Inverse kinematics algorithms are commonly used in robotic systems to transform tasks to joint references, 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 setbased tasks, i.e. tasks with a range of valid values, in addition to equality tasks, which have a specific desired value. Examples of set-based 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. The practical implementation of the proposed algorithm is discussed, and experimental results are presented where a number of both set-based and equality tasks have been implemented on a 6 degree of freedom UR5 which is an industrial robotic arm from Universal Robots. The experiments validate the theoretical results and confirm the effectiveness of the proposed approach.
['Signe Moe', 'Gianluca Antonelli', 'Andrew R. Teel', 'Kristin Ytterstad Pettersen', 'Johannes Schrimpf']
Set-Based Tasks within the Singularity-Robust Multiple Task-Priority Inverse Kinematics Framework: General Formulation, Stability Analysis, and Experimental Results