Continuous-time iterative linear-quadratic regulator

TL;DR

This paper introduces a continuous-time iterative linear-quadratic regulator with a novel regularization and backtracking line-search, enabling effective trajectory optimization for non-convex problems like cart-pole swing-up, while leveraging high-order adaptive solvers.

Contribution

It presents a continuous-time version of the iterative LQ algorithm with new regularization and line-search techniques, improving non-convex trajectory optimization.

Findings

Successfully applied to cart-pole swing-up problem

Compatible with high-order adaptive-step numerical solvers

Balances function evaluations and discretization error effectively

Abstract

We present a continuous-time equivalent to the well-known iterative linear-quadratic algorithm including an implementation of a backtracking line-search policy and a novel regularization approach based on the necessary conditions in the Riccati pass of the linear-quadratic regulator. This allows the algorithm to effectively solve trajectory optimization problems with non-convex cost functions, which is demonstrated on the cart-pole swing-up problem. The algorithm compatibility with state-of-the-art suites of numerical integration solvers allows for the use of high-order adaptive-step methods. Their use results in a variable number of time steps both between passes of the algorithm and across iterations, maintaining a balance between the number of function evaluations and the discretization error.