Cooperative Control of Multirobot Systems Subject to Control Gain Uncertainty

This article addresses the problem of cooperative control of double-integrator type multirobot systems. Different from some conventional results with the control gain explicitly known, the control gain in this article is subject to uncertainty. Three different collective behaviors are explored, i.e., leaderless consensus, leader-following consensus, and formation control. For leaderless consensus, a sliding variable is constructed, based on which a novel continuous controller is designed such that the sliding surface is reached in finite-time and thus the state agreement of all agents is realized. For leader-following consensus, two different cases are investigated, i.e., the leader with constant velocity and with time-varying velocity. In both cases, sliding-mode based controllers are developed and corresponding stability conditions are established to ensure that the leader state is tracked by all followers. Finally, the theoretical results are applied to achieve formation control of nonholonomic mobile robots and corresponding experimental studies are conducted to demonstrate the effectiveness of the proposed controllers.