Stability analysis for set-based control within the singularity-robust multiple task-priority inverse kinematics framework

Inverse kinematics algorithms are commonly used in robotic systems to accomplish desired behavior, and several methods exist to ensure the achievement of several tasks simultaneously. The multiple task-priority inverse kinematics framework allows tasks to be considered in a prioritized order by projecting task velocities through the nullspaces of higher priority tasks. This paper extends this framework to handle set-based tasks, i.e. tasks with a range of valid values, in addition to equality tasks, which have a specific desired value. Examples of such tasks are joint limit and obstacle avoidance. The proposed method is proven to ensure asymptotic convergence of the equality task errors and the satisfaction of all high-priority set-based tasks. Simulations results confirm the effectiveness of the proposed approach.