Prioritized Inverse Kinematics with Multiple Task Definitions

We are proposing a general framework that incorporates multiple task definitions in the prioritized inverse kinematics problem. First, a mathematical description of multiple task definitions is constructed that provides an efficient way to show unprioritized or prioritized accumulations of tasks. Then, smooth transitions between all task definitions are studied, so a method, called task transition control, is developed that interpolates joint trajectories using barycentric coordinates and linear dynamical systems to overcome difficulties of interpolating task trajectories in the conventional methods. Consequently, smooth, arbitrary, and consecutive task transitions are achieved in a simple, direct, and general manner and also boundedness of joint trajectories is assured regardless of singularity. Lastly, the idea is tested by two kinematic simulations: obstacle avoidance with the KUKA LWR and task scheduling of a humanoid robot.