Integrated Hierarchical Decision-Making in Inverse Kinematic Planning and Control

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 decisionmaking from inverse kinematics (some times approximated by reachability methods), or employ efficient but less versatile ℓ1-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 ℓ0-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.• Planning (SHIK-P): directly solving nonlinear sparse hierarchical IK and decision-making planning problems.• Control (SHIK-C): solving sparse hierarchical IK and decision-making instantaneously for real-time control.The main contributions of this work are as follows:• We propose a novel and efficient sequential sparse hierarchical quadratic programming solver (S-SHQP) for sparse hierarchical nonlinear programs (SH-NLP).This enables robot IK planning and control with autonomous and reliable hierarchical decision-making, for example when choosing among multiple Cartesian locations with different prioritized end-effector tasks.Prioritization overcomes the difficulty of weighting tasks against logarithmic surrogate functions of the used ℓ 0 -norm formulations.• Our method enables real-time decision-making in milliseconds for complex whole-body robotic systems due to linear dependency on the number of candidates.This enables efficient selection from a large set of candidate locations without relying on reachability approximations.By simultaneously considering whole-body IK, an immediate certificate of kinematic reachability is obtained.• Unlike sparse programming methods based on the ℓ 1 -norm, our ℓ 0 -norm based formulation is versatile and agnostic to the specific formulation of the decision-functions.For example, it enables decision-making with vector-valued functions which have been turned into scalars by leastsquares.• Our method enables parallel decision-making from the same set of candidates while avoiding double-allocation.This is important in robotics as end-effectors like the left and right feet typically choose from the same set of candidate locations.• A wide range of whole-body IK planning and control applications with integrated hierarchical decision-making for both humanoids and manipulators are presented, while reiterating on the advantages of the ℓ 0 -norm over the ℓ 1norm and MINLP.