Jonathan Frey

Alessandro Saviolo, Jonathan Frey, Abhishek Rathod et al.

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.

Andrea Ghezzi, Jasper Hoffman, Jonathan Frey et al.

This work presents a novel loss function for learning nonlinear Model Predictive Control policies via Imitation Learning. Standard approaches to Imitation Learning neglect information about the expert and generally adopt a loss function based on the distance between expert and learned controls. In this work, we present a loss based on the Q-function directly embedding the performance objectives and constraint satisfaction of the associated Optimal Control Problem (OCP). However, training a Neural Network with the Q-loss requires solving the associated OCP for each new sample. To alleviate the computational burden, we derive a second Q-loss based on the Gauss-Newton approximation of the OCP resulting in a faster training time. We validate our losses against Behavioral Cloning, the standard approach to Imitation Learning, on the control of a nonlinear system with constraints. The final results show that the Q-function-based losses significantly reduce the amount of constraint violations while achieving comparable or better closed-loop costs.

Amon Lahr, Joshua Näf, Kim P. Wabersich et al.

Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based dynamics models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.

Jonathan Frey, Katrin Baumgärtner, Gianluca Frison et al.

The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms. While approaches presented in the machine learning community are limited to convex or unconstrained formulations, this paper discusses the computation of solution sensitivities of general nonlinear programs (NLPs) using the implicit function theorem (IFT) and smoothed optimality conditions treated in interior-point methods (IPM). We detail sensitivity computation within a sequential quadratic programming (SQP) method which employs an IPM for the quadratic subproblems. The publication is accompanied by an efficient open-source implementation within the framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solver mpc.pytorch.