Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning

Gaussian Process priors with uncertain inputs? Application to multiple-step ahead time series forecasting

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form y t = f(Yt-1 ,..., Yt-L ), the prediction of y at time t + k is based on the point estimates of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction

Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting

The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods

Intrinsic Gaussian processes on complex constrained domains

We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising as complex subsets of Euclidean space. in-GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the proposed approach is to utilise the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels. This enables in-GPs to be practically applied in great generality, while existing approaches for smoothing on constrained domains are limited to simple special cases. The broad utilities of the in-GP approach is illustrated through simulation studies and data examples

Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly and instead use a set of informative "representatives" are desirable. The paper investigates this problem for the grouped mixed-effect GP model where each individual response is given by a fixed-effect, taken from one of a set of unknown groups, plus a random individual effect function that captures variations among individuals. Such models have been widely used in previous work but no sparse solutions have been developed. The paper presents the first sparse solution for such problems, showing how the sparse approximation can be obtained by maximizing a variational lower bound on the marginal likelihood, generalizing ideas from single-task Gaussian processes to handle the mixed-effect model as well as grouping. Experiments using artificial and real data validate the approach showing that it can recover the performance of inference with the full sample, that it outperforms baseline methods, and that it outperforms state of the art sparse solutions for other multi-task GP formulations.Comment: Preliminary version appeared in ECML201

Probabilistic movement modeling for intention inference in human-robot interaction.

Intention inference can be an essential step toward efficient humanrobot interaction. For this purpose, we propose the Intention-Driven Dynamics Model (IDDM) to probabilistically model the generative process of movements that are directed by the intention. The IDDM allows to infer the intention from observed movements using Bayes ’ theorem. The IDDM simultaneously finds a latent state representation of noisy and highdimensional observations, and models the intention-driven dynamics in the latent states. As most robotics applications are subject to real-time constraints, we develop an efficient online algorithm that allows for real-time intention inference. Two human-robot interaction scenarios, i.e., target prediction for robot table tennis and action recognition for interactive humanoid robots, are used to evaluate the performance of our inference algorithm. In both intention inference tasks, the proposed algorithm achieves substantial improvements over support vector machines and Gaussian processes.

Fast methods for training Gaussian processes on large data sets

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise when dealing with large data sets. Here, we derive some simple results which we have found useful for speeding up the learning stage in the GPR algorithm, and especially for performing Bayesian model comparison between different covariance functions. We apply our techniques to both synthetic and real data and quantify the speed-up relative to using nested sampling to numerically evaluate model evidences.Comment: Fixed missing reference