MPC (Model predictive control)-based motion planning and trajectory generation are essential in applications such as unmanned aerial vehicles, robotic manipulators, and rocket control. However, the real-time implementation of such optimization-based planning faces significant challenges arising from non-convex problem structures and inherent limitations of nonlinear programming -- notably the difficulty in guaranteeing solution quality and the unpredictability of computation time. To improve robustness and computational efficiency, this paper introduces a two-layer motion planning algorithm for intelligent ground vehicles based on convex optimization. The proposed algorithm iteratively constructs discrete optimal control subproblems with small, fixed terminal times, referred to as planning cycles. Each planning cycle is further solved within progressively constructed convex sets generated by utilizing customized search algorithms. The entire solution to the original problem is obtained by incrementally composing the solutions of these subproblems. The proposed algorithm demonstrates enhanced reliability and significantly reduced computation time. We support our approach with theoretical analysis under practical assumptions and numerical experiments. Comparative results with standard sequential convex programming (SCP) methods demonstrate the superiority of our method -- include a significant improved computational speed under dynamic environments while maintain a near optimal final time.

翻译：基于模型预测控制（MPC）的运动规划与轨迹生成在无人机、机器人操作臂及火箭控制等应用中至关重要。然而，此类基于优化的规划在实时实现中面临非凸问题结构及非线性规划固有局限性的重大挑战——尤其是难以保证解的质量以及计算时间的不确定性。为提高鲁棒性与计算效率，本文提出一种基于凸优化的智能地面车辆双层运动规划算法。该算法迭代构建具有小而固定终端时间的离散最优控制子问题，称为规划周期。每个规划周期进一步在利用定制搜索算法生成的渐进构建凸集内求解。原问题的完整解通过逐步组合这些子问题的解获得。所提算法展现出更高的可靠性及显著减少的计算时间。我们在实际假设下通过理论分析与数值实验验证了该方法的有效性。与标准序列凸规划（SCP）方法的对比结果表明，本方法在动态环境下具有显著提升的计算速度，同时保持接近最优的最终时间，体现了其优越性。