IKSPARK: 凸最適化による障害物を考慮した逆運動学
IKSPARK: Obstacle-Aware Inverse Kinematics via Convex Optimization
逆運動学を半正定値計画問題として定式化し、ランク最小化で解くことで、障害物回避を含む複雑な制約下でも高精度な解を求める手法を提案した。
著者: Liangting Wu, Roberto Tron
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using Semidefinite Programming And RanK minimization), an obstacle-aware IK solver for robots with diverse morphologies, including open and closed kinematic chains with spherical, revolute, and prismatic joints. Our formulation expresses IK as a semidefinite programming (SDP) problem with additional rank-1 constraints on symmetric matrices with fixed traces. IKSPARK first solves the relaxed SDP, whose infeasibility certifies infeasibility of the original IK problem, and then recovers a rank-1 solution using iterative rank-minimization methods with proven local convergence. Obstacle avoidance is handled through a convexified formulation of mixed-integer constraints. Extensive experiments show that IKSPARK computes highly accurate solutions across various kinematic structures and constrained environments without post-processing. In obstacle-rich settings, especially fixed workcell environments, IKSPARK achieves substantially higher success rates than traditional nonlinear optimization methods.
