Pose Optimization of Task-Redundant Robots in Second-Order Rest-to-Rest Motion with Cascaded Dynamic Programming and Nullspace Projection

An optimal trajectory for the redundant coordinate for robots in tasks with rotational symmetry such as machining has to be found to ensure good performance and overall feasibility. Due to high nonlinearity of performance criteria especially for parallel robots a sole local optimization may lead to infeasible solutions for large-scale motion. A pointing task consisting of multiple rest-to-rest trajectories with given dense sample times is regarded as given. Constraints regarding system limits on position, velocity and acceleration have to be met. The proposed algorithm combines nullspace projection for local optimization between the rest poses with dynamic programming at the rest poses in a cascaded scheme to optimize the rotation around the tool axis. Applications to other types of redundancy are also possible. The proposed local/global optimization scheme only needs wide discretization of the redundant coordinate and therefore has acceptable computational performance for offline optimization of robot motion. It is able to find feasible and near-optimal trajectories for a six-degree-of-freedom (DoF) parallel robot in several exemplary five-DoF tractories with many constraints.