時空間制約付き最適制御問題に対する高速半正定値凸緩和
A Fast Semidefinite Convex Relaxation for Optimal Control Problems With Spatio-Temporal Constraints
時間スケーリングと半正定値計画による凸緩和で、時空間制約付き最適制御問題を高速かつ高精度に解く手法を提案し、クアッドロータの飛行実験で有効性を示した。
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著者: Shiying Dong, Zhipeng Shen, Rudolf Reiter, Hailong Huang, Bingzhao Gao, Hong Chen, Wen-Hua Chen
分類: cs.RO
原文アブストラクト
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However, the nonlinear programs approximating the OCPs are inherently nonconvex due to the coupling between the dynamics and the event timing, and therefore, they are challenging to solve. Most approaches address this challenge by predefining waypoint times or just using nonconvex trajectory optimization, which simplifies the problem but often yields suboptimal solutions. To significantly improve the numerical properties, we propose a formulation with a time-scaling direct multiple shooting scheme that partitions the prediction horizon into segments aligned with characteristic time constraints. Moreover, we develop a fast semidefinite-programming-based convex relaxation that exploits the sparsity pattern of the lifted formulation. Comprehensive simulation studies demonstrate the solution optimality and computational efficiency. Furthermore, real-world experiments on a quadrotor waypoint flight task with constrained open time windows validate the practical applicability of the approach in complex environments.
