Real-Time Conformal-Seeded Hybrid Inverse Kinematics for Offset Redundant Manipulators

2026-10-03

AI Summary

This study addresses the limited accuracy of analytical methods and the initial-value sensitivity of numerical approaches in the inverse kinematics of offset-redundant manipulators by proposing a two-stage hybrid solving strategy. First, an approximate model generates candidate solutions. Subsequently, split conformal prediction is introduced to establish an upper bound on calibration difficulty, which, combined with a lightweight learned predictor, efficiently selects the optimal seed. The Levenberg–Marquardt algorithm then refines this solution on the full model. Achieving computation times below 40 microseconds and a 100% target-reaching success rate, the proposed method demonstrates superior real-time performance and reliability, as validated through extensive simulations and humanoid robot experiments.

Abstract

This paper presents a conformal-seeded hybrid strategy for solving inverse kinematics of offset, redundant 7-DoF robot arms of the humanoid class. Analytical inverse kinematics (AIK) provides closed-form solutions with very low computational cost. However, for offset kinematic structures, the exact closed-form solution is generally unavailable, and practical AIK must rely on an approximate or simplified kinematic model. In contrast, numerical inverse kinematics (NIK) can achieve high-precision solutions on the full kinematic model. However, its convergence is highly sensitive to initialization. To overcome these limitations, we propose a two-stage hybrid inverse kinematics framework with conformal-calibrated seed selection. First, an approximate analytical model efficiently enumerates a finite set of candidate joint solutions. Second, we rank these candidates using a lightweight learned predictor of post-refinement difficulty, wrapped by split-conformal prediction into a calibrated upper bound that serves as the selection score. The best-ranked seed is then refined using a Levenberg-Marquardt solver on the full kinematic model. The proposed method combines fast candidate generation, learned seed ranking with a calibrated difficulty bound, and accurate numerical refinement, achieving real-time performance of less than 40us and a success rate of 100% in our evaluation on reachable targets. We validate the approach through large-scale stochastic simulation across the workspace and experimental demonstrations with motion planning on a humanoid robot arm. Demonstration videos are available at https://youtu.be/aeiBmw1XRbw.

Problem

• Inverse Kinematics
• Redundant Manipulators
• Offset Kinematic Structure
• Analytical Inverse Kinematics
• Numerical Inverse Kinematics

Innovation

• Inverse Kinematics
• Conformal Prediction
• Redundant Manipulators
• Hybrid Framework
• Seed Selection