多項式分離超曲面による任意形状移動ロボットのオンライン軌道最適化
Online Trajectory Optimization for Arbitrary-Shaped Mobile Robots via Polynomial Separating Hypersurfaces
凸近似を不要にする多項式分離超曲面を導入し、任意形状ロボットの衝突回避軌道を非線形計画で最適化する手法を提案した。
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著者: Shuoye Li, Zhiyuan Song, Yulin Li, Zhihai Bi, Jun Ma
分類: cs.RO
原文アブストラクト
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require convex approximations of both the robot and obstacles, which becomes an overly conservative assumption in cluttered and narrow environments. In this work, we unequivocally remove this limitation by introducing nonlinear separating hypersurfaces parameterized by polynomial functions. We first generalize the classical separating hyperplane theorem and prove that any two disjoint bounded closed sets in Euclidean space can be separated by a polynomial hypersurface, serving as the theoretical foundation for nonlinear separation of arbitrary geometries. Building on this result, we formulate a nonlinear programming (NLP) problem that jointly optimizes the robot's trajectory and the coefficients of the separating polynomials, enabling geometry-aware collision avoidance without conservative convex simplifications. The optimization remains efficiently solvable using standard NLP solvers. Simulation and real-world experiments with nonconvex robots demonstrate that our method achieves smooth, collision-free, and agile maneuvers in environments where convex-approximation baselines fail.
