Self-Triggered Distributed Model Predictive Control via Path Parameter Synchronization

This paper investigates the formation tracking problem for multiple mobile robots via self-triggered distributed model predictive control (DMPC) strategy and path-parameter communication manner. To ensure the robots follow the desired formation structure along the predefined paths, we establish appropriate tracking error models that form a multi-agent system. At triggered instants, each agent exchanges a sequence of path parameters representing the robot's position, resolves the optimal control problem (OCP) and subsequently determines the open-loop phase. Different from existing coordination methodology, the proposed scheme exhibits two essential merits in environments where resources are particularly limited: (1) The tracking task of robots is achieved by designing an appropriate OCP under the DMPC scheme, and the formation task of robots is achieved through the synchronization of one-dimensional path parameters instead of the multi-dimensional state information, which demands less communication load; (2) The incorporation of the self-triggered scheduler acquires the desired control performance with less calculation time, thereby relieving the computational and communication costs. Sufficient conditions are proposed to guarantee the recursive feasibility of the OCP and the closed-loop stability. Simulation results illustrate the validity of the proposed control algorithm.