Autonomous motion planning is challenging in multi-obstacle environments due to nonconvex collision avoidance constraints. Directly applying numerical solvers to these nonconvex formulations fails to exploit the constraint structures, resulting in excessive computation time. In this paper, we present an accelerated collision-free motion planner, namely regularized dual alternating direction method of multipliers (RDADMM or RDA for short), for the model predictive control (MPC) based motion planning problem. The proposed RDA addresses nonconvex motion planning via solving a smooth biconvex reformulation via duality and allows the collision avoidance constraints to be computed in parallel for each obstacle to reduce computation time significantly. We validate the performance of the RDA planner through path-tracking experiments with car-like robots in both simulation and real-world settings. Experimental results show that the proposed method generates smooth collision-free trajectories with less computation time compared with other benchmarks and performs robustly in cluttered environments. The source code is available at https://github.com/hanruihua/RDA_planner.

翻译：自主运动规划在多障碍环境中面临挑战，原因在于非凸碰撞规避约束。直接对这些非凸公式应用数值求解器无法利用约束结构，导致计算时间过长。本文针对基于模型预测控制（MPC）的运动规划问题，提出一种加速无碰撞运动规划器，即正则化对偶交替方向乘子法（RDADMM，简称RDA）。所提出的RDA通过对偶性将非凸运动规划转化为光滑双凸重构问题，并允许每个障碍物的碰撞规避约束并行计算，从而显著减少计算时间。我们通过在仿真和真实环境中对类车机器人进行路径跟踪实验，验证了RDA规划器的性能。实验结果表明，与其他基准方法相比，该方法能够生成光滑无碰撞轨迹，且计算时间更短，并在杂乱环境中具有鲁棒性。源代码见https://github.com/hanruihua/RDA_planner。