Inverse dynamics control and feedforward linearization techniques are typically used to convert the complex nonlinear dynamics of robots to a set of decoupled double integrators, and then a standard, outer-loop controller can be used to calculate the commanded acceleration for the linearized system. However, these methods typically depend on having a very accurate system model, which is not available in practice. While this challenge has been addressed in the literature using different learning approaches, most of these approaches do not provide safety guarantees in terms of stability of the learning-based control system. In this paper, we provide a novel, learning-based control approach based on Gaussian processes (GPs) that ensures both stability of the closed-loop system and high-accuracy tracking. In our proposed approach, we use GPs to approximate the error between the commanded acceleration and the actual acceleration of the system, and then use the predicted mean and variance of the GP to calculate an upper bound on the uncertainty of the linearization. This uncertainty bound is then used in a robust, outer-loop controller to ensure stability of the overall system. Moreover, we show that using our proposed strategy, the tracking error converges to a ball with a radius that can be made arbitrarily small through appropriate control design. Furthermore, we verify the effectiveness of the proposed approach via simulations on (i) a 2 degree-of-freedom (DOF) planar manipulator, and (ii) a 6 DOF industrial manipulator using the Gazebo simulator.
In @cite_1 @cite_14 , GPs are utilized to learn the errors in the output torques of the inverse dynamics model online. In @cite_1 , the GP learning is combined with a state-of-the-art gradient descent method for learning feedback terms online. The main idea behind this approach is that the gradient descent method would correct for fast perturbations, while the GP is responsible for correcting slow perturbations. This allows for exponential smoothing of the GP hyperparameters, which increases the robustness of the GP at the cost of having slower reactiveness. Nevertheless, @cite_1 does not provide a proof of the robust stability of the closed-loop system. @cite_14 , the variance of the GP prediction is utilized to adapt the parameters of an outer-loop PD controller online, and the uniform ultimate boundedness of the tracking error is proved under some assumptions on the structure of the PD controller (e.g., the gain matrix was assumed to be diagonal, which imposes a decentralized gain control scheme). The results of @cite_14 are verified via simulations on a 2 DOF manipulator.
@cite_14 @cite_1
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Learning of inverse dynamics modeling errors is key for compliant or force control when analytical models are only rough approximations. Thus, designing real time capable function approximation algorithms has been a necessary focus towards the goal of online model learning. However, because these approaches learn a mapping from actual state and acceleration to torque, good tracking is required to observe data points on the desired path. Recently it has been shown how online gradient descent on a simple modeling error offset term to minimize tracking at acceleration level can address this issue. However, to adapt to larger errors a high learning rate of the online learner is required, resulting in reduced compliancy. Thus, here we propose to combine both approaches: The online adapted offset term ensures good tracking such that a nonlinear function approximator is able to learn an error model on the desired trajectory. This, in turn, reduces the load on the adaptive feedback, enabling it to use a lower learning rate. Combined this creates a controller with variable feedback and low gains, and a feedforward model that can account for larger modeling errors. We demonstrate the effectiveness of this framework, in simulation and on a real system. This paper introduces a learning-based robust control algorithm that provides robust stability and performance guarantees during learning. The approach uses Gaussian process (GP) regression based on data gathered during operation to update an initial model of the system and to gradually decrease the uncertainty related to this model. Embedding this data-based update scheme in a robust control framework guarantees stability during the learning process. Traditional robust control approaches have not considered online adaptation of the model and its uncertainty before. As a result, their controllers do not improve performance during operation. Typical machine learning algorithms that have achieved similar high-performance behavior by adapting the model and controller online do not provide the guarantees presented in this paper. In particular, this paper considers a stabilization task, linearizes the nonlinear, GP-based model around a desired operating point, and solves a convex optimization problem to obtain a linear robust controller. The resulting performance improvements due to the learning-based controller are demonstrated in experiments on a quadrotor vehicle. Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian Process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other nonparametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and nu-SVR. Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other non-parametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and ν-SVR. We present a policy search method for learning complex feedback control policies that map from high-dimensional sensory inputs to motor torques, for manipulation tasks with discontinuous contact dynamics. We build on a prior technique called guided policy search (GPS), which iteratively optimizes a set of local policies for specific instances of a task, and uses these to train a complex, high-dimensional global policy that generalizes across task instances. We extend GPS in the following ways: (1) we propose the use of a model-free local optimizer based on path integral stochastic optimal control (PI2), which enables us to learn local policies for tasks with highly discontinuous contact dynamics; and (2) we enable GPS to train on a new set of task instances in every iteration by using on-policy sampling: this increases the diversity of the instances that the policy is trained on, and is crucial for achieving good generalization. We show that these contributions enable us to learn deep neural network policies that can directly perform torque control from visual input. We validate the method on a challenging door opening task and a pick-and-place task, and we demonstrate that our approach substantially outperforms the prior LQR-based local policy optimizer on these tasks. Furthermore, we show that on-policy sampling significantly increases the generalization ability of these policies. We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling. We present a new Gaussian process (GP) regression model whose co-variance is parameterized by the the locations of M pseudo-input points, which we learn by a gradient based optimization. We take M ≪ N, where N is the number of real data points, and hence obtain a sparse regression method which has O(M2N) training cost and O(M2) prediction cost per test case. We also find hyperparameters of the covariance function in the same joint optimization. The method can be viewed as a Bayesian regression model with particular input dependent noise. The method turns out to be closely related to several other sparse GP approaches, and we discuss the relation in detail. We finally demonstrate its performance on some large data sets, and make a direct comparison to other sparse GP methods. We show that our method can match full GP performance with small M, i.e. very sparse solutions, and it significantly outperforms other approaches in this regime. The varied and complex dynamics of deformable terrain are significant impediments toward real-world viability of locomotive robotics, particularly for legged machines. We explore vertical jumping on granular media (GM) as a model task for legged locomotion on uncharacterized deformable terrain. By integrating (Gaussian process) GP-based regression and evaluation to estimate ground forcing as a function of state, a one-dimensional jumper acquires the ability to learn forcing profiles exerted by its environment in tandem to achieving its control objective. The GP-based dynamical model initially assumes a baseline rigid, non-compliant surface. As part of an iterative procedure, the optimizer employing this model generates an optimal control to achieve a target jump height while respecting known hardware limitations of the robot model. Trajectory and forcing data recovered from evaluation on the true GM surface model simulation is applied to train the GP, and in turn, provide the optimizer a more richly informed dynamical model of the environment. After three iterations, predicted optimal control trajectories coincide with execution results, within 1.2 jumping height error, as the GP-based approximation converges to the true GM model. GPS-equipped taxis can be viewed as pervasive sensors and the large-scale digital traces produced allow us to reveal many hidden "facts" about the city dynamics and human behaviors. In this paper, we aim to discover anomalous driving patterns from taxi's GPS traces, targeting applications like automatically detecting taxi driving frauds or road network change in modern cites. To achieve the objective, firstly we group all the taxi trajectories crossing the same source destination cell-pair and represent each taxi trajectory as a sequence of symbols. Secondly, we propose an Isolation-Based Anomalous Trajectory (iBAT) detection method and verify with large scale taxi data that iBAT achieves remarkable performance (AUC>0.99, over 90 detection rate at false alarm rate of less than 2 ). Finally, we demonstrate the potential of iBAT in enabling innovative applications by using it for taxi driving fraud detection and road network change detection. We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISSGP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling. While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive way to tackle these problems, by incorporating GPs in sum-product networks (SPNs), a recently proposed tractable probabilistic model allowing exact and efficient inference. In particular, by using GPs as leaves of an SPN we obtain a novel flexible prior over functions, which implicitly represents an exponentially large mixture of local GPs. Exact and efficient posterior inference in this model can be done in a natural interplay of the inference mechanisms in GPs and SPNs. Thereby, each GP is -- similarly as in a mixture of experts approach -- responsible only for a subset of data points, which effectively reduces inference cost in a divide and conquer fashion. We show that integrating GPs into the SPN framework leads to a promising probabilistic regression model which is: (1) computational and memory efficient, (2) allows efficient and exact posterior inference, (3) is flexible enough to mix different kernel functions, and (4) naturally accounts for non-stationarities in time series. In a variate of experiments, we show that the SPN-GP model can learn input dependent parameters and hyper-parameters and is on par with or outperforms the traditional GPs as well as state of the art approximations on real-world data. We present a novel algorithm to produce descriptive online 3D occupancy maps using Gaussian processes (GPs). GP regression and classification have met with recent success in their application to robot mapping, as GPs are capable of expressing rich correlation among map cells and sensor data. However, the cubic computational complexity has limited its application to large-scale mapping and online use. In this paper we address this issue first by proposing test-data octrees, octrees within blocks of the map that prune away nodes of the same state, condensing the number of test data used in a regression, in addition to allowing fast data retrieval. We also propose a nested Bayesian committee machine which, after new sensor data is partitioned among several GP regressions, fuses the result and updates the map with greatly reduced complexity. Finally, by adjusting the range of influence of the training data and tuning a variance threshold implemented in our method's binary classification step, we are able to control the richness of inference achieved by GPs - and its tradeoff with classification accuracy. The performance of the proposed approach is evaluated with both simulated and real data, demonstrating that the method may serve both as an improved-accuracy classifier, and as a predictive tool to support autonomous navigation. A deep fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP) in the limit of infinite network width. This correspondence enables exact Bayesian inference for neural networks on regression tasks by means of straightforward matrix computations. For single hidden-layer networks, the covariance function of this GP has long been known. Recently, kernel functions for multi-layer random neural networks have been developed, but only outside of a Bayesian framework. As such, previous work has not identified the correspondence between using these kernels as the covariance function for a GP and performing fully Bayesian prediction with a deep neural network. In this work, we derive this correspondence and develop a computationally efficient pipeline to compute the covariance functions. We then use the resulting GP to perform Bayesian inference for deep neural networks on MNIST and CIFAR-10. We find that the GP-based predictions are competitive and can outperform neural networks trained with stochastic gradient descent. We observe that the trained neural network accuracy approaches that of the corresponding GP-based computation with increasing layer width, and that the GP uncertainty is strongly correlated with prediction error. We connect our observations to the recent development of signal propagation in random neural networks. This paper presents a method for correcting dead reckoning parameters, which are heading and step size, for a pedestrian navigation system. In this method, the compass bias error and the step size error can be estimated during the period that the Global Positioning System (GPS) signal is available. The errors are used for correcting those parameters to improve the accuracy of position determination using only the dead reckoning system when the GPS signal is not available. The results show that the parameters can be estimated with reasonable accuracy. Moreover, the method also helps to increase the positioning accuracy when the GPS signal is available. A partially observable Markov decision process (POMDP) has been proposed as a dialog model that enables automatic optimization of the dialog policy and provides robustness to speech understanding errors. Various approximations allow such a model to be used for building real-world dialog systems. However, they require a large number of dialogs to train the dialog policy and hence they typically rely on the availability of a user simulator. They also require significant designer effort to hand-craft the policy representation. We investigate the use of Gaussian processes (GPs) in policy modeling to overcome these problems. We show that GP policy optimization can be implemented for a real world POMDP dialog manager, and in particular: 1) we examine different formulations of a GP policy to minimize variability in the learning process; 2) we find that the use of GP increases the learning rate by an order of magnitude thereby allowing learning by direct interaction with human users; and 3) we demonstrate that designer effort can be substantially reduced by basing the policy directly on the full belief space thereby avoiding ad hoc feature space modeling. Overall, the GP approach represents an important step forward towards fully automatic dialog policy optimization in real world systems. This paper addresses the path following control problem of wheeled mobile robots in the presence of wheel skidding and slipping. A conditional global positioning system (GPS)-based path following controller is proposed for four generic WMRs to achieve high-precision path following performance. The proposed controller utilizes real-time kinematic-GPS and other aiding sensors to determine the robot's pose and wheel skidding and slipping perturbations to achieve accurate path following control. The reported simulation and experimental results suggest that with this control scheme, the WMRs are able to maneuver with precision. © 2009 Wiley Periodicals, Inc. In genetic programming (GP), learning problems can be classified broadly into two types: those using data sets, as in supervised learning, and those using an environment as a source of feedback. An increasing amount of research has concentrated on the robustness or generalization ability of the programs evolved using GP. While some of the researchers report on the brittleness of the solutions evolved, others proposed methods of promoting robustness generalization. It is important that these methods are not ad hoc and are applicable to other experimental setups. In this paper, learning concepts from traditional machine learning and a brief review of research on generalization in GP are presented. The paper also identifies problems with brittleness of solutions produced by GP and suggests a method for promoting robustness generalization of the solutions in simulating learning behaviors using GP. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] 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. So far, many of the computational models for rendering music performance have been proposed, but they often consist of many heuristic rules and tend to be complex. It makes difficult to generate and select the useful rules, or perform the optimization of parameters in the rules. In this study, we present a new approach that automatically learns a computational model for rendering music performance with score information as an input and the corresponding real performance data as an output. We use a Gaussian Process (GP) incorporated with a Bayesian Committee Machine to reduce naive GP's heavy computation cost, to learn those input-output relationships. We compared three normalized errors: dynamics, attack time and release time between the real and predicted performance by the trained GP to evaluate our proposed scheme. We evaluated the learning ability and the generalization ability. The results show that the trained GP has an acceptable learning ability for 'known' pieces, but show insufficient generalization ability for 'unknown' pieces, suggesting that the GP can learn the expressive music performance without setting many parameters manually, but the size of the current training dataset is not sufficiently large so as to generalize the training pieces to 'unknown' test pieces.