凸多面体間の障害物回避のための制御バリア関数を用いた反復凸最適化
Iterative Convex Optimization with Control Barrier Functions for Obstacle Avoidance among Polytopes
凸多面体ロボットと障害物の正確な最近点計算から支持超平面を導出し、線形離散時間制御バリア関数制約を構築。反復凸MPC-DCBFフレームワークにより、非線形ダイナミクスでも高速なオンライン安全制御と軌道計画を実現した。
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著者: Shuo Liu, Zhe Huang, Calin A. Belta
分類: cs.RO
原文アブストラクト
Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids, which allow differentiable distance expressions but distort the true geometry and restrict the feasible set. Other approaches integrate exact polytope distances into nonlinear model predictive control (MPC), resulting in nonconvex programs that limit real-time performance. In this paper, we construct linear discrete-time control barrier function (DCBF) constraints by deriving supporting hyperplanes from exact closest-point computations between convex polytopes. We then propose a novel iterative convex MPC-DCBF framework, where local linearization of system dynamics and robot geometry ensures convexity of the finite-horizon optimization at each iteration. The resulting formulation reduces computational complexity and enables fast online implementation for safety-critical control and trajectory planning of general nonlinear dynamics. The framework extends to multi-robot and three-dimensional environments. Numerical experiments demonstrate collision-free navigation in cluttered maze scenarios with millisecond-level solve times.
