Real-Time Optimal Control via Transformer Networks and Bernstein Polynomials

TL;DR

This paper introduces a Transformer-based method trained offline with Bernstein collocation data to rapidly generate near-optimal control trajectories for real-time applications like autonomous vehicle motion planning.

Contribution

It presents a novel framework combining Transformers and Bernstein polynomials for real-time solutions to infinite-dimensional optimal control problems.

Findings

Effective in generating feasible trajectories for control tasks.

Demonstrates rapid computation suitable for real-time applications.

Shows promising results on classical and obstacle avoidance problems.

Abstract

In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data generated by solving a sample of infinite- dimensional optimization problems using composite Bernstein collocation. Once trained, the Transformer efficiently generates near-optimal, feasible trajectories, making it well-suited for real-time applications. In motion planning for autonomous vehicles, for instance, these trajectories can serve to warm- start optimal motion planners or undergo rigorous evaluation to ensure safety. We demonstrate the effectiveness of this method through numerical results on a classical control problem and an online obstacle avoidance task. This data-driven approach offers a promising solution for real-time optimal control of nonlinear, nonconvex systems.