Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees validity and asymptotic optimality. Validity: Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization. Asymptotic Optimality: We use a conservative piecewise approximation of the trajectory with automatically adjustable resolution of its discretization. The trajectory converges under refinement to the first-order stationary point of the exact nonconvex programming problem. Our method has additional practical advantages including joint optimality in terms of trajectory and time-allocation, and robustness to challenging environments as demonstrated in our experiments.
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. Our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for timeoptimal 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 10 − 100× speedup, while generating trajectories of comparable qualities as state-of-theart P-IPM solver.
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