Spline-based energy-optimal trajectory planning for functionally redundant robots

The design of optimal trajectories for automatic machines is an effective tool to reduce their energy consumption. This work investigates the topic by proposing a method tailored for functionally redundant robots, i.e., the ones which have more degrees of freedom than the ones required by the task. The test case under consideration is a serial 3R robot used for a positioning task in a planar space, described by a sequence of via-points in the operative space. Speed limits and smoothness constraints, in terms of speed and jerk limitations are taken into account to ensure trajectory feasibility. The method finds the optimal time intervals between two consecutive via-points, as well as the optimal robot configurations at the via-points (i.e., the optimal solution of the inverse kinematic problem among the infinite ones). The results show the capability of the method in producing energy-efficient motion profile, and the improved results over the optimization of just the time intervals.