Robust Differential Dynamic Programming

TL;DR

This paper introduces a robust variant of Differential Dynamic Programming that incorporates uncertainties through convex relaxations, enhancing trajectory generation for nonlinear systems under uncertain conditions.

Contribution

It develops a robust DDP algorithm using generalized plants and multiplier relaxations to handle uncertainties in nonlinear control problems.

Findings

Provides a new robust trajectory generation method for nonlinear systems.

Uses convex relaxations to effectively manage uncertainties.

Extends the Bellman principle to uncertain dynamic programming.

Abstract

Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input constraints. In this contribution, we develop a robust version of Differential Dynamic Programming that uses generalized plants and multiplier relaxations for uncertainties. To this end, we study a version of the Bellman principle and use convex relaxations to account for uncertainties in the dynamic program. The resulting algorithm can be seen as a robust trajectory generation tool for nonlinear systems.