J-PARSE: Jacobian-based Projection Algorithm for Resolving Singularities Effectively in Inverse Kinematic Control of Serial Manipulators

2025-05-01

AI Summary

Conventional first-order inverse kinematics control of serial manipulators becomes unstable and discontinuous near kinematic singularities. Method: This paper proposes a smooth velocity control method based on a “safe Jacobian” matrix and adaptive scaling projection along singularity directions. It achieves singularity-robust motion by decomposing task-space degrees of freedom, decoupling singular and nonsingular subspaces, constraining the aspect ratio of the manipulability ellipsoid, and employing right pseudo-inverse mapping—eliminating the need for explicit constraints. Contribution/Results: The approach theoretically guarantees asymptotic stability during singularity traversal for the first time without requiring manually tuned damping parameters or switching logic. Experiments demonstrate significantly improved end-effector velocity tracking accuracy near singularities compared to least-squares and damped least-squares methods, expanded operational workspace, and successful deployment in servo control, teleoperation, and learning-based control scenarios.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Natural Language Processing: Safety and Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

J-PARSE is a method for smooth first-order inverse kinematic control of a serial manipulator near kinematic singularities. The commanded end-effector velocity is interpreted component-wise, according to the available mobility in each dimension of the task space. First, a substitute"Safety"Jacobian matrix is created, keeping the aspect ratio of the manipulability ellipsoid above a threshold value. The desired motion is then projected onto non-singular and singular directions, and the latter projection scaled down by a factor informed by the threshold value. A right-inverse of the non-singular Safety Jacobian is applied to the modified command. In the absence of joint limits and collisions, this ensures smooth transition into and out of low-rank poses, guaranteeing asymptotic stability for target poses within the workspace, and stability for those outside. Velocity control with J-PARSE is benchmarked against the Least-Squares and Damped Least-Squares inversions of the Jacobian, and shows high accuracy in reaching and leaving singular target poses. By expanding the available workspace of manipulators, the method finds applications in servoing, teleoperation, and learning.

Problem

• Resolving kinematic singularities in serial manipulator control
• Ensuring smooth motion near low-rank poses
• Improving accuracy in reaching singular target poses

Innovation

• Uses Safety Jacobian to maintain manipulability ellipsoid
• Projects motion onto non-singular and scaled singular directions
• Ensures smooth transitions near kinematic singularities