Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics

TL;DR

This paper introduces a data-driven framework for rapid approximate global optimization in robotics, leveraging precomputed solutions to solve new problems efficiently, with theoretical analysis and practical application to inverse kinematics.

Contribution

It presents a novel approach to global optimization that uses precomputed solution maps, with theoretical conditions for sampling and demonstrated effectiveness in inverse kinematics.

Findings

Achieves near-globally optimal solutions in sub-millisecond time.

Provides theoretical bounds on sample requirements for approximation quality.

Successfully applied to collision-free inverse kinematics problems.

Abstract

This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near-globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics (IK) problems, wherein large solution databases are used to produce near-optimal solutions in sub-millisecond time on a standard PC.