Distributed Lyapunov-based model predictive control for collision avoidance of multi-agent formation

This study addresses the problem of distributed formation control for a multi-agent system with collision avoidance between agents and with obstacles, in the presence of various constraints. The authors proposed solution incorporates a control Lyapunov function (CLF) into a distributed model predictive control scheme, which inherits the strong stability property of the CLF and optimises the formation performance. For each agent, the formation tracking objective is formulated through the CLF, while the collision avoidance objective being explicitly considered as constraints. A relaxation parameter is introduced into the CLF condition to make the trade-off between the two conflicting objectives. The terminal constraint is constructed based on the concept of velocity obstacle, which characterises the set of states that lead to collisions. They show that the terminal constraint together with the relaxed CLF-based constraint guarantees the recursive feasibility and stability of the multi-agent system for almost any prediction horizon. Furthermore, the theoretical effectiveness and advantageous implementation properties are demonstrated through simulation for multi-agent formation control with several obstacles.