A spatio-temporal reference trajectory planner approach to collision-free continuum deformation coordination

This paper proposes a spatio-temporal reference trajectory planner approach to safely plan continuum deformation coordination of a multi-agent system (MAS) in an obstacle-laden environment. We formulate a desired n-D continuum deformation as a leader–follower problem guided by n+1 leaders and followed by the remaining follower agents either through direct communication with leaders or communication with neighboring agents. To plan a safe continuum deformation coordination, we first provide sufficient conditions for inter-agent and obstacle collision avoidance. Then, we spatially optimize the continuum deformation coordination using the A* search to determine leaders’ desired waypoints in an obstacle-laden environment. Leaders’ desired waypoints are connected through C¹ continuous paths that are assigned by the spline curve fitting method. The desired trajectories of the leaders are then determined by planning a piece-wise constant reference input such that travel time is minimized and safety of the continuum deformation coordination is ensured.