Deterministic Trajectory Optimization through Probabilistic Optimal Control

TL;DR

This paper introduces two algorithms for deterministic trajectory optimization based on probabilistic optimal control, leveraging the Expectation-Maximization algorithm to improve convergence and stability in nonlinear systems.

Contribution

It presents novel algorithms derived from probabilistic optimal control that enhance convergence and stability in deterministic nonlinear trajectory optimization.

Findings

Algorithms show improved convergence speed

Enhanced numerical stability demonstrated

Effective on various nonlinear systems

Abstract

In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an emerging theoretical paradigm that we refer to as probabilistic optimal control. The paradigm reformulates stochastic optimal control as an equivalent probabilistic inference problem and can be viewed as a generalisation of the former. The merit of this perspective is that it allows to address the problem using the Expectation-Maximization algorithm. It is shown that the application of this algorithm results in a fixed point iteration of probabilistic policies that converge to the deterministic optimal policy. Two strategies for policy evaluation are discussed, using state-of-the-art uncertainty quantification methods resulting into two distinct algorithms. The algorithms are structurally closest related to the differential dynamic programming algorithm and related methods that use sigma-point methods to avoid direct gradient evaluations. The main advantage of the algorithms is an improved balance between exploration and exploitation over the iterations, leading to improved numerical stability and accelerated convergence. These properties are demonstrated on different nonlinear systems.