Overcoming Kinematic Singularities with the Filtered Inverse Approach

In this work, we propose a solution to the inverse kinematics problem based on the differential kinematics and on a recently proposed algorithm which estimates the inverse of the Jacobian matrix dynamically. The output of the algorithm can be interpreted as a filtered inverse (FI) of the Jacobian matrix. An interesting property of the FI algorithm is its ability to cope with kinematic singularities. The update law of the estimator is driven by error signals that consider both the left and the right inverse matrices, thus enabling trajectory tracking and minimization of the control effort simultaneously. This paper shows that the FI algorithm can be applied to a Jacobian matrix augmented with additional constraints, which allows for setting the priority or weight to different control objectives, such as obstacle avoidance. Simulation results are presented to illustrate the performance and feasibility of the proposed solution.