An adaptive mesh dynamic programming algorithm for robotic manipulator trajectory planning

An adaptive mesh initialisation algorithm is proposed to compute a collision free trajectory of a robotic manipulator. To this end, we model the problem as a discrete optimal control problem in the joint space. Constraints are imposed on the joint positions and velocities. Moreover, nonlinear geometric collision avoidance constraints account for a detailed obstacle and robot geometry, imposing additional intricacies on the problem. The problem is solved numerically using a backward Semi-Lagrangian dynamic programming method in conjunction with a penalization of the nonconvex collision constraints, as proposed in [1]. Further, to adhere to the curse of dimensions an iterative algorithm is proposed to locally refine the initial state space discretisation. The main contribution of this paper is the introduction of a refinement criterion, which is independent of the value function and solely based on a signed distance function estimated from the collision geometry. Optimal trajectories resulting from adaptive and equidistant grid structures are compared and evaluated for the problem of a robotic manipulator operating in a dynamic environment.