Propagative Distance Optimization for Constrained Inverse Kinematics

TL;DR

This paper introduces PDO-IK, a novel distance-based inverse kinematics method that exploits chain structure to significantly improve computational efficiency and success rates, enabling real-time control of complex robots.

Contribution

The paper proposes PDO-IK, a chain-structure-aware distance optimization approach that accelerates inverse kinematics solving and enhances success rates over existing methods.

Findings

PDO-IK is up to 100 times faster than previous distance-based methods.

PDO-IK achieves up to three times higher success rates than joint-angle-based methods.

Enables real-time obstacle avoidance for a 19-DoF humanoid robot.

Abstract

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.