HJCD-IK: GPU-Accelerated Inverse Kinematics through Batched Hybrid Jacobian Coordinate Descent

2025-10-08

AI Summary

To address the slow convergence, susceptibility to local minima, and poor generalizability of numerical and analytical inverse kinematics (IK) solvers for high-degree-of-freedom robots, this paper proposes a GPU-accelerated batched hybrid IK solver. Our method comprises three key innovations: (1) a pose-aware greedy coordinate descent initialization strategy to improve initial solution quality; (2) a lightweight Jacobian-based refinement mechanism that balances accuracy and computational efficiency; and (3) an end-to-end GPU-parallelized architecture enabling simultaneous batch sampling and optimization. Experiments demonstrate that our approach dominates the accuracy–latency Pareto frontier, achieving up to an order-of-magnitude speedup in inference time compared to state-of-the-art methods. Moreover, it yields more uniformly distributed solutions—as quantified by the lowest Maximum Mean Discrepancy (MMD)—thereby offering superior efficiency, robustness, and solution diversity.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Inverse Kinematics (IK) is a core problem in robotics, in which joint configurations are found to achieve a desired end-effector pose. Although analytical solvers are fast and efficient, they are limited to systems with low degrees-of-freedom and specific topological structures. Numerical optimization-based approaches are more general, but suffer from high computational costs and frequent convergence to spurious local minima. Recent efforts have explored the use of GPUs to combine sampling and optimization to enhance both the accuracy and speed of IK solvers. We build on this recent literature and introduce HJCD-IK, a GPU-accelerated, sampling-based hybrid solver that combines an orientation-aware greedy coordinate descent initialization scheme with a Jacobian-based polishing routine. This design enables our solver to improve both convergence speed and overall accuracy as compared to the state-of-the-art, consistently finding solutions along the accuracy-latency Pareto frontier and often achieving order-of-magnitude gains. In addition, our method produces a broad distribution of high-quality samples, yielding the lowest maximum mean discrepancy. We release our code open-source for the benefit of the community.

Problem

• Solving inverse kinematics for robotic joint configurations efficiently
• Overcoming limitations of analytical and numerical optimization methods
• Accelerating convergence speed while maintaining high solution accuracy

Innovation

• GPU-accelerated batched hybrid IK solver
• Combines coordinate descent with Jacobian polishing
• Achieves Pareto frontier in accuracy-latency tradeoff