Latent Linear Quadratic Regulator for Robotic Control Tasks

2024-07-15

arXiv.org

AI Summary

To address the high computational cost and poor real-time deployability of nonlinear Model Predictive Control (MPC), this paper proposes Learned Linear Quadratic Regulator (LaLQR)—the first framework to learn an implicit latent-space transformation that maps nonlinear dynamics and non-quadratic costs into linear dynamics and quadratic costs in the latent space, enabling efficient LQR-based control synthesis. LaLQR jointly optimizes the latent mapping and controller via end-to-end differentiable imitation learning, balancing accuracy, real-time performance, and generalization. The method integrates deep neural networks for representation learning, classical LQR theory, and MPC-driven supervised learning. Evaluated across diverse robotic control tasks, LaLQR achieves over 10× faster inference than standard nonlinear MPC while significantly outperforming both traditional MPC and learned neural controllers in generalization—without sacrificing control accuracy.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a $ extbf{la}$tent $ extbf{l}$inear $ extbf{q}$uadratic $ extbf{r}$egulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.

Problem

• Efficient robotic control using latent space
• Reducing computational cost in MPC
• Improving generalization in nonlinear dynamics

Innovation

• Latent space linearization
• Quadratic cost optimization
• MPC imitation learning