Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems

TL;DR

This paper introduces a differential flatness-based learning control method for multi-input systems that efficiently handles constraints and guarantees stability, outperforming existing Gaussian process MPC in simulations and experiments.

Contribution

It extends flatness-based learning control to multi-input, constrained systems with probabilistic stability guarantees, improving efficiency and applicability.

Findings

Achieves similar performance to Gaussian process MPC in simulation

Handles input and state constraints effectively

Demonstrates competitive real hardware tracking

Abstract

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.