Cooperative Control of Multi-robot Nonholonomic Systems with Dynamics Uncertainties and Control Time-Delays

Abstract

In practical applications,multi-robot systems may have to simultaneously deal with several tasks: collision-free maneuvers in dynamic environments; tracking certain desired trajectories; forming suitable patterns or geometrical shapes, and/or varying the pattern when necessary. These important issues are addressed in this paper. First a dynamic model for a robot prototype is presented. By appropriate coordinate transformation, this class of time-varying nonlinear systems, subject to modeling uncertainties and input time-delays, is further linearized into classical singularly perturbed systems. A robust compensation tracking controller is then developed and justified based on Lyapunov stability theorem. The compensated system effectively suppresses the perturbation effects to guarantee robust stability and tracking errors exponentially convergent to a bounded residual set. To achieve these typical complex formation missions, a previously developed two-layer hierarchical architecture for multi-robot nonholonomic systems is employed. In the upper layer, task specifications are assigned along with the desired behaviors in the task space and a null-space method is then utilized to integrate and prioritize these tasks and generate reference trajectories. In the lower layer, the local robust control scheme guarantees asymptotical tracking of the desired trajectories. A realistic case study illustrates the effectiveness of the modeling and robust control design.