Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Propagative Distance Optimization for Constrained Inverse Kinematics

Yu Chen, Yilin Cai, Jinyun Xu, Zhongqiang Ren, Guanya Shi, Howie Choset

TL;DR

Constrained inverse kinematics for high-DOF robots are challenging due to joint limits and obstacle collisions. The paper introduces PDO-IK, a propagative distance-based IK that leverages the kinematic chain by computing forward kinematics and Jacobians along the chain, and optimizes via an augmented Lagrangian with slack variables and angle-decomposition to handle box constraints. It presents a novel distance-based kinematic formulation, efficient forward rollout and Jacobian propagation, and shows that PDO-IK achieves up to 2 orders of magnitude faster runtimes and up to 3x higher success rates than baselines, with tighter numerical accuracy. The approach enables real-time IK for complex systems, demonstrated on 19-DOF humanoids in dynamic obstacle scenarios, highlighting its practical impact for collision avoidance in cluttered and changing environments.

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.

Propagative Distance Optimization for Constrained Inverse Kinematics

TL;DR

Constrained inverse kinematics for high-DOF robots are challenging due to joint limits and obstacle collisions. The paper introduces PDO-IK, a propagative distance-based IK that leverages the kinematic chain by computing forward kinematics and Jacobians along the chain, and optimizes via an augmented Lagrangian with slack variables and angle-decomposition to handle box constraints. It presents a novel distance-based kinematic formulation, efficient forward rollout and Jacobian propagation, and shows that PDO-IK achieves up to 2 orders of magnitude faster runtimes and up to 3x higher success rates than baselines, with tighter numerical accuracy. The approach enables real-time IK for complex systems, demonstrated on 19-DOF humanoids in dynamic obstacle scenarios, highlighting its practical impact for collision avoidance in cluttered and changing environments.

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 (101500 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.
Paper Structure (19 sections, 44 equations, 5 figures, 3 algorithms)

This paper contains 19 sections, 44 equations, 5 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Denavit–Hartenberg Parameters
  4. Quasi-Newton Method
  5. Kinematics and Constraints Formulation
  6. Kinematic Chain
  7. Joint Limit Constraints
  8. Collision Avoidance Constraints
  9. End Effector Pose Objective
  10. Algorithm
  11. Forward Rollout
  12. Jacobian Computation
  13. Inverse Kinematics
  14. Complexity Analysis
  15. Experiments
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Kinematics model, constraints, and objective under distance-based representation, as well as the propagation structure in our method. (a) The kinematic chain of a linkage of revolute joints. (b) Joint angle decomposition. (c) Collision avoidance constraint. (d) End effector pose objective. (e) The propagation structure in a diagonal matrix of distances in the forward rollout. The propagation in Jacobian computation follows the inverse direction of the forward rollout.
  • Figure 2: Visualization of experimental setups. (a)-(c) Robot arm platforms (UR10, Franka, and KUKA). Their occupation space are composed of spheres or spheroids in our formulation, visualized here as translucent hulls. (d) An example of a KUKA robot in the environment with 9 random obstacles. (e) Visualization of obstacles as point clusters.
  • Figure 3: Experimental results on UR10, KUKA, and Franka. The $x$-axis are the number of obstacles. The $y$-axis are success rate, logarithm of runtime in seconds, joint limit violation rate, collision rate, and end effector objective failure rate.
  • Figure 4: Convergence precision experiments results.
  • Figure 5: Dynamic obstacle avoidance for humanoid robot. (a) Key frames of the H1 robot avoiding obstacles. (b) Speed of PDO-IK in C++ implementation. (c) The trajectory of CoM of the robot and its feasible region. (d) Demonstrations of some additional collision avoidance experiments.