Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.

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“…The inputs to the system are the motor duty cycle p and the steering angle δ. For details on the system modeling please refer to [44], [28].…”

Section: A Car Dynamicsmentioning

confidence: 99%

Cautious Model Predictive Control Using Gaussian Process Regression

Hewing

Kabzan

Zeilinger

2020

IEEE Trans. Contr. Syst. Technol.

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415

334

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“…where the policies π j k|t are defined in (5). Now, we notice that by linearity of system (1), if a state x ∈ CS j is expressed as a convex combination of the stored states x = X j λ j , then the input u = U j λ j ∈ U will keep the evolution of the system in CS j for all disturbance realizations.…”

Section: Set Of Safe Policiesmentioning

confidence: 99%

“…Afterwards, robust MPC strategies for additive [28] or parametric [29], [30] uncertainty are used to guarantee recursive constraint satisfaction. Another strategy to identify the system dynamics is to fit a Gaussian Process (GP) to experimental data [2]- [5]. U.…”

Section: Introductionmentioning

confidence: 99%

“…Rosolia GP can be used to identify a nominal model and confidence bounds, which may be used to tighten the constraint set over the planning horizon. This strategy provides high-probability safety guarantees [3], [5]. The effectiveness of GP-based strategies on experimental platform has been shown in [4], [5], where an MPC is used to race a 1/43-scale vehicle and to safely fly a drone.…”

Section: Introductionmentioning

confidence: 99%

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Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

Rosolia

Borrelli

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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A robust Learning Model Predictive Controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task the closed-loop state, input and cost are stored and used in the controller design. This paper first illustrates how to construct robust invariant sets and safe control policies exploiting historical data. Then, we propose an iterative LMPC design procedure, where data generated by a robust controller at iteration j are used to design a robust LMPC at the next j + 1 iteration. We show that this procedure allows us to iteratively enlarge the domain of the control policy and it guarantees recursive constraints satisfaction, input to state stability and performance bounds for the certainty equivalent closed-loop system. The use of an adaptive prediction horizon is the key element of the proposed design. The effectiveness of the proposed control scheme is illustrated on a linear system subject to bounded additive disturbance. arXiv:1911.09234v1 [eess.SY]

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“…In particular, our approach is related to the ones based on optimal control framework, see, e.g., [19]- [21], [24]- [26]. For example, in [19], the authors have utilized the GP model to learn the dynamics of the plant, and they have formulated a model predictive control (MPC), in which the optimal control problem is solved for each time step based on the knowledge about the dynamics learned by the GP. In contrast to these previous methods, we provide an approach that jointly learns the dynamics of the plant and the self-triggered controller, aiming at reducing the number of communication time steps for NCSs.…”

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confidence: 99%

Learning Self-Triggered Controllers With Gaussian Processes

Hashimoto

Yoshimura

Ushio

2021

IEEE Trans. Cybern.

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This paper investigates the design of self-triggered controllers for networked control systems (NCSs), where the dynamics of the plant is unknown apriori. To deal with the unknown transition dynamics, we employ the Gaussian process (GP) regression in order to learn the dynamics of the plant. To design the self-triggered controller, we formulate an optimal control problem, such that the optimal pair of the inter-communication time step and control input can be determined based on the GP dynamics of the plant. Moreover, we provide an overall implementation algorithm that jointly learns the dynamics of the plant and the self-triggered controller based on a reinforcement learning framework. Finally, a numerical simulation illustrates the effectiveness of the proposed approach.

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Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

Cited by 107 publications

References 21 publications

Cautious Model Predictive Control Using Gaussian Process Regression

Cautious Model Predictive Control Using Gaussian Process Regression

Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

Learning Self-Triggered Controllers With Gaussian Processes

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