Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

Abstract

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties.