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.

翻译：解析方法与优化方法在解决逆运动学问题上的研究贯穿了整个机器人学发展史。这两种策略具有互补的优势与不足，但开发一种统一的方法以充分利用两者已被证明具有挑战性。优化方法面临的一个关键挑战是关节角度与末端执行器位姿之间复杂的非线性关系。当这一问题需要与诸如避障等额外的非凸约束同时处理时，优化逆运动学算法的失败率可能很高。我们提出了一种新的优化逆运动学公式，该公式使用解析逆运动学解作为变量替换，从根本上更易于优化器求解。我们在三种流行的求解器上测试了我们的方法，这三种求解器代表了约束非线性优化的三种不同范式。广泛的实验比较表明，在各种具有挑战性的逆运动学问题（包括避障、抓取选择和人形机器人稳定性）上，我们的新公式比旧公式及基线方法实现了更高的成功率。