  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.
