Time-optimal trajectory generation with multi-level continuous kinodynamics constraints

Time-optimal trajectory generation (TOTG) is critical in robotics applications to minimize travel time and increase robot task efficiency. To ensure the trajectory is feasible and executable by the robot, it is important to constrain the trajectory kinodynamics subject to the robot actuator limits. A typical actuator has multiple limits, 1) peak limit, and 2) multi-level continuous limits with different operation time windows. The peak limit bounds the instantaneous kinodynamics (IKD), whereas the continuous limits bound the system continuous kinodynamics (CKD). Existing works only constrain IKD, usually by the actuator peak limit, to achieve time optimality. However, a joint capable of operating at its peak limit momentarily will overheat and damage robot life if the motion continues. Alternatively, users can constrain the IKD with a reduced peak limit to avoid violating continuous limits. However, the reduced peak limit would inevitably sacrifice task efficiency. To address the challenge, this paper studies TOTG with both IKD and CKD, and proposes TOTG-C. It formulates the TOTG as a nonlinear programming (NLP). In particular, it proposes a novel formulation to encode the multi-level CKD constraints efficiently. To the best of our knowledge, TOTG-C is the first work that explicitly considers multi-level CKD constraints. We demonstrate the effectiveness and robustness of the proposed TOTG-C both in simulation and real robot experiments. Index Terms—Time-Optimal Trajectory Generation, Continuous kinodynamics Constraints, Constrained Nonlinear Programming.