A direct variational method for planning monotonically optimal paths for redundant manipulators in constrained workspaces

This paper proposes a path planner for serial manipulators with large number of degrees of freedom, working in cluttered workspaces. Based on the variational principles, this approach involves formulating the path planning problem as constrained minimization of a functional representing the total joint movement over the complete path. We use modified boundary conditions at both ends of the trajectory to find more suitable start and end configurations. The concept of monotonic optimality is introduced in order to optimize the manipulator paths between the resulting end configurations. For obstacle avoidance, volume and proximity based penalizing schemes are developed and used. The presented planner uses a global approach to search for feasible paths and at the same time involves no pre-processing task. A variety of test cases have been presented to establish the efficacy of the presented scheme in providing good quality paths. The extent of advantage accruing out of the measures of free end-configurations and monotonic optimality are also analyzed quantitatively.