Hierarchical quadratic programming: Fast online humanoid-robot motion generation

TLDR

Hierarchical least‑square optimization is commonly used in robotics to solve inverse problems with multiple incompatible objectives, such as inverse kinematics or dynamics, where objectives can be expressed as equalities or satisfaction areas like point‑to‑point tasks or joint ranges. The paper proposes a complete solution for solving multiple least‑square quadratic problems with equality and inequality constraints in a strict hierarchy, aiming to resolve humanoid robot redundancy and generate complex movements in constrained environments. The generic solver handles inequalities at any level and solves equality hierarchies ten times faster than iterative‑projection hierarchical solvers, operating at typical control frequencies on whole‑body size problems. Our method solves a hierarchy of only equalities 10 times faster than iterative‑projection hierarchical solvers and can consider inequalities at any level while running at the typical control frequency on whole‑body size problems.

Abstract

Hierarchical least-square optimization is often used in robotics to inverse a direct function when multiple incompatible objectives are involved. Typical examples are inverse kinematics or dynamics. The objectives can be given as equalities to be satisfied (e.g. point-to-point task) or as areas of satisfaction (e.g. the joint range). This paper proposes a complete solution to solve multiple least-square quadratic problems of both equality and inequality constraints ordered into a strict hierarchy. Our method is able to solve a hierarchy of only equalities 10 times faster than the iterative-projection hierarchical solvers and can consider inequalities at any level while running at the typical control frequency on whole-body size problems. This generic solver is used to resolve the redundancy of humanoid robots while generating complex movements in constrained environments.