Viable Multi-Contact Posture Computation for Humanoid Robots using Nonlinear Optimization on Manifolds

Abstract

Humanoid robots are complex poly-articulated structures with nonlinear kinematics and dynamics. Finding viable postures to realize set-point task objectives under a set of constraints (intrinsic and extrinsic limitations) is a key issue in the planning of robot motion and animportant feature of any robotics framework. It is handled by the so called posture generator (PG) that consists in formalizing the viable posture as the solution to a nonlinear optimization problem. We present several extensions to the state-of-the-art by exploring new formulationsand resolution methods for posture generation problems. We reformulate the notion of contact constraints by adding variables to enrich the optimization problem and allow the solver to decide the shape of intersection of contact polygons, or of the location of a contactpoint on a non-flat surface. We present a reformulation of the posture generation problem that encompasses non-Euclidean manifolds natively and presents a more elegant and efficient mathematical formulation of it. To solve such problems, we implemented a new SQP solver that is particularly suited to handle non-Euclidean manifolds structures. By doing so, we have a better mastering in the way to tune and specialize our solver for robotics problems.