Leader-Following Bipartite Formation Control of Multiple Nonholonomic Robot Systems Over Signed Graph

Abstract

Abstract This paper studies the bipartite formation control problem of multiple nonholonomic robot systems over signed graph. To overcome nonholonomic and underactuated control challenges, the hand position output is defined to obtain a linear hand position subsystem. A distributed control law is designed, which uses sliding mode control technology to eliminate the influence of dynamic leader, so that the global index of position formation error converges to an arbitrary small neighborhood of the origin. Then, the zero dynamic equation is computed, and based on it and Lyapunov method, the convergence conditions on controller parameters and on leader’s velocities are derived to guarantee the angle error is bounded and convergent. Finally, a simulation example containing eight robots and one leader is given to demonstrate the effectiveness of the proposed control strategy. In contrast to related results, this paper presents the complete stability analysis and corresponding stability conditions, in addition to the control law and stability of position subsystems.