Model Predictive Control (MPC)-based trajectory planning has been widely used in robotics, and incorporating Control Barrier Function (CBF) constraints into MPC can greatly improve its obstacle avoidance efficiency. Unfortunately, traditional optimizers are resource-consuming and slow to solve such non-convex constrained optimization problems (COPs) while learning-based methods struggle to satisfy the non-convex constraints. In this paper, we propose SOMTP algorithm, a self-supervised learning-based optimizer for CBF-MPC trajectory planning. Specifically, first, SOMTP employs problem transcription to satisfy most of the constraints. Then the differentiable SLPG correction is proposed to move the solution closer to the safe set and is then converted as the guide policy in the following training process. After that, inspired by the Augmented Lagrangian Method (ALM), our training algorithm integrated with guide policy constraints is proposed to enable the optimizer network to converge to a feasible solution. Finally, experiments show that the proposed algorithm has better feasibility than other learning-based methods and can provide solutions much faster than traditional optimizers with similar optimality.

翻译：基于模型预测控制（MPC）的轨迹规划已在机器人领域广泛应用，而将控制障碍函数（CBF）约束融入MPC可显著提升其避障效率。然而，传统优化器在求解此类非凸约束优化问题时资源消耗大、求解速度慢，基于学习的方法又难以满足非凸约束。本文提出SOMTP算法——一种面向CBF-MPC轨迹规划的自监督学习优化器。具体而言，首先，SOMTP通过问题转录满足大部分约束；其次，提出可微分的SLPG修正方法将解推向安全集，随后将其转化为训练过程中的引导策略；接着，受增广拉格朗日方法（ALM）启发，我们提出了集成引导策略约束的训练算法，使优化器网络收敛到可行解。实验表明，该算法相比其他学习方法具有更优的可行性，且能在保持相近最优性的前提下，以远超传统优化器的速度提供解。