Formation control of nonholonomic mobile robots with omnidirectional visual servoing and motion segmentation

We consider the problem of having a team of nonholonomic mobile robots follow a desired leader-follower formation using omnidirectional vision. By specifying the desired formation in the image plane, we translate the control problem into a separate visual servoing task for each follower. We use a rank constraint on the omnidirectional optical flows across multiple frames to estimate the position and velocities of the leaders in the image plane of each follower. We show that the direct feedback-linearization of the leader-follower dynamics suffers from degenerate configurations due to the nonholonomic constraints of the robots and the nonlinearity of the omnidirectional projection model. We therefore design a nonlinear tracking controller that avoids such degenerate configurations, while preserving the formation input-to-state stability. Our control law naturally incorporates collision avoidance by exploiting the geometry of omnidirectional cameras. We present simulations and experiments evaluating our omnidirectional vision-based formation control scheme.

[1]  Peter J Seiler,et al.  Mesh stability of unmanned aerial vehicle clusters , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[2]  J. Hedrick,et al.  String stability of interconnected systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[3]  Vijay Kumar,et al.  The effect of feedback and feedforward on formation ISS , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[4]  Vijay Kumar,et al.  A Framework for Vision Based Formation Control , 2002 .

[5]  J. A. Fax,et al.  Graph Laplacians and Stabilization of Vehicle Formations , 2002 .

[6]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[7]  S. Shankar Sastry,et al.  Multibody motion estimation and segmentation from multiple central panoramic views , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[8]  Xiaoming Hu,et al.  Formation constrained multi-agent control , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[9]  Kostas Daniilidis,et al.  A Unifying Theory for Central Panoramic Systems and Practical Applications , 2000, ECCV.

[10]  Camillo J. Taylor,et al.  A vision-based formation control framework , 2002, IEEE Trans. Robotics Autom..

[11]  George J. Pappas,et al.  Feasible formations of multi-agent systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[12]  G. Inalhan,et al.  Decentralized overlapping control of a formation of unmanned aerial vehicles , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Daniel E. Koditschek,et al.  Visual servoing via navigation functions , 2002, IEEE Trans. Robotics Autom..