Collision-free predefined-time formation control for nonholonomic mobile robots along parametric curves

This paper studies the problem of formation control for nonholonomic mobile robots along parametric curves with collision/obstacle avoidance, which commonly appears in practical tasks such as environment monitoring. First, a parametric representation of the target curve is obtained through curve fitting, with its coefficients characterizing the curve’s geometry shape. Then, based on the curve coefficients, predefined-time (PT) stability and control barrier functions, a collision-free guidance module is designed, which generates safe reference signals to achieve the PT formation convergence and simultaneously ensure collision/obstacle avoidance. Then, a novel tracking controller equipped by a barrier function is constructed to keep each robot’s tracking error within a preset boundary. Finally, the effectiveness of the proposed scheme is illustrated by numerical simulations. Compared with the existing results, which lack physical safety considerations, the scheme ensures that robots not only form the curve in predefined time but also avoid collisions. Besides, the designed guidance module offers a plug-and-play function for robot products without altering their inter-loop control structures.