Adaptive Model Predictive Control for High-Accuracy Trajectory Tracking in Changing Conditions

Robots and automated systems are increasingly being introduced to unknown and dynamic environments where they are required to handle disturbances, unmodeled dynamics, and parametric uncertainties. Robust and adaptive control strategies are required to achieve high performance in these dynamic environments. In this paper, we propose a novel adaptive model predictive controller that combines model predictive control (MPC) with an underlying $\mathcal{L}_1$ adaptive controller to improve trajectory tracking of a system subject to unknown and changing disturbances. The $\mathcal{L}_1$ adaptive controller forces the system to behave in a predefined way, as specified by a reference model. A higher-level model predictive controller then uses this reference model to calculate the optimal reference input based on a cost function, while taking into account input and state constraints. We focus on the experimental validation of the proposed approach and demonstrate its effectiveness in experiments on a quadrotor. We show that the proposed approach has a lower trajectory tracking error compared to non-predictive, adaptive approaches and a predictive, non-adaptive approach, even when external wind disturbances are applied

Barrier-Certified Adaptive Reinforcement Learning with Applications to Brushbot Navigation

This paper presents a safe learning framework that employs an adaptive model learning algorithm together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique. We use the learned model in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding particular undesirable regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate an action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring the greedy policy improvement under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has previously been used under stationarity assumptions in the safe learnings literature, and is then tested on a real robot, the brushbot, whose dynamics is unknown, highly complex and nonstationary.Comment: \copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work