J-PARSE: Jacobian-based Projection Algorithm for Resolving Singularities Effectively in Inverse Kinematic Control of Serial Manipulators
For roboticists, J-PARSE provides a principled method to handle kinematic singularities in real-time control, improving safety and workspace utilization in teleoperation and servoing.
J-PARSE enables smooth inverse kinematic control of serial manipulators near singularities by projecting desired motion onto non-singular and singular directions, scaling down the singular component. It guarantees asymptotic stability for reachable targets and shows high accuracy in reaching and leaving singular poses, expanding the usable workspace.
J-PARSE is an algorithm 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 safe transition into and out of low-rank configurations, guaranteeing asymptotic stability for reaching target poses within the workspace, and stability for those outside. Velocity control with J-PARSE is benchmarked against approaches from the literature, and shows high accuracy in reaching and leaving singular target poses. By expanding the available workspace of manipulators, the algorithm finds applications in teleoperation, servoing, and learning. Videos and code are available at https://jparse-manip.github.io/.