On the Convergence of a Closed-Loop Inverse Kinematics Solver with Time-Varying Task Functions

Many control algorithms devised to allow redundant robots to execute complex multiple tasks with priorities require a numerical inverse kinematics (IK) solver. The present letter investigates the conditions that, if satisfied, guarantee that a specific module of closed-loop numerical IK solvers, which is at the kernel of some of the aforementioned algorithms, converges to a feasible solution. The investigation has the objective to prove the convergence in those cases when the task function is time- varying. The conditions found to ensure convergence include not only the initial task error and the loop gain - as it happens for stationary task functions - but also the maximum sampling time to be used in the computation of the solution.