Omnidirectional Vision-based Distributed Formation Control

In [1-3], we consider the problem of distributed formation control for nonholonomic mobile robots equipped with central-panoramic cameras. Our approach is to translate the formation control problem from the configuration space into separate visual servoing tasks in the image plane. We present an algorithm for infinitesimal multi-body motion estimation and segmentation from multiple central panoramic views. We derive a rank constraint on the optical flows across many frames, from which one can estimate the position and velocities of each leader in the paracatadioptric plane of the follower. We design a tracking controller for each mobile robot and show that there exist degenerate formation configurations due to the nonholonomy of the robot dynamics and the nonlinearity of the central-panoramic projection model. The control law naturally incorporates collision avoidance by using a navigation function that exploits the geometry of central-panoramic cameras. We present experimental results on multi-body motion estimation, segmentation of a real image sequence, and simulation results on vision-based control for many formation configurations.

Figure 1: A sample motion segmentation of mobile robots based on omni-directional vision.

Figure 2: Three mobile robots switching from a triangle to a line formation while avoiding collision.

[1]

R. Vidal, O. Shakernia, and S. Sastry, "Omni-Directional Vision-based Distributed Formation Control of Nonholonomic Mobile Robots," IEEE Int. Conf. Robotics and Automation, 2003 (submitted).

[2]

R. Vidal, O. Shakernia, and S. Sastry, "Distributed Formation Control with Omnidirectional Vision Based Motion Segmentation and Visual Servoing," IEEE Magazine on Panoramic Robotics, 2002 (submitted).

[3]

R. Vidal, O. Shakernia, and S. Sastry, "Omnidirectional Vision-based Formation Control," Allerton Conf. Communication, Control, and Computing, Monticello, IL, October 2002.