Real-Time Local Greedy Search for Multiaxis Globally Time-Optimal Trajectory

Time-optimal trajectory planning aims to minimize the traversal time of arbitrary geometric paths. The demand for real-time planning widely exists in robotics, numerical control manufacturing, and autonomous vehicle applications. Existing trajectory planning methods either compromise on time optimality to improve computational efficiency or suffer from at least linear time complexity, preventing the planning of long trajectories in real time. Motivated by these challenges, this article proposes a novel set invariant trajectory planning (SITP) method to address the problem of real-time time-optimal planning for continuous multiaxis trajectories under complete second-order kinodynamic constraints. First, a backup control strategy is synthesized to construct an implicit control invariant set (CIS). This set is designed so that a feasible control input always exists to keep the system within the defined kinodynamic bounds. Then, utilizing the principles of bang-bang control theory, the optimal control is sought within the CIS. A local greedy linear programming method is proposed to calculate the time-optimal trajectory at each control cycle. The proposed method is computationally efficient for even 1-kHz real-time applications and the planned results maintain strict global time optimality, which makes it promising in real-time planning scenarios of various automatic applications.