A Framework for Combining Optimization-Based and Analytic Inverse Kinematics

2026-02-04

AI Summary

This work proposes a novel framework for inverse kinematics (IK) optimization that addresses the high failure rates commonly caused by the nonlinear relationship between joint variables and end-effector poses, as well as non-convex constraints such as obstacle avoidance. By introducing analytical IK solutions as a change of variables within the optimization process, the method uniquely combines the precision of analytical approaches with the flexibility of numerical optimization, substantially simplifying the problem structure. Evaluated across three mainstream optimizers, the approach demonstrates significantly higher success rates than conventional optimization techniques and baseline methods in complex tasks—including obstacle avoidance, grasp selection, and humanoid robot stability—thereby achieving an effective unification of analytical and optimization-based IK strategies.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Constraint Satisfaction and Optimization: Solvers and Tools
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• inverse kinematics
• optimization
• analytic methods
• nonlinear constraints
• collision avoidance

Innovation

• inverse kinematics
• optimization
• analytic solution
• change of variables
• collision avoidance