Input-constrained formation control of differential-drive mobile robots: geometric analysis and optimisation

This study considers the formation control of differential-drive mobile robots subject to diamond-shaped input constraints. A basic controller form in terms of two feedback functions is proposed in a leader-follower setup. The existence of suitable feedback functions, guaranteeing the achievement of desired formation and the satisfaction of input constraints, is confirmed by a sufficient condition derived from geometric analysis. The geometric analysis also helps selections of feedback functions. Optimal feedback functions are designed to fully exploit the maneuverability of mobile robots. In addition, the performance assignment, which confines the velocities of the follower robot in a specified subset of diamond-shaped input domain to avoid slippage and reduce mechanical wear, is discussed. Simulation results are included to verify the effectiveness of the proposed controllers.