Distributed fixed-time formation tracking of multi-robot systems with nonholonomic constraints

This paper addresses the fixed-time formation tracking problem of multi-robot systems with nonholonomic constraints. A new type of distributed nonlinear controller for each robot is designed. Some corresponding sufficient conditions are derived by using algebraic graph theory, matrix analysis and fixed-time stability theory. In addition, an upper bound of the settling time for the multi-robot systems is also explicitly given. It is shown that the obtained upper bound of settling time is regardless of initial errors of systems, which implies that it can facilitate the pre-design of the convergence time off-line. Numerical example is provided to illustrate the effectiveness of the present theoretical results.