Gaussian Process Dynamical Models Research Articles

Prediction With Approximated Gaussian Process Dynamical Models

The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human–robot interaction, are often challenging or even infeasible due to the complexity of the system dynamics. In contrast, data-driven approaches need only a minimum of prior knowledge and scale with the complexity of the system. In particular, Gaussian process dynamical models (GPDMs) provide very promising results for the modeling of complex dynamics. However, the control properties of these GP models are just sparsely researched, which leads to a “blackbox” treatment in modeling and control scenarios. In addition, the sampling of GPDMs for prediction purpose respecting their nonparametric nature results in non-Markovian dynamics making the theoretical analysis challenging. In this article, we present approximated GPDMs, which are Markov and analyze their control theoretical properties. Among others, the approximated error is analyzed and conditions for boundedness of the trajectories are provided. The outcomes are illustrated with numerical examples that show the power of the approximated models while the computational time is significantly reduced.

Wearable Inertial Sensor-Based Limb Lameness Detection and Pose Estimation for Horses

Accurate objective, automated limb lameness detection and pose estimation play an important role for animal well-being and precision livestock farming. We present a wearable sensor-based limb lameness detection and pose estimation for horse walk and trot locomotion. The gait event and lameness detection are first built on a recurrent neural network (RNN) with long short-term memory (LSTM) cells. Its outcomes are used in the limb pose estimation. A learned low-dimensional motion manifold is parameterized by a phase variable with a Gaussian process dynamic model. We compare the RNN-LSTM-based lameness detection method with a feature-based multi-layer classifier (MLC) and a multi-class classifier (MCC) that are built on support vector machine/K-nearest-neighbors and deep convolutional neural network methods, respectively. Experimental results show that using only accelerometer measurements, the RNN-LSTM-based approach achieves 95% lameness detection accuracy and also outperforms the feature-based MLC or MCC in terms of several assessment criteria. The pose estimation scheme can predict the 24 limb joint angles in the sagittal plane with average errors less than 5 and 10 degs under normal and induced lameness conditions, respectively. The presented work demonstrate the successful use of machine learning techniques for high performance lameness detection and pose estimation in equine science. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Automation technologies are increasingly used for precision agriculture but few have focused on monitoring individual animals in open field for precision livestock farming. Limb lameness detection and pose estimation in open field is labor-intensive, unsafe for farmers, and inefficient. The presented machine learning-enabled, wearable inertial sensor-based design provides an effective and efficient approach for horse limb lameness detection and pose estimation applications. We present an RNN-LSTM for lameness detection and an integrated manifold learning model is used to predict the horse limb joint angles in walk and trot gaits under normal and induced lameness conditions. We also present a systematic analysis and experiments to demonstrate the impacts of the wearable sensor locations and signal information on lameness detection and pose estimation performance. Several other machine learning-based lameness detection methods are also presented and compared. The extensive multi-horse testing results are presented to demonstrate the superior accuracy and higher performance than other types of machine learning methods. One attractive feature of the proposed design lies in its high performance and fast computational capability for potential real-time applications in open field.

Estimation and visualization of process states using latent variable models based on Gaussian process.

The estimation and visualization of process states are important for process control in chemical and industrial plants. Since industrial processes are related to Gaussian distributions theoretically, this study focused on Gaussian process latent variable models. Process state estimation and visualization methods are proposed using two latent variables based on the Bayesian Gaussian process latent variable model (BGPLVM), infinite warped mixture model (iWMM), and Gaussian process dynamical models (GPDM). The Tennessee Eastman process dataset was analyzed and it was confirmed that the performance of estimating the process states was highest in the order of GPDM, iWMM, and BGPLVM. Moreover, time-delayed process variables were added to the process variables to consider the process dynamics, which further improved the performance of estimating the process states. Particularly in the case of GPDM, only two latent variables could estimate the process states, with approximately 100% accuracy for four process states. Additionally, even 10 process states could be estimated with approximately 90% accuracy, and it was confirmed that the process state estimation and process state visualization could be achieved simultaneously.

Ensemble just-in-time model based on Gaussian process dynamical models for nonlinear and dynamic processes

Process data have a number of characteristics, such as noise, nonlinearity, process dynamics, and autocorrelation. Ideally, adaptive soft sensors would be used to solve model degradation problems resulting from changes in process characteristics. However, it is necessary to optimize the hyperparameters for each model and, depending on the state of the process, the optimal hyperparameters will change. In this study, we focus on a Gaussian process dynamical model (GPDM), a dimension-reduction method that considers all of the data characteristics. We combine a just-in-time (JIT) model and ensemble learning, and then predict y-values with multiple JIT models that have different sets of hyperparameters. Each JIT model is constructed using latent variables obtained by the GPDM. The weights of the JIT models are determined based on Bayes’ theorem in consideration of their predictive ability. Analysis of two industrial datasets confirms that the proposed model is more accurate than existing approaches.

Whole-Body Joint Angle Estimation for Real-Time Humanoid Robot Imitation Based on Gaussian Process Dynamical Model and Particle Filter

Real-time imitation enables a humanoid robot to mirror the behavior of humans, being important for applications of human–robot interaction. For imitation, the corresponding joint angles of the humanoid robot should be estimated. Generally, a humanoid robot comprises dozens of joints that construct a high-dimensional exploration space for estimating the joint angles. Although a particle filter can estimate the robot state and provides a solution for estimating joint angles, the computational cost becomes prohibitive given the high dimension of the exploration space. Furthermore, a particle filter can only estimate the joint angles accurately using a motion model. To realize accurate joint angle estimation at low computational cost, Gaussian process dynamical models (GPDMs) can be adopted. Specifically, a compact state space can be constructed through the GPDM learning of high-dimensional time-series motion data to obtain a suitable motion model. We propose a GPDM-based particle filter using a compact state space from the learned motion models to realize efficient estimation of joint angles for robot imitation. Simulations and real experiments demonstrate that the proposed method efficiently estimates humanoid robot joint angles at low computational cost, enabling real-time imitation.

MÉTODOS COMPUTACIONALES PARA LA DELAMINACIÓN DE GRAFITO UTILIZANDO SURFACTANTES ANIONICOS PARA PRODUCIR GRAFENO

Today, using thermal and chemical reduction and solubility, graphene oxide is produced in large scale. Since there are various methods for producing graphene, each of which allocates properties to the produced graphene, the purpose of this research is to investigate graphite delamination using anionic surfactants and produce graphene by means of computational methods. The research method was applied in order to perform molecular dynamics analysis, first, (the minimum) force that each atom imposes to other atoms was calculated. This is the total gradient of the system’s energy according to the coordinates of the related atom. A Bayesian method was used for dynamic modeling, which, on average, uses dynamic parameters instead of their estimates. The Gaussian Process Dynamic Model (GPDM) was completely defined by a set of low-level data representations and was observed by both dynamics and modeling of GP regression (Gaussian process regression). Then, using the Gaussian software, along with empirical results or just using this software, the molecular state and reactions and their mechanisms were simulated. The results indicated that the presence of benzene, ether and carbo xyl groups in the optimal structure facilitates the entry of surfactants into the sheets and that the agent to start the separation of the graphene sheets adhered to each other by comparing the results of this study between the two surfactants, it was found that the gap to change by separation layers between the graphene plates is different for two surfactants. Besides, the difference in the polarity of the surfactants resulted in the final polarization of the surfactant and graphene system. Therefore, the difference in the polarity causes the difference in the solubility.

Projection Analysis Optimization for Human Transition Motion Estimation

It is a difficult task to estimate the human transition motion without the specialized software. The 3-dimensional (3D) human motion animation is widely used in video game, movie, and so on. When making the animation, human transition motion is necessary. If there is a method that can generate the transition motion, the making time will cost less and the working efficiency will be improved. Thus a new method called latent space optimization based on projection analysis (LSOPA) is proposed to estimate the human transition motion. LSOPA is carried out under the assistance of Gaussian process dynamical models (GPDM); it builds the object function to optimize the data in the low dimensional (LD) space, and the optimized data in LD space will be obtained to generate the human transition motion. The LSOPA can make the GPDM learn the high dimensional (HD) data to estimate the needed transition motion. The excellent performance of LSOPA will be tested by the experiments.

Pedestrian Path, Pose, and Intention Prediction Through Gaussian Process Dynamical Models and Pedestrian Activity Recognition

According to several reports published by worldwide organizations, thousands of pedestrians die in road accidents every year. Due to this fact, vehicular technologies have been evolving with the intent of reducing these fatalities. This evolution has not finished yet, since, for instance, the predictions of pedestrian paths could improve the current automatic emergency braking systems. For this reason, this paper proposes a method to predict future pedestrian paths, poses, and intentions up to 1 s in advance. This method is based on balanced Gaussian process dynamical models (B-GPDMs), which reduce the 3-D time-related information extracted from key points or joints placed along pedestrian bodies into low-dimensional spaces. The B-GPDM is also capable of inferring future latent positions and reconstruct their associated observations. However, learning a generic model for all kinds of pedestrian activities normally provides less accurate predictions. For this reason, the proposed method obtains multiple models of four types of activity, i.e., walking, stopping, starting, and standing, and selects the most similar model to estimate future pedestrian states. This method detects starting activities 125 ms after the gait initiation with an accuracy of 80% and recognizes stopping intentions 58.33 ms before the event with an accuracy of 70%. Concerning the path prediction, the mean error for stopping activities at a time-to-event (TTE) of 1 s is 238.01 ± 206.93 mm and, for starting actions, the mean error at a TTE of 0 s is 331.93 ± 254.73 mm.

Gaussian Process Trajectory Learning and Synthesis of Individualized Gait Motions.

This paper proposes a Gaussian process-based method for trajectory learning and generation of individualized gait motions at arbitrary user-designated walking speeds, intended to be used in generating reference motions for robotic gait rehabilitation systems. We utilize a nonlinear dimension reduction technique based on Gaussian process dynamical models (GPDMs), in which the internal dynamics is modeled as a second-order Markov process evolving in a lower-dimensional latent space. After the GPDM parameters are identified with training data obtained from gait motions of healthy subjects walking at different speeds, our method then employs Gaussian process regression (GPR) to predict the initial two states of the latent space dynamics from any arbitrary desired walking speed and the anthropometric parameters of the test subject. Motions are then generated by directly mapping the latent space dynamics to joint trajectories. Experimental studies involving more than 100 subjects indicate that our method generates gait patterns with 30% less mean square prediction errors compared to recent state-of-the-art methods, while also allowing for arbitrary user-specified walking speeds.

Humanoid Robot Motion Modeling Based on Time-Series Data Using Kernel PCA and Gaussian Process Dynamical Models

In this article, contrary to popular studies on human motion learning, we focus on addressing the problem of humanoid robot motions directly. Performances of different kernel functions with principal components analysis (PCA) in Gaussian process dynamical models (GPDM) are investigated to build efficient humanoid robot motion models. A novel kernel-PCA-GPDM method is proposed for building different types of humanoid robot motion models. Compared with the standard-PCA-GPDM and auto-encoder-GPDM methods, our proposed method is more efficient in humanoid robot motion modeling. In this work, three types of NAO robot motion models are studied: walk-model, lateral-walk model, and wave-hand model, where motion data are collected from an Aldebaran NAO robot using magnetic rotary encoder sensors. Using kernel-PCA-GPDM method, the motion data are first projected from the high 23-dimension observation space to a 3-dimension low latent space. Then, three types of humanoid robot motion models are learned in the 3D latent space. Compared with other kernel-PCA-GPDM or auto-encoder-GPDM methods, our proposed novel kernel-PCA-GPDM method performs efficiently in motion learning. Finally, we realize humanoid robot motion representation to verify the motion models that we build. The experimental results show that our proposed kernel-PCA-GPDM method builds efficient and smooth motion models.

Spatially recursive estimation and Gaussian process dynamic models of bat flapping flight

Bats exhibit exceptional agility, maneuverability, and efficiency during flight due to the complex articulated multibody structure of their wings and to the nonlinear and unsteady dynamics that govern their motion. While excellent progress has been made in the study of the kinematics of bat flapping flight, there still does not exist a dynamic model which is suitable for use in state estimation. This issue is typically overcome by using a few high-frame-rate cameras to capture motion; however, such systems are expensive and prone to measurement occlusion. This paper establishes a methodology that is designed to exploit an emerging class of experimental hardware which employs low-resolution, low-cost, and highly redundant imaging networks. The redundant camera network ameliorates the issue of self-occlusion, but the large-baseline, nonlinear motion of points in image space makes tracking difficult without a suitable motion prior. To remedy this issue, this paper exploits the tree topology of the bat skeleton and introduces a conditionally independent Bayes’ filter implemented with inboard state correction. Our results show that at low frame rates, this estimator performs better than both the standard and conditionally independent without inboard correction approaches for state estimation of an open kinematic chain. In addition to the estimation strategy, we construct a Gaussian process dynamic model (GPDM) of flight dynamics which we will use in future work as a suitable motion prior for state estimation. The GPDM presented in this paper is the first nonlinear dimensionality reduction of bat flight.

Making the Coupled Gaussian Process Dynamical Model Modular and Scalable with Variational Approximations

We describe a sparse, variational posterior approximation to the Coupled Gaussian Process Dynamical Model (CGPDM), which is a latent space coupled dynamical model in discrete time. The purpose of the approximation is threefold: first, to reduce training time of the model; second, to enable modular re-use of learned dynamics; and, third, to store these learned dynamics compactly. Our target applications here are human movement primitive (MP) models, where an MP is a reusable spatiotemporal component, or “module” of a human full-body movement. Besides re-usability of learned MPs, compactness is crucial, to allow for the storage of a large library of movements. We first derive the variational approximation, illustrate it on toy data, test its predictions against a range of other MP models and finally compare movements produced by the model against human perceptual expectations. We show that the variational CGPDM outperforms several other MP models on movement trajectory prediction. Furthermore, human observers find its movements nearly indistinguishable from replays of natural movement recordings for a very compact parameterization of the approximation.

When Vehicles &lt;italic&gt;See&lt;/italic&gt; Pedestrians With Phones: A Multicue Framework for Recognizing Phone-Based Activities of Pedestrians

The intelligent vehicle community has devoted considerable efforts to model driver behavior, and in particular, to detect and overcome driver distraction in an effort to reduce accidents caused by driver negligence. However, as the domain increasingly shifts toward autonomous and semiautonomous solutions, the driver is no longer integral to the decision-making process, indicating a need to refocus efforts elsewhere. To this end, we propose to study pedestrian distraction instead. In particular, we focus on detecting pedestrians who are engaged in secondary activities involving their cellphones and similar hand-held multimedia devices from a purely vision-based standpoint. To achieve this objective, we propose a pipeline incorporating articulated human pose estimation, followed by a soft object label transfer from an ensemble of exemplar support vector machines trained on the nearest neighbors in pose feature space. We additionally incorporate head gaze features and prior pose information to carry out cellphone related pedestrian activity recognition. Finally, we offer a method to reliably track the articulated pose of a pedestrian through a sequence of images using a particle filter with a Gaussian process dynamical model, which can then be used to estimate sequentially varying activity scores at a very low computational cost. The entire framework is fast (especially for sequential data) and accurate, and easily extensible to include other secondary activities and sources of distraction.

Visualizing States of Time-Series Data by Autoregressive Gaussian Process Dynamical Models

Gaussian process dynamical models (GPDMs) are used for nonlinear dimensionality reduction in time series by means of Gaussian process priors. An extension of GPDMs is proposed for visualizing the states of time series. The conventional GPDM approach associates a state with an observation value. Therefore, observations changing over time cannot be represented by a single state. Consequently, the resulting visualization of state transition is difficult to understand, as states change when the observation values change. To overcome this issue, autoregressive GPDMs, called ARGPDMs, are proposed. They associate a state with a vector autoregressive (VAR) model. Therefore, observations changing over time can be represented by a single state. The resulting visualization is easier to understand, as states change only when the VAR model changes. We demonstrate experimentally that the ARGPDM approach provides better visualization compared with conventional GPDMs.

On Stabilizing Control of Gaussian Processes for Unknown Nonlinear Systems

This paper proposes a novel controller design to stabilize Gaussian process (GP) dynamical models for partially unknown nonlinear systems. The unknown system is identified as the GP model. Because existing GP models are difficult to analyze in terms of controller design, a novel GP identification method is proposed that obtains the state dependent coefficient matrix of the system, making the controller design more efficient. The GP model is represented as a piecewise linear system with a bounded uncertainty that is derived based on the characteristics of the GP. Extending quadratic stability theory derives a novel stabilizing controller for such systems.

Characterizing Dynamic Walking Patterns and Detecting Falls with Wearable Sensors Using Gaussian Process Methods.

By incorporating a growing number of sensors and adopting machine learning technologies, wearable devices have recently become a prominent health care application domain. Among the related research topics in this field, one of the most important issues is detecting falls while walking. Since such falls may lead to serious injuries, automatically and promptly detecting them during daily use of smartphones and/or smart watches is a particular need. In this paper, we investigate the use of Gaussian process (GP) methods for characterizing dynamic walking patterns and detecting falls while walking with built-in wearable sensors in smartphones and/or smartwatches. For the task of characterizing dynamic walking patterns in a low-dimensional latent feature space, we propose a novel approach called auto-encoded Gaussian process dynamical model, in which we combine a GP-based state space modeling method with a nonlinear dimensionality reduction method in a unique manner. The Gaussian process methods are fit for this task because one of the most import strengths of the Gaussian process methods is its capability of handling uncertainty in the model parameters. Also for detecting falls while walking, we propose to recycle the latent samples generated in training the auto-encoded Gaussian process dynamical model for GP-based novelty detection, which can lead to an efficient and seamless solution to the detection task. Experimental results show that the combined use of these GP-based methods can yield promising results for characterizing dynamic walking patterns and detecting falls while walking with the wearable sensors.

High-Order Gaussian Process Dynamical Models for Traffic Flow Prediction

Traffic flow prediction, which predicts the future flow using historic flows, is an important task in intelligent transportation systems (ITS). Efficient and accurate models for traffic flow prediction greatly contribute to the development of ITS. In this paper, we adopt the Gaussian process dynamical model (GPDM) to a fourth-order GPDM, which is more suitable for modeling traffic flow data. Specifically, the latent variables in the fourth-order GPDM is a fourth-order Markov Gaussian process, and the weighted $k$ - NN is incorporated in the model to predict latent variables for efficient prediction. After training the model, the future flow is estimated by the average of the results predicted by the fourth-order GPDM and $k$ - NN. Compared with other popular methods, the proposed method performs best and yields significant improvements of prediction performance.

Dynamic texture modeling and synthesis using multi-kernel Gaussian process dynamic model

Dynamic texture (DT) widely exists in various social video media. Therefore, DT modeling and synthesis plays an important role in social media analyzing and processing. In this paper, we propose a Bayesian-based nonlinear dynamic texture modeling method for dynamic texture synthesis. To capture the non-stationary distribution of DT, we utilize the Gaussian process latent variable model for dimensional reduction. Furthermore, we design a multi-kernel dynamic system for the latent dynamic behavior modeling. In our model, we do not make strong assumption on the nonlinear function. Instead, our model automatically constructs a suitable nonlinear kernel for dynamic modeling and therefore is capable of fitting various types of dynamics. We evaluate the effectiveness our methods on the DynTex database and compared with representative DT synthesis method. Experimental results show that our method can achieve synthesis results with higher visual quality.

Visualizing State of Time-Series Data by Supervised Gaussian Process Dynamical Models

Gaussian Process Dynamical Models (GPDMs) constitute a nonlinear dimensionality reduction technique that provides a probabilistic representation of time series data in terms of Gaussian process priors. In this paper, we report a method based on GPDMs to visualize the states of time-series data. Conventional GPDMs are unsupervised, and therefore, even when the labels of data are available, it is not possible to use this information. To overcome the problem, we propose a supervised GPDM (S-GPDM) that utilizes both the data and their corresponding labels. We demonstrate experimentally that the S-GPDM can locate related motion data closer together than conventional GPDMs.

Non-Myopic Adaptive Route Planning in Uncertain Congestion Environments

We consider the problem of adaptively routing a fleet of cooperative vehicles within a road network in the presence of uncertain and dynamic congestion conditions. To tackle this problem, we first propose a Gaussian process dynamic congestion model that can effectively characterize both the dynamics and the uncertainty of congestion conditions. Our model is efficient and thus facilitates real-time adaptive routing in the face of uncertainty. Using this congestion model, we develop efficient algorithms for non-myopic adaptive routing to minimize the collective travel time of all vehicles in the system. A key property of our approach is the ability to efficiently reason about the long-term value of exploration, which enables collectively balancing the exploration/exploitation trade-off for entire fleets of vehicles. Our approach is validated by traffic data from two large Asian cities. Our congestion model is shown to be effective in modeling dynamic congestion conditions. Our routing algorithms also generate significantly faster routes compared to standard baselines, and achieve near-optimal performance compared to an omniscient routing algorithm. We also present the results from a preliminary field study, which showcases the efficacy of our approach.