Singularity resolution in equality and inequality constrained hierarchical task-space control by adaptive non-linear least-squares

Kai Pfeiffer 1 Adrien Escande 1 Abderrahmane Kheddar 2, 1
2 IDH - Interactive Digital Humans
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We propose a robust method to handle kinematic and algorithmic singularities of any kinematically redundant robot under task-space hierarchical control with ordered equalities and inequalities. Our main idea is to exploit a second order model of the non-linear kinematic function, in the sense of the Newton's method in optimization. The second order information is provided by a hierarchical BFGS algorithm omitting the heavy computation required for the true Hessian. In the absence of singularities, which is robustly detected, we use the Gauss-Newton algorithm that has quadratic convergence. In all cases we keep a least-squares formulation enabling good computation performances. Our approach is demonstrated in simulation with a simple robot and a humanoid robot, and compared to state-of-the-art algorithms.
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Kai Pfeiffer, Adrien Escande, Abderrahmane Kheddar. Singularity resolution in equality and inequality constrained hierarchical task-space control by adaptive non-linear least-squares. IEEE Robotics and Automation Letters, IEEE 2018, 3 (4), pp.3630-3637. ⟨10.1109/LRA.2018.2855265⟩. ⟨hal-01852576⟩

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