Time-Optimal Velocity Planning of Single-Axis Multipoint Motion with Global Dynamic Programming Algorithm

To solve the time-optimal problem of velocity planning, various optimization-based methods were proposed in the literature, but these existing methods typically have limitations on completeness and real-time performance. For the scenario of single-axis multipoint (SAMP) motion, this article proposes a global dynamic programming algorithm with local greedy strategies to solve the time-optimal velocity planning problem, which is important for the multiaxis synchronous velocity planning problem. The proposed method, which is called SAMP algorithm, transfers the problem into the splicing problem of interval endpoints and acceleration. Then, based on the assumptions of continuity and monotonicity of piecewise polynomial functions, it derives the optimal motion mapping in these different intervals. Finally, the SAMP algorithm obtains the global time-optimal solution by employing the global dynamic programming with a backtracking algorithm. Simulation and experiments demonstrate that the SAMP algorithm not only has time optimization but also shows good numerical efficiency.