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Kinematic control of redundant manipulators: generalizing the task priority framework to inequality tasks

Oussama Kanoun 1, 2, * Florent Lamiraux 3 Pierre-Brice Wieber 4, 5 
* Corresponding author
3 LAAS-GEPETTO - Équipe Mouvement des Systèmes Anthropomorphes
LAAS - Laboratoire d'analyse et d'architecture des systèmes
5 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : The redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an Ordinary Differential Equation. When facing simultaneous tasks, the corresponding equations can be grouped in a single system, or better, sorted in priority and solved each in the solutions set of higher priority tasks. This elegant framework for hierarchical task regulation has been implemented as a sequence of Least Squares problems. Its limitation lies in the handling of inequality constraints, which are usually transformed into more restrictive equality constraints through potential fields. In this paper, we propose a new prioritized task regulation framework based on a sequence of quadratic programs (QP) that removes the limitation. At the basis of the proposed algorithm is a study of the optimal sets resulting from the sequence of QPs. The algorithm is implemented and illustrated in simulation on the humanoid robot HRP-2.
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Oussama Kanoun, Florent Lamiraux, Pierre-Brice Wieber. Kinematic control of redundant manipulators: generalizing the task priority framework to inequality tasks. IEEE Transactions on Robotics, IEEE, 2011, 27 (4), pp.785-792. ⟨10.1109/TRO.2011.2142450⟩. ⟨hal-00486755v2⟩

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