This paper investigates a constrained inverse kinematic (IK) problem that seeks a feasible configuration of an articulated robot under various constraints such as joint limits and obstacle collision avoidance. Due to the high-dimensionality and complex constraints, this problem is often solved numerically via iterative local optimization. Classic local optimization methods take joint angles as the decision variable, which suffers from non-linearity caused by the trigonometric constraints. Recently, distance-based IK methods have been developed as an alternative approach that formulates IK as an optimization over the distances among points attached to the robot and the obstacles. Although distance-based methods have demonstrated unique advantages, they still suffer from low computational efficiency, since these approaches usually ignore the chain structure in the kinematics of serial robots. This paper proposes a new method called propagative distance optimization for constrained inverse kinematics (PDO-IK), which captures and leverages the chain structure in the distance-based formulation and expedites the optimization by computing forward kinematics and the Jacobian propagatively along the kinematic chain. Test results show that PDO-IK runs up to two orders of magnitude faster than the existing distance-based methods under joint limits constraints and obstacle avoidance constraints. It also achieves up to three times higher success rates than the conventional joint-angle-based optimization methods for IK problems. The high runtime efficiency of PDO-IK allows the real-time computation (10$-$1500 Hz) and enables a simulated humanoid robot with 19 degrees of freedom (DoFs) to avoid moving obstacles, which is otherwise hard to achieve with the baselines.

翻译：本文研究了一种约束逆运动学问题，该问题旨在为关节式机器人在关节限位和避障等多种约束下寻找可行构型。由于问题的高维性和复杂约束，通常需要通过迭代局部优化进行数值求解。经典局部优化方法以关节角度为决策变量，但受限于三角函数约束导致的非线性问题。近年来，基于距离的逆运动学方法作为替代方案被提出，该方法将逆运动学问题转化为机器人附着点与障碍物之间距离的优化问题。尽管基于距离的方法展现出独特优势，但由于通常忽略串联机器人运动学中的链式结构，其计算效率仍然较低。本文提出一种名为约束逆运动学传播距离优化的新方法，该方法在距离优化框架中捕捉并利用链式结构，通过沿运动学链传播计算正向运动学与雅可比矩阵来加速优化过程。测试结果表明，在关节限位约束与避障约束下，PDO-IK 比现有基于距离方法的运行速度提升达两个数量级。相较于传统基于关节角度的逆运动学优化方法，其成功率最高可提升三倍。PDO-IK 的高运行效率支持实时计算（10$-$1500 Hz），使具有19自由度的仿人机器人能够规避运动障碍，而基准方法难以实现此功能。