Robust Multi-Robot Trajectory Optimization Using Alternating Direction Method of Multiplier
This work addresses trajectory optimization for multi-UAVs and robot arms, offering faster computation for robotics applications, but it is incremental as it builds on existing ADMM and P-IPM frameworks.
The authors tackled the problem of constrained trajectory optimization for multi-robot systems by proposing an ADMM variant that breaks joint optimization into sub-problems, achieving an order of magnitude speedup while maintaining collision avoidance and homotopy preservation comparable to state-of-the-art methods.
We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Starting from a collision-free initial trajectory, our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation throughout optimization, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights an order of magnitude's speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.