Newton methods for k-order Markov Constrained Motion Problems

TL;DR

This paper presents a flexible framework for robot motion optimization using classical constrained optimization methods, including a novel anytime Augmented Lagrangian approach, designed for efficiency and generality.

Contribution

It introduces a general problem formulation and abstractions that facilitate the application of classical optimization algorithms to robot motion problems, including a new anytime Augmented Lagrangian method.

Findings

Efficient application of classical optimization methods to robot motion problems.

Introduction of a novel anytime Augmented Lagrangian algorithm.

Framework supports a broad class of robot motion optimization problems.

Abstract

This is a documentation of a framework for robot motion optimization that aims to draw on classical constrained optimization methods. With one exception the underlying algorithms are classical ones: Gauss-Newton (with adaptive step size and damping), Augmented Lagrangian, log-barrier, etc. The exception is a novel any-time version of the Augmented Lagrangian. The contribution of this framework is to frame motion optimization problems in a way that makes the application of these methods efficient, especially by defining a very general class of robot motion problems while at the same time introducing abstractions that directly reflect the API of the source code.