用解析解做变量变换，让优化求解逆运动学更稳定高效
A Framework for Combining Optimization-Based and Analytic Inverse Kinematics
- 以解析逆运动学解为变量变换，简化优化问题非线性关系
- 在避障、抓取、人形机器人平衡等挑战任务中成功率显著提升
- 适用于需要高鲁棒性的工业机器人控制与复杂场景运动规划
逆运动学求解的解析法与优化法长期独立发展，各具优劣。优化法因关节角与末端位姿间的复杂非线性关系，叠加碰撞避免等非凸约束时易失败。本文提出一种新优化框架，将解析逆运动学解作为变量变换，使优化问题本质更易求解。在三种代表不同优化范式的主流求解器上测试，结果表明该方法在多种复杂逆运动学任务（包括碰撞避免、抓取选择、人形机器人稳定性）中均实现更高成功率，优于传统公式与基线方法。
原文摘要 · Abstract (English)
Analytic and optimization methods for solving inverse kinematics (IK) problems have been deeply studied throughout the history of robotics. The two strategies have complementary strengths and weaknesses, but developing a unified approach to take advantage of both methods has proved challenging. A key challenge faced by optimization approaches is the complicated nonlinear relationship between the joint angles and the end-effector pose. When this must be handled concurrently with additional nonconvex constraints like collision avoidance, optimization IK algorithms may suffer high failure rates. We present a new formulation for optimization IK that uses an analytic IK solution as a change of variables, and is fundamentally easier for optimizers to solve. We test our methodology on three popular solvers, representing three different paradigms for constrained nonlinear optimization. Extensive experimental comparisons demonstrate that our new formulation achieves higher success rates than the old formulation and baseline methods across various challenging IK problems, including collision avoidance, grasp selection, and humanoid stability.
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