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

Abstract

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.