Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control

Abstract

This paper considers optimal control of a system of nonholonomic robots. Control effort and deviation from a desired formation are minimized for the system of robots traveling between specified initial and final configurations, with a bifurcation parameter which is the relative weighting assigned to the control effort versus the formation constraint. The main contribution of this paper is an extension of our previous work which considered the nature of multiple solutions to a holonomic optimal control problem for a distributed system. An important aspect of the previous work was that symmetries in the holonomic system guaranteed symmetries in the bifurcations of the solutions to the optimization problem. In the current work, a system of relatively simple nonholonomic robots break the symmetry in the system, which results in symmetry-breaking in the bifurcations.