Integrated Hierarchical Decision-Making in Inverse Kinematic Planning and Control

TL;DR

This paper introduces a novel nonlinear programming framework that integrates hierarchical decision-making with whole-body inverse kinematic planning, enabling efficient and versatile solutions to complex robotics problems.

Contribution

It develops a sparse hierarchical nonlinear programming solver that leverages the $$-norm and hierarchical structure, addressing complex inverse kinematic decision-making tasks previously unaddressed.

Findings

Solver efficiently handles complex nonlinear hierarchical problems.

Enables simultaneous selection of end-effector locations from many candidates.

Addresses inverse kinematic control with bi-manual grasp selection on rotated objects.

Abstract

This work presents a novel and efficient nonlinear programming framework that tightly integrates hierarchical decision-making with whole-body inverse kinematic planning and control. Decision-making plays a central role in many aspects of robotics, from sparse inverse kinematic control with a minimal number of joints, to inverse kinematic planning while simultaneously selecting a discrete end-effector location from multiple candidates. Current approaches often rely on heavy computations using mixed-integer nonlinear programming, separate decision-making from inverse kinematics (some times approximated by reachability methods), or employ efficient but less versatile $\ell_1$-norm formulations of linear sparse programming, without addressing the underlying nonlinear problem formulations. In contrast, the proposed sparse hierarchical nonlinear programming solver is efficient, versatile, and accurate by exploiting sparse hierarchical structure and leveraging the $\ell_0$-norm which is rarely used in robotics. The solver efficiently tackles complex nonlinear hierarchical decision-making problems previously unaddressed in the literature, such as inverse kinematic planning with simultaneous prioritized selection of end-effector locations from a large set of candidates, or inverse kinematic control with simultaneous selection of bi-manual grasp locations on a randomly rotated box.