Constraint-based specification of hybrid position-impedance-force tasks

This work aims to extend the application field of the constraint-based control framework called iTaSC (instantaneous task specification using constraints) toward tasks where physical interaction between the robot and the environment, or a human, is contemplated. iTaSC, in its original formulation, allows for a systematic derivation of control schemes from task descriptions; tasks are defined as constraints enforced on outputs (e.g. distances, angles), and the iTaSC control takes care to fulfil such constraints by computing desired velocities to be commanded to the robot(s) joints. This approach, being based on a velocity resolution scheme, principally addresses tasks where positioning is the main issue. However, tasks that involve contacts with the environment or with the user, either desired or accidental, can be considered as well, taking advantage of impedance control, when position is controlled, or with force control. This paper describes the implementation of force tasks, and, by the combination of conflicting force and position tasks, impedance control, within the iTaSC formalism. This result is achieved by taking advantage of an approximate physical modelling of the robotic system and the environment. The proposed control scheme is tested by means of experiments where constraints on forces and/or positions described in cylindrical coordinates are imposed on a Kuka LWR arm.