Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods

1986/01/01 by Charles Wampler, Charles W. Wampler · 834 citations
Engineering · Mathematics · #Applied mathematics #Artificial intelligence #Classical mechanics #Computer science #Control theory (sociology) #Dynamics and Control of Mechanical Systems #Geometry #Gravitational singularity #Inverse #Inverse kinematics #Inverse problem #Iterative Learning Control Systems #Jacobian matrix and determinant #Kinematics #Least-squares function approximation #Mathematical analysis #Mathematics #Physics #Position (finance) #Robot #Robot end effector #Robotic Mechanisms and Dynamics

paper · doi:10.1109/tsmc.1986.289285

published in IEEE Transactions on Systems Man and Cybernetics 16(1), 93-101 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Inverse kinematic solutions are used in manipulator controllers to determine corrective joint motions for errors in end-effector position and orientation. Previous formulations of these solutions, based on the Jacobian matrix, are inefficient and fail near kinematic singularities. Vector formulations of inverse kinematic problems are developed that lead to efficient computer algorithms. To overcome the difficulties encountered near kinematic singularities, the exact inverse problem is reformulated as a damped least-squares problem, which balances the error in the solution against the size of the solution. This yields useful results for all manipulator configurations.

Citations

• Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms
• Review of pseudoinverse control for use with kinematically redundant manipulators

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