IKSel: Selecting Good Seed Joint Values for Fast Numerical Inverse Kinematics Iterations

TL;DR

This work tackles numerical inverse kinematics by focusing on seed selection to accelerate convergence, introducing a KDTree-based seed framework augmented with joint-space linearity ranking and a re-selection mechanism to avoid deadlocks. By storing seed joint configurations with their TCP poses and Jacobian pseudo-inverses, the method narrows seed candidates with a workspace threshold and chooses those minimizing required joint-space adjustments, eliminating the need for a scaling factor. Across four manipulators and extensive ablations, the approach achieves high success rates with competitive runtimes, often outperforming traditional numerical solvers and remaining competitive with learning-based methods, while avoiding the training and inference costs of neural networks. The findings offer practical guidance for configuring seed density, solver choice, and re-selection strategies, making numerical IK viable for time-sensitive applications and adaptable to different robotic platforms.

Abstract

This paper revisits the numerical inverse kinematics (IK) problem, leveraging modern computational resources and refining the seed selection process to develop a solver that is competitive with analytical-based methods. The proposed seed selection strategy consists of three key stages: (1) utilizing a K-Dimensional Tree (KDTree) to identify seed candidates based on workspace proximity, (2) sorting candidates by joint space adjustment and attempting numerical iterations with the one requiring minimal adjustment, and (3) re-selecting the most distant joint configurations for new attempts in case of failures. The joint space adjustment-based seed selection increases the likelihood of rapid convergence, while the re-attempt strategy effectively helps circumvent local minima and joint limit constraints. Comparison results with both traditional numerical solvers and learning-based methods demonstrate the strengths of the proposed approach in terms of success rate, time efficiency, and accuracy. Additionally, we conduct detailed ablation studies to analyze the effects of various parameters and solver settings, providing practical insights for customization and optimization. The proposed method consistently exhibits high success rates and computational efficiency. It is suitable for time-sensitive applications.

Figures (6)

• Figure 1: Comparison of success and failure seed joint configurations for numerical IK: (a) Several candidate seed configurations with small workspace deviations from the target Tool Center Point (abbreviated as TCP, indicated by the dashed coordinate frame). (b) Two representative seeds were selected for comparison. Based on the Euclidean distance metric in the workspace, the TCP of the red seed is closer to the target TCP than that of the blue seed. (c) However, without applying a scaling coefficient, the red seed significantly deviates after the first numerical iteration. (d) In contrast, the blue seed rapidly converges to the target TCP within only four iterations, without requiring any coefficient adjustment. This paper proposes a method to effectively identify and select seeds similar to the blue one, thereby reducing iteration counts and enhancing IK solving efficiency.
• Figure 2: (a) 200 candidate seed configurations. The green robot with a dashed coordinate frame is the solution. (b) The seed labeled with ① has the smallest joint space adjustment and is selected for numerical iteration. However, after several steps, the robot's first joint approximates its joint limit and fails to converge. (c) The most distant joint configuration from the failed seed is re-selected for a new numerical solution. The re-selection is performed within the top 20 candidates with the smallest joint space adjustment in order to impose a strong linearity condition near the new selection and thus increase the likelihood of fast convergence. (d) The re-selected seed finally converges to the target.
• Figure 3: Conceptual sketch of the re-selection strategy.
• Figure 4: Kinematic structures of the manipulators used in the experiments. The dark blue line segments represent the motion axes of the joints. The dark blue circular arrows represent the rotational directions.
• Figure 5: Comparison of different seed selection methods in terms of success rate and average inference time with respect to maximally allowed re-selection attempts. The solid line corresponds to the proposed joint adjustment and re-selection framework, the dashed line corresponds to sorted by only joint space adjustment, and the dotted line corresponds to the workspace proximity-based selection method.