Safe and robust learning control with Gaussian processes

Berkenkamp, Felix; Schoellig, Angela P.

doi:10.1109/ecc.2015.7330913

Cited by 137 publications

(123 citation statements)

References 18 publications

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“…These numerical variance values can be used to provide an indication of the quality of models created. Recently, it has been applied to learn partial quadrotor dynamics [22]. Another learning based MPC method can be found in [23].…”

Section: Introductionmentioning

confidence: 99%

Gaussian Process Model Predictive Control of unmanned quadrotors

Cao

Lai

Alam

2016

2016 2nd International Conference on Control, Automation and Robotics (ICCAR)

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Two issues of quadrotor control without deterministic dynamical equations are addressed in this paper by using Gaussian Process (GP) based Model Predictive Control (MPC) algorithm. Firstly, the first issue of modelling unknown dynamical motions is solved by using GP models based on sampled data. In this way, the model uncertainty can be numerically evaluated during modelling and prediction process. This is not easy when using other data-driven methods, such as Artificial Neural Networks (ANN) and Fuzzy Models (FMs). Then a MPC scheme based on obtained GP models is proposed to address the second issue of designing appropriate quadrotor controllers. The proposed algorithm directly takes model uncertainty into account when planning MPC policies, and can be computationally efficiently implemented through using analytical gradients in the optimization process. The performance of quadrotor control using proposed approach is demonstrated by simulations on a trajectory tracking problem.

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Section: Introductionmentioning

confidence: 99%

Gaussian Process Model Predictive Control of unmanned quadrotors

Cao

Lai

Alam

2016

2016 2nd International Conference on Control, Automation and Robotics (ICCAR)

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“…The next data point is selected by sampling the most uncertain decision. This approach is used to learn a stabilization task on a quadrotor vehicle in [1].…”

Section: Safe Explorationmentioning

confidence: 99%

Combined Optimization and Reinforcement Learning for Manipulation Skills

Englert

Toussaint

Robotics: Science and Systems XII

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Abstract-This work addresses the problem of how a robot can improve a manipulation skill in a sample-efficient and secure manner. As an alternative to the standard reinforcement learning formulation where all objectives are defined in a single reward function, we propose a generalized formulation that consists of three components: 1) A known analytic control cost function; 2) A black-box return function; and 3) A black-box binary success constraint. While the overall policy optimization problem is highdimensional, in typical robot manipulation problems we can assume that the black-box return and constraint only depend on a lower-dimensional projection of the solution. With our formulation we can exploit this structure for a sample-efficient learning framework that iteratively improves the policy with respect to the objective functions under the success constraint. We employ efficient 2nd-order optimization methods to optimize the high-dimensional policy w.r.t. the analytic cost function while keeping the lower dimensional projection fixed. This is alternated with safe Bayesian optimization over the lower-dimensional projection to address the black-box return and success constraint. During both improvement steps the success constraint is used to keep the optimization in a secure region and to clearly distinguish between motions that lead to success or failure. The learning algorithm is evaluated on a simulated benchmark problem and a door opening task with a PR2.

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“…of the sum of the functions available with (8), is used for conditioning on the output of the individual functions (5). The hyperparameter vector is extended accordingly, ψ sum = [ψ a ψ b ] and also determined by optimization (4), where K = K sum and y f = y sum .…”

Section: B Expressing Structure In Kernelsmentioning

confidence: 99%

“…and k f , K f are computed according to (8) and (5) for the SE kernel. Under this assumption, Proposition 1 can be relaxed with respect to the choice of the gain k c .…”

Section: Tighter Bound With Training Datamentioning

confidence: 99%

“…However, a formal analysis from a control point of view is missing. The necessary convergence analysis of a Gaussian process dynamical model was first conducted in [6], [7] and the work in [8] uses a GP to safely explore the state space of a dynamical system. For the stability analysis, it makes use of a further favorable property of a GP: It provides, along with the estimated function value, a measure for the model fidelity depending on the state space region.…”

Section: Introductionmentioning

confidence: 99%

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Feedback linearization using Gaussian processes

Umlauft

Beckers

Kimmel

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-Data-driven approaches from machine learning provide powerful tools to identify dynamical systems with limited prior knowledge of the model structure. This paper utilizes Gaussian processes, a Bayesian nonparametric approach, to learn a model for feedback linearization. By using a proper kernel structure, the training data for identification is collected while an existing controller runs the system. Using the identified dynamics, an improved controller, based on feedback linearization, is proposed. The analysis shows that the resulting system is globally uniformly ultimately bounded. We further derive a relationship between the training data of the system and the size of the ultimate bound to which the system converges with a certain probability. A simulation of a robotic system illustrates the proposed method.

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Safe and robust learning control with Gaussian processes

Cited by 137 publications

References 18 publications

Gaussian Process Model Predictive Control of unmanned quadrotors

Gaussian Process Model Predictive Control of unmanned quadrotors

Combined Optimization and Reinforcement Learning for Manipulation Skills

Feedback linearization using Gaussian processes

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