Motion generation for formations of robots: A geometric approach

Develops a method for generating smooth trajectories for mobile robots in formation. The problem of trajectory generation is cast in terms of designing optimal curves on the Euclidean group, SE(3). Specifically, the method generates the trajectory that minimizes the total energy associated with the translations and rotations of the robots, while maintaining a rigid formation. When the mobile robots are nonholonomic, trajectories that allow rigid formations to be maintained must satisfy appropriate constraints. An efficient non-iterative algorithm to obtain near-optimal trajectories is described. Finally, the approach is illustrated with examples involving formations of aircrafts.

[1]  Vijay Kumar,et al.  Hybrid control of formations of robots , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[2]  Kar-Han Tan,et al.  High Precision Formation Control of Mobile Robots Using Virtual Structures , 1997, Auton. Robots.

[3]  Vijay Kumar,et al.  On the generation of smooth three-dimensional rigid body motions , 1998, IEEE Trans. Robotics Autom..

[4]  Kar-Han Tan,et al.  Virtual structures for high-precision cooperative mobile robotic control , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[5]  Wolfram Burgard,et al.  Collaborative multi-robot exploration , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[6]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[7]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[8]  Wei Kang,et al.  Formation control of autonomous agents in 3D workspace , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[9]  Vijay R. Kumar,et al.  New metrics for rigid body motion interpolation , 2000 .

[10]  Jun Ota,et al.  Motion planning for cooperative transportation of a large object by multiple mobile robots in a 3D environment , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[11]  P. Tabuada,et al.  Position Tracking for Underactuated Rigid Bodies on SE(3) , 2001 .

[12]  Vijay Kumar,et al.  An Efficient, Geometric Approach to Rigid Body Motion Interpolation , 2000 .

[13]  Wolfram Burgard,et al.  A Probabilistic Approach to Collaborative Multi-Robot Localization , 2000, Auton. Robots.

[14]  Georges Bastin,et al.  Control of Nonholonomic Wheeled Mobile Robots by State Feedback Linearization , 1995, Int. J. Robotics Res..

[15]  Francesco Martinelli,et al.  Robot group formations: a dynamic programming approach for a shortest path computation , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[16]  William H. Press,et al.  Numerical recipes in C , 2002 .

[17]  R. Beard,et al.  Constellation Templates: An Approach to Autonomous Formation Flying , 1998 .

[18]  Vijay Kumar,et al.  Controlling formations of multiple mobile robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).