This paper proposes a two-stage approach to formulate the time-optimal point-to-point motion planning problem, involving a first stage with a fixed time grid and a second stage with a variable time grid. The proposed approach brings benefits through its straightforward optimal control problem formulation with a fixed and low number of control steps for manageable computational complexity and the avoidance of interpolation errors associated with time scaling, especially when aiming to reach a distant goal. Additionally, an asynchronous nonlinear model predictive control (NMPC) update scheme is integrated with this two-stage approach to address delayed and fluctuating computation times, facilitating online replanning. The effectiveness of the proposed two-stage approach and NMPC implementation is demonstrated through numerical examples centered on autonomous navigation with collision avoidance.

翻译：本文提出了一种两阶段方法，用于构建时间最优的点到点运动规划问题，其中第一阶段采用固定时间网格，第二阶段采用可变时间网格。该方法通过使用固定且较少的控制步数来简化最优控制问题公式，从而降低计算复杂度，并避免了与时间缩放相关的插值误差，特别是在需要到达远距离目标时。此外，该方法还集成了异步非线性模型预测控制（NMPC）更新方案，以应对延迟和波动的计算时间，从而促进在线重规划。通过以避障自主导航为中心的数值示例，验证了所提出的两阶段方法和NMPC实现的有效性。