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

arXiv: https://arxiv.org/abs/2510.07514 · HTML: https://mlsanity.com/paper/2510.07514/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2025.

## Built on by (most cited first, 1 of 1)

- [RAM: Reachability Across Morphologies](https://mlsanity.com/paper/2606.09108/) (2026)

## Abstract (arXiv)

Inverse Kinematics (IK) is a core problem in robotics, in which joint configurations are found to achieve a (collision-free) desired end-effector pose. Modern IK solvers face a fundamental trade-off: analytical methods are fast but lack generality, while numerical optimization-based methods are broadly applicable but prone to local minima and high computational costs. To overcome this challenge, we introduce HJCD-IK, a GPU-accelerated, sampling-based hybrid solver. By pairing a novel orientation-aware greedy coordinate descent initialization with Jacobian-based polishing and a parallel collision filter, our method achieves up to order-of-magnitude gains in speed and accuracy over state-of-the-art solvers, consistently finding collision-free solutions on the accuracy-latency Pareto frontier, while producing a diverse distribution of high-quality samples. We validate our solver on a physical Franka manipulator and release our code open-source.