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A prioritized inverse kinematics (PIK) solution can be considered as a(regulation or output tracking) control law of a dynamical system withprioritized multiple outputs. We propose a method that guarantees that a jointtrajectory generated from a class of PIK solutions exists uniquely in anonsingular configuration space. We start by assuming that desired tasktrajectories stay in nonsingular task spaces and find conditions for tasktrajectories to stay in a neighborhood of desired task trajectories in which wecan guarantee existence and uniqueness of a joint trajectory in a nonsingularconfiguration space. Based on this result, we find a sufficient condition fortask convergence and analyze various stability notions such as stability,uniform stability, uniform asymptotic stability, and exponential stability inboth continuous and discrete times. We discuss why the number of tasks islimited in discrete time and show how preconditioning can be used in order toovercome this limitation.

Prioritized Inverse Kinematics: Desired Task Trajectories in Nonsingular Task Spaces