Incorporating set-based control within the singularity-robust multiple task-priority inverse kinematics

Inverse kinematics is an active research domain in robotics since several years due to its importance in multiple robotics application. Among the various approaches, differential inverse kinematics is widely used due to the possibility to real-time implementation. Redundant robotic systems exhibit more degrees of freedom than those strictly required to execute a given end-effector task, in such a case, multiple tasks can be handled simultaneously in, e.g, a task-priority architecture. This paper addresses the systematic extension of the multiple tasks singularity robust solution, also known as Null-space Based Behavioral control, to the case of set-based control tasks, i.e, tasks for which a range, rather than a specific value, is assigned. This is the case for several variables such as, for example, mechanical joint limits of robotic arms as well as obstacle avoidance for any kind of robots. Numerical validation are provided to support the solution proposed.