On continuous null space projections for torque-based, hierarchical, multi-objective manipulation

The technological progress in the field of robotics results in more and more complex manipulators. However, having an increasing number of degrees of freedom raises the question of how to use them effectively. In turn, establishing manipulators in human environments, e.g., as service robots, calls for the fulfillment of various constraints and tasks at the same time. In the context of torque controlled robotic systems, we provide an approach to simultaneously deal with a multitude of tasks and constraints which are arranged in a hierarchy, utilizing the large number of actuated joints of the manipulator. To this end, we propose a continuous null space projection technique to consider unilateral constraints, singular Jacobian matrices and dynamic variations of the priority order within the hierarchical structure. We show that activating and deactivating tasks as well as crossing singularities does not lead to a discontinuous control law. Simulations and experiments on the humanoid Justin of the German Aerospace Center (DLR) validate our approach. The presented concept is supposed to contribute to whole-body control frameworks.