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

International audienceWe 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

Multi-Contact Postures Computation on Manifolds

International audienceWe propose a framework to generate static robot configurations satisfying a set of physical and geometrical constraints. This is done by formulating nonlinear constrained optimization problems over non-Euclidean manifolds and solving them. To do so, we present a new sequential quadratic programming (SQP) solver working natively on general manifolds, and propose an interface to easily formulate the problems, with the tedious and error-prone work automated for the user. We also introduce several new types of constraints for having more complex contacts or working on forces/torques. Our approach allows an elegant mathematical description of the constraints and we exemplify it through formulation and computation examples in complex scenarios with humanoid robots

Numerical approximation of a control problem for advection-diffusion processes

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