FileSize: 7.5MB [download]

4. Case Study 4: 3 Robot in quadratic field, with formation shape change.
- Motion Planning solved using Method II: Penalty Based Formulation.

- FileSize: 7.5MB [download]

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Related Publications - Journal Articles:
[07] M. Abou-Samah, C. P. Tang, R. M. Bhatt, and V. Krovi, "Kinematically Compatible Framework for Cooperative Payload Transport by Nonholonomic Mobile Manipulators", Autonomous Robots, September 2006. [PDF]
[06] C. P. Tang, and V. Krovi, "Manipulability-Based Configuration Evaluation of Cooperative Payload Transport by Mobile Manipulator Collectives", Robotica, August 2006. [PDF]
[05] W. A. Khan, C. P. Tang, and V. Krovi, "Modular and Distributed Forward Dynamic Simulation of Constrained Mechanical Systems - A Comparative Study", Mechanism and Machine Theory, July 2006. [PDF]
[04] R. M. Bhatt, and V. Krovi, "DynaFlexPro for Maple - A Review," IEEE Control Systems Magazine. (to appear) [PDF]
[03] C. P. Tang, R. M. Bhatt, M. Abou-Samah, and V. Krovi, "Screw-Theoretic Analysis Framework for Payload Transport by Mobile Manipulator Collectives", IEEE/ASME Transactions on Mechatronics, Vol. 11, No. 2, pp. 169-178, April 2006. [PDF]
[02] W. A. Khan, V. Krovi, S. K. Saha, and J. Angeles, "Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator", ASME Journal of Dynamic Systems Measurement and Control, Vol. 127, No. 4, pp. 529-536, December 2005. [PDF]
[01] W. A. Khan, V. Krovi, S. K. Saha, and J. Angeles, "Modular and Recursive Kinematics and Dynamics for Parallel Manipulators", Multibody Systems Dynamics, Springer Netherlands, Vol. 14, No. 3-4, pp. 419-455, November 2005. [PDF]
     
 Related Publications - Conference Proceedings:
[10] Lee, L-F., and Krovi, V., “A Standardized Testing-Ground for Artificial Potential-Field based Motion Planning for Robot Collectives,” Proceedings of the 2006 Performance Metrics for Intelligent Systems Workshop, Gaithersburg, MD, August 21 -23, 2006. [PDF]
[09] R. Bhatt, C. P. Tang, M. Abou-Samah, and V. Krovi, "A Screw-Theoretic Analysis Framework for Payload Manipulation by Mobile Manipulator Collectives," IMECE2005-81525, Proceedings of 2005 ASME International Mechanical Engineering Congress & Exposition, Orlando, Florida, USA, November 5-11, 2005. [PDF]
[08] Lee, L.-F., Bhatt, R. M., and Krovi, V., "Comparison of Alternate Methods for Distributed Motion Planning of Robot Collectives within a Potential-Field Framework", Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, April 18 - 22, 2005. [PDF]
[07] Tang, C. P., and Krovi, V., "Manipulability-Based Configuration Evaluation of Cooperative Payload Transport by Mobile Robot Collectives," Proceedings of the 2004 ASME Design Engineering Technical Conferences and Computer and Information in Engineering Conference, Salt Lake City Utah, September 28 - October 2, 2004. [PDF]
[06] Bhatt, R. M., Tang, C. P., and Krovi, V., "Geometric Motion Planning and Formation Optimization for a Fleet of Nonholonomic Wheeled Mobile Robots", Proceedings of the 2004 IEEE International Conference on Robotics and Automation, New Orleans, Louisiana, April 26-May 1, 2004. [PDF]
[05] Tang, C. P., Bhatt, R. M., and Krovi, V., "Decentralized Kinematic Control of Payload Transport by a System of Mobile Manipulators", Proceedings of the 2004 IEEE International Conference on Robotics and Automation, New Orleans, Louisiana, April 26-May 1, 2004. [PDF]
[04] Khan, W. A., Krovi, V., Saha, S.K., and Angeles, J., ˇ°Recursive Kinematics and Inverse Dynamics for Parallel Manipulatorsˇ±, IMECE2003-42868, Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition, Washington D.C., November 15 - 21, 2003. [PDF]
[03] Abou-Samah M. and Krovi, V., "Decentralized Kinematic Control Of Cooperating System Of Mobile Manipulators", IMECE2002-32691, Proceedings of the 2001 ASME International Mechanical Engineering Congress and Exposition, New Orleans, November 17 - 22, 2002. [PDF]
[02] Khan, W. A., and V. Krovi, V.,  "Comparison of Two Alternate Methods for Distributed Forward Dynamic Simulation of a Four-Bar Linkage," Proceedings of the NSF Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Eds. C. M. Gosselin and I. Ebert-Uphoff, Quebec City, Canada, October 3¨C4, 2002. [PDF]
[01] Abou-Samah M. and Krovi, V., "Optimal Configuration Selection For A Cooperating System Of Mobile Manipulators," DETC2002/MECH-34358, Proceedings of the 2001 ASME Design Engineering Technical Conferences, Montreal, Quebec, Canada, September 29 - October 2, 2002. [PDF]
     
 Related Publications - Theses:
[06] White, G. D., Simultaneous Motion and Interaction Force Control of a Nonholonomic Mobile Manipulator, M.S. Thesis, Dept. of Mechanical & Aerospace Engineering, SUNY at Buffalo, Jun. 2006. [PDF][PPS]
[05] Lee, L.-F., Decentralized Motion Planning within an Artificial Potential Framework (APF) for Cooperative Payload Transport by Multi-Robot Collectives, M.S. Thesis, Dept. of Mechanical & Aerospace Engineer, SUNY at Buffalo, Feb. 2005. [PDF][PPS]
[04] Tang, C. P., Manipulability-Based Analysis for Payload Transport by Robot Collectives, M.S. Thesis, Department of Mechanical & Aerospace Engineering, SUNY at Buffalo, Jun 2004. [PDF][PPS]
[03] Bhatt, R. M., Formation Motion Planning for Payload Transport by Modular Wheeled Mobile Manipulators, M.S. Thesis, Department of Mechanical & Aerospace Engineering, SUNY at Buffalo, Feb 2004. [PDF][PPS]
[02] Khan, W. A., Distributed Dynamics of Systems with Closed Kinematic Chains, M.S. Thesis, Mechanical Engineering, McGill University, November 2002. [PDF][PPS]
[01] Abou-Samah M., A Kinematically Compatible Framework for Collaboration of Multiple Non-holonomic Wheeled Mobile Robots, M.S. Thesis, Mechanical Engineering, McGill University, December 2001 [PDF][PPS]

 

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Last Updated: April 22, 2012