制御バリア関数を用いた多面体間の障害物回避のための安全臨界制御と計画
Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions
離散時間制御バリア関数(DCBF)と双対変数に基づく最適化定式化を提案し、多面体障害物間の衝突回避を短いホライズンでオンライン計画できるようにした。
著者: Akshay Thirugnanam, Jun Zeng, Koushil Sreenath
分類: cs.RO, cs.SY, eess.SY, math.OC
原文アブストラクト
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.
