@Article{pfeiffer:ral:2018,
  author    = {Pfeiffer, Kai and Escande, Adrien and Kheddar, Abderrahmane},
  title     = {Singularity resolution in equality and inequality constrained hierarchical task-space control by adaptive non-linear least-squares},
  journal   = {IEEE Robotics and Automation Letters},
  year      = {2018},
  volume    = {3},
  number    = {4},
  pages     = {3630--3637},
  month     = {October},
  doi       = {10.1109/LRA.2018.2855265},
  url       = {https://hal.science/hal-01852576v1/file/2018\_PfeifferEscandeKheddar\_singularityResolution.pdf},
  keywords  = {Redundant robots, humanoid robots, kinematics, motion control, optimization and optimal control.},
  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 nonlinear 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 trueHessian. 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.},
  publisher = {IEEE-INST Electrical Electronics Engineers Inc},
  address   = {445 Hoes Lane, Piscataway, NJ 08855-4141, USA}
}