Fixed-Time Rigidity-Based Formation Maneuvering for Nonholonomic Multirobot Systems With Prescribed Performance

This article presents rigidity-based formation maneuvering for a group of nonholonomic mobile robots subject to limited sensing capability, where the performance bounds are introduced to constrain the distance and angle errors. The time-varying and asymmetric performance constraints can prescribe the transient and steady-state performance of the closed-loop systems, which further specify collision avoidance and connectivity maintenance among neighboring robots and avoid the controller singularity issue. To satisfy the constraint requirements and fixed-time convergence, universal barrier Lyapunov functions are incorporated with control design such that angle errors are fixed-time stable and distance errors can converge to a small neighborhood around zero in fixed time. Under the proposed control protocol, all robots can track the desired time-varying velocity while generating and maintaining the predefined formation defined by a minimally and infinitesimally rigid graph. Simulation and experiment studies are carried out to illustrate the effectiveness of the proposed control protocol.