Distributed Trajectory Optimization for Time-Optimal Reconfiguration of Multi-Agent Formation

This paper presents a distributed algorithm for the minimum-time reconfiguration of multi-agent formation. The reconfiguration problem is formulated as an optimal control problem where the manifold of terminal states includes parameters to be optimized. The proposed algorithm lays its foundation on the control vector parametrization (CVP) method, the sequential convex programming (SCP) method, and the distributed alternating direction method of multipliers (D-ADMM). By using the CVP method, the original optimal control problem is firstly transcribed into a nonlinear programming problem, which can then be solved by the SCP method. To achieve the distributed implementation the SCP method is integrated with D-ADMM. The effectiveness of the algorithm is demonstrated in a case study of the time-optimal formation reconfiguration of four satellites. A comparison with the global optimization technique shows that the algorithm outputs the global minimum for the studied case.