Non-Linear Model Predictive Control with Adaptive Time-Mesh Refinement

TL;DR

This paper introduces an adaptive time-mesh refinement strategy for Non-Linear Model Predictive Control, significantly improving real-time trajectory optimization accuracy and efficiency in UAV simulations.

Contribution

It proposes a novel adaptive time-mesh refinement method for NMPC that enhances accuracy and computational speed, suitable for real-time applications.

Findings

Achieves high-accuracy trajectory planning within milliseconds.

Validates approach on UAV simulation platform.

Open-source implementation available.

Abstract

In this paper, we present a novel solution for real-time, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs over an adaptive lattice. In common approximated OCP solutions, the number of discretization points composing the lattice represents a critical upper bound for real-time applications. The proposed NMPC-based technique refines the initially uniform time horizon by adding time steps with a sampling criterion that aims to reduce the discretization error. This enables a higher accuracy in the initial part of the receding horizon, which is more relevant to NMPC, while keeping bounded the number of discretization points. By combining this feature with an efficient Least Square formulation, our solver is also extremely time-efficient, generating trajectories of multiple seconds within only a few milliseconds. The performance of the proposed approach has been validated in a high fidelity simulation environment, by using an UAV platform. We also released our implementation as open source C++ code.