Infinite-Horizon Value Function Approximation for Model Predictive Control

TL;DR

This paper proposes a neural network-based method to approximate the infinite horizon value function in model predictive control, enhancing stability and safety in robotic motion planning with real-time constraints.

Contribution

It introduces a novel approach to approximate the infinite horizon value function using neural networks, enabling stable and safe MPC with large horizons and constraints.

Findings

Neural network approximation improves MPC stability.

Using the value function as a terminal cost enhances safety.

Validated on toy problems and real-world obstacle avoidance.

Abstract

Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and stability. In practice, practitioners have to carefully design cost functions that can imitate an infinite horizon formulation, which is tedious and often results in local minima. In this work, we study how to approximate the infinite horizon value function of constrained optimal control problems with neural networks using value iteration and trajectory optimization. Furthermore, we experimentally demonstrate how using this value function approximation as a terminal cost provides global stability to the model predictive controller. The approach is validated on two toy problems and a real-world scenario with online obstacle avoidance on an industrial manipulator where the value function is conditioned to the goal and obstacle.