Differential dynamic programming with stagewise equality and inequality constraints using interior point method

TL;DR

This paper introduces an interior point method for Differential Dynamic Programming that efficiently handles arbitrary stagewise equality and inequality constraints, demonstrated through various control system examples.

Contribution

It presents a novel interior point approach for DDP with explicit update formulas, enabling effective handling of complex constraints in optimal control problems.

Findings

Successfully applied to inverted pendulum and other systems

Demonstrates improved constraint handling in DDP

Provides explicit formulas for variable updates

Abstract

Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as augmented lagrangian methods, active set methods, and barrier methods. In this paper, we use an interior point method, which is a type of barrier method, to incorporate arbitrary stagewise equality and inequality state and control constraints. We also provide explicit update formulas for all the involved variables. Finally, we apply this algorithm to example systems such as the inverted pendulum, a continuously stirred tank reactor, car parking, and obstacle avoidance.