Abstract
With this work we introduce the notion of physical feasibility into our previously presented method of kinematic and algorithmic singularity resolution for kinematics based robotic control. We begin by deriving Newton's method of multi-level constrained optimization and give a suitable expression for the hierarchical analytic Hessian. The link between optimization and robotic control is then created. We proceed to first reveal the difficulties of damping approaches for singularity resolution in acceleration based control. Consequently, Newton's method and the previously presented Quasi-Newton method are only well-defined in the velocity domain. This requires the conversion of the second-order equation of motion and motion controllers into first order by suitably applying forward integration. This way we achieve dynamically feasible kinematic control while being robust towards singularities by switching from the Gauss-Newton algorithm to the Newton's method using a reliable switching method. We verify our approach in three robot experiments on the HRP-2KAI humanoid robot where we supersede a classical damping based constrained optimization controller in terms of accuracy. Furthermore , the need for damping tuning is discarded. Thereby, the least-squares formulation of the Gauss-Newton algorithm and the Newton's method greatly facilitates real-time control by enabling the use of fast state-of-the art hierarchical quadratic programming solvers.