Distributed observer-based practical prescribed-time formation tracking control of nonholonomic mobile robots under position and orientation disturbances

This article proposes a novel formation tracking scheme for networked nonholonomic mobile robots (NMRs) subject to external position and orientation disturbances, leveraging prescribed-time stability to guarantee an upper bound for the settling time (UBST). A distributed NMR observer is first designed in Cartesian coordinates to estimate the leader NMR’s state precisely within a user-defined time. Subsequently, a prescribed-time formation control protocol is developed to ensure accurate and timely formation tracking. In contrast to existing formation control approaches for NMRs, the proposed method offers the following key advantages: (1) the UBST of the estimation errors is determined solely by a single tunable parameter, independent of initial conditions; (2) the practical prescribed-time formation tracking problem of NMRs under both position and orientation disturbances is effectively addressed, enabling user-specified convergence time and desired tracking accuracy. Numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed control strategy.