Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems
2026-04-27 • Machine Learning
Machine LearningRobotics
AI summaryⓘ
The authors developed a new control method that helps robots follow paths accurately by learning from past movements, but in a way that runs faster on computers. Their approach uses a special mathematical property called differential flatness, which many robots have, to handle complicated systems with multiple controls. Unlike previous methods, theirs can respect limits on the robot's inputs and states and works on a wide range of machines. They tested their method in simulations and real robots, finding it performs well and is much more efficient than some existing techniques.
learning-based controldifferential flatnessnonlinear systemsmulti-input systemsinput constraintsLyapunov stabilityconvex optimizationmodel predictive controlGaussian process
Authors
Tobias A. Farger, Adam W. Hall, Angela P. Schoellig
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.