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，原因在于非凸避碰约束。直接对这类非凸形式应用数值求解器会忽视约束结构，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，提出了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（简称RDADMM或RDA）。所提出的RDA方法通过对偶性求解光滑双凸重构问题，从而解决非凸运动规划，并允许对每个障碍物并行计算避碰约束，显著减少计算时间。我们通过仿真与真实环境中类车机器人的路径跟踪实验验证了RDA规划器的性能。实验结果表明，与其它基准方法相比，所提方法生成光滑无碰撞轨迹所需的计算时间更少，且在杂乱环境中具有鲁棒性。源代码见https://github.com/hanruihua/RDA_planner。