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

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.