Controlling an uncertain mobile robot with prescribed performance

Uncertain mobile robot (UMR) has been playing an increasingly important role in modern industry. Implementing motion control of UMR is a critical and challenging problem due to the uncertainty. This study investigates the tracking control problem of UMR with prescribed transient and steady-state performance, in which uncertainty is (possibly fast) time-varying, bounded but with unknown bounds, and includes mismatched portions, i.e., not all the uncertainties are within the range space of the input matrix. The control is designed via constraint-following, i.e., formulating the tracking goals as servo constraints. Therefore, the system performance is indexed by the constraint-following error and the desired transient and steady state performance specifications are imposed on the constraint-following error. By a state transformation technique incorporating the prescribed performance, we are able to design a class of adaptive robust controls rendering the system motion to approximately follow the servo constraints with the prescribed performance satisfied, in which an adaptive law is constructed to emulate the unknown uncertainty bounds. The control is approximation-free and does not assume mismatched uncertainties to be sufficiently small, thus can tolerate large mismatched uncertainties. The effectiveness of the proposed approach is illustrated by rigorous proof and the simulation results.