Signed Distance-Based Moving Formation Control of Double-Integrator Agents

Existing distance-based formation control laws often lead to flip, flex, and reflection ambiguities in a desired formation. To avoid these ambiguities, sign-distance rigidity was introduced. This paper presents two formation control laws based on sign-distance rigidity for double-integrator agents. We propose a combined flocking and signed distance-based formation control law, enabling agents to achieve velocity consensus and converge to the desired formation without ambiguities. Then, we demonstrate that the proposed control law is also applicable to address the formation tracking control problem, where the leader of the multi-agent system moves with a constant velocity. We show that the followers under this control law are able to track the leader’s velocity and achieve the desired formation without ambiguities. Next, we propose a robust adaptive signed distance-based formation control law and show that agents not only achieve the desired formation without ambiguities, but also effectively reject unknown time-varying disturbances without requiring knowledge of their upper bounds. The stability analysis of both control laws is rigorously studied, and simulation results are also provided to validate the effectiveness of the proposed control laws.