Tag Archives: Gaussian Processes

Using multiple data with diverse fidelities to provide surrogate simulations through GPs

November 14, 2024 16:42 ,

Ben Yang, Boyi Chen, Yanbin Liu, Jinbao Chen, Gaussian process fusion method for multi-fidelity data with heterogeneity distribution in aerospace vehicle flight dynamics, Engineering Applications of Artificial Intelligence, Volume 138, Part A, 2024, DOI: 10.1016/j.engappai.2024.109228.

In the engineering design of aerospace vehicles, design data at different stages exhibit hierarchical and heterogeneous distribution characteristics. Specifically, high-fidelity design data (such as from computational fluid dynamics simulations and flight tests) are costly and time-consuming to obtain. Moreover, the limited high-precision samples that are acquired often fail to cover the entire design space, resulting in a distribution characterized by small sample sizes. A critical challenge in data-driven modeling is efficiently fusing low-fidelity data with limited heterogeneous high-fidelity data to improve model accuracy and predictive performance. In response to this challenge, this paper introduces a Gaussian process fusion method for multi-fidelity data, founded on distribution characteristics. Multi-fidelity data are represented as intermediate surrogates using Gaussian processes, identifying heteroscedastic noise properties and deriving posterior distributions. The fusion is then treated as an optimization problem for prediction variance, using K-nearest neighbors and spatial clustering to determine optimal weights, which are adaptively adjusted based on sample density. These weights are adaptively adjusted based on the sample density to strengthen the local modeling behavior. The paper concludes with a comparative analysis, evaluating the proposed method against other conventional approaches using numerical cases and an aerodynamic prediction scenario for aerospace vehicles. A comparative analysis shows that the proposed method improves global modeling accuracy by 45% and reduces the demand for high-fidelity samples by over 40% compared to traditional methods. Applied in aerospace design, the method effectively merges multi-source data, establishing a robust hypersonic aerodynamic database while controlling modeling costs and demonstrating robustness to sample distribution.

Posted in: Systems and Signals , Tagged: , ,

Robot exploration through decision-making + gaussian processes

October 24, 2024 06:18 ,

Stephens, A., Budd, M., Staniaszek, M. et al. Planning under uncertainty for safe robot exploration using Gaussian process prediction, Auton Robot 48, 18 (2024) DOI: 10.1007/s10514-024-10172-6.

The exploration of new environments is a crucial challenge for mobile robots. This task becomes even more complex with the added requirement of ensuring safety. Here, safety refers to the robot staying in regions where the values of certain environmental conditions (such as terrain steepness or radiation levels) are within a predefined threshold. We consider two types of safe exploration problems. First, the robot has a map of its workspace, but the values of the environmental features relevant to safety are unknown beforehand and must be explored. Second, both the map and the environmental features are unknown, and the robot must build a map whilst remaining safe. Our proposed framework uses a Gaussian process to predict the value of the environmental features in unvisited regions. We then build a Markov decision process that integrates the Gaussian process predictions with the transition probabilities of the environmental model. The Markov decision process is then incorporated into an exploration algorithm that decides which new region of the environment to explore based on information value, predicted safety, and distance from the current position of the robot. We empirically evaluate the effectiveness of our framework through simulations and its application on a physical robot in an underground environment.

Posted in: Robot motion planning , Tagged: , ,

A kind of reinforcement learning that decouples modelling from planning using Gaussian Processes for the former

October 10, 2019 15:07 ,

Rakicevic, N. & Kormushev, P., Active learning via informed search in movement parameter space for efficient robot task learning and transfer. Auton Robot (2019) 43: 1917, DOI: 10.1007/s10514-019-09842-7.

Learning complex physical tasks via trial-and-error is still challenging for high-degree-of-freedom robots. Greatest challenges are devising a suitable objective function that defines the task, and the high sample complexity of learning the task. We propose a novel active learning framework, consisting of decoupled task model and exploration components, which does not require an objective function. The task model is specific to a task and maps the parameter space, defining a trial, to the trial outcome space. The exploration component enables efficient search in the trial-parameter space to generate the subsequent most informative trials, by simultaneously exploiting all the information gained from previous trials and reducing the task model’s overall uncertainty. We analyse the performance of our framework in a simulation environment and further validate it on a challenging bimanual-robot puck-passing task. Results show that the robot successfully acquires the necessary skills after only 100 trials without any prior information about the task or target positions. Decoupling the framework’s components also enables efficient skill transfer to new environments which is validated experimentally.

Posted in: Applications of reinforcement learning to robots , Tagged:

A novel paradigm for motion planning based on probabilistic inference

November 27, 2018 13:29 ,

Mukadam, M., Dong, J., Yan, X., Dellaert, F., & Boots, B. , Continuous-time Gaussian process motion planning via probabilistic inference, The International Journal of Robotics Research, 37(11), 1319–1340, DOI: 10.1177/0278364918790369.

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.

Posted in: Robot motion planning , Tagged: ,

Mapping the wifi signal for robot localization both precisely and accurately through a complex model of the signal

March 28, 2018 09:22 ,

Renato Miyagusuku, Atsushi Yamashita, Hajime Asama, Precise and accurate wireless signal strength mappings using Gaussian processes and path loss models, Robotics and Autonomous Systems, Volume 103, 2018, Pages 134-150, DOI: 10.1016/j.robot.2018.02.011.

In this work, we present a new modeling approach that generates precise (low variance) and accurate (low mean error) wireless signal strength mappings. In robot localization, these mappings are used to compute the likelihood of locations conditioned to new sensor measurements. Therefore, both mean and variance predictions are required. Gaussian processes have been successfully used for learning highly accurate mappings. However, they generalize poorly at locations far from their training inputs, making those predictions have high variance (low precision). In this work, we address this issue by incorporating path loss models, which are parametric functions that although lacking in accuracy, generalize well. Path loss models are used together with Gaussian processes to compute mean predictions and most importantly, to bound Gaussian processes’ predicted variances. Through extensive testing done with our open source framework, we demonstrate the ability of our approach to generating precise and accurate mappings, and the increased localization accuracy of Monte Carlo localization algorithms when using them; with all our datasets and software been made readily available online for the community.

Posted in: Communication networks, Mobile Robot Localization , Tagged: ,

Robots that pre-compute a number of possible behaviours (in simulation) and then learn their performance with them (propragating that performance measures to similar behaviors through Gaussian Processes Regression) and select the best at each situation (through Bayesian Optimization), thus confronting varying environments and damages to the robot

June 27, 2017 09:02 ,

A. Cully, et al. Robots that can adapt like animals, Nature, 521 (2015), pp. 503–507, DOI: 10.1038/nature14422.

Robots have transformed many industries, most notably manufacturing, and have the power to deliver tremendous benefits to society, such as in search and rescue, disaster response, health care and transportation. They are also invaluable tools for scientific exploration in environments inaccessible to humans, from distant planets to deep oceans. A major obstacle to their widespread adoption in more complex environments outside factories is their fragility. Whereas animals can quickly adapt to injuries, current robots cannot think outside the box to find a compensatory behaviour when they are damaged: they are limited to their pre-specified self-sensing abilities, can diagnose only anticipated failure modes, and require a pre-programmed contingency plan for every type of potential damage, an impracticality for complex robots. A promising approach to reducing robot fragility involves having robots learn appropriate behaviours in response to damage, but current techniques are slow even with small, constrained search spaces. Here we introduce an intelligent trial-and-error algorithm that allows robots to adapt to damage in less than two minutes in large search spaces without requiring self-diagnosis or pre-specified contingency plans. Before the robot is deployed, it uses a novel technique to create a detailed map of the space of high-performing behaviours. This map represents the robotâ €™ s prior knowledge about what behaviours it can perform and their value. When the robot is damaged, it uses this prior knowledge to guide a trial-and-error learning algorithm that conducts intelligent experiments to rapidly discover a behaviour that compensates for the damage. Experiments reveal successful adaptations for a legged robot injured in five different ways, including damaged, broken, and missing legs, and for a robotic arm with joints broken in 14 different ways. This new algorithm will enable more robust, effective, autonomous robots, and may shed light on the principles that animals use to adapt to injury.

Posted in: Robotics , Tagged: , ,

Efficient computation of determinant and inversion of gaussian covariance matrices in the context of gaussian processes

February 24, 2016 18:45 ,

Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W. Hogg, and Michael O’Neil, Fast Direct Methods for Gaussian Processes, in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.38, no.2, pp.252-265, Feb. 1 2016, DOI: 10.1109/TPAMI.2015.2448083
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A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation of the corresponding Gaussian density. In the n-dimensional setting, however, it requires the inversion of an n x n covariance matrix, C, as well as the evaluation of its determinant, det(C). In many cases, such as regression using Gaussian processes, the covariance matrix is of the form C = σ2I + K, where K is computed using a specified covariance kernel which depends on the data and additional parameters (hyperparameters). The matrix C is typically dense, causing standard direct methods for inversion and determinant evaluation to require O(n3) work. This cost is prohibitive for large-scale modeling. Here, we show that for the most commonly used covariance functions, the matrix C can be hierarchically factored into a product of block low-rank updates of the identity matrix, yielding an O(n log2 n) algorithm for inversion. More importantly, we show that this factorization enables the evaluation of the determinant det(C), permitting the direct calculation of probabilities in high dimensions under fairly broad assumptions on the kernel defining K. Our fast algorithm brings many problems in marginalization and the adaptation of hyperparameters within practical reach using a single CPU core. The combination of nearly optimal scaling in terms of problem size with high-performance computing resources will permit the modeling of previously intractable problems. We illustrate the performance of the scheme on standard covariance kernels.

Posted in: Probability and statistics , Tagged: ,

Brief but nice related work about structured prediction (MRFs, CRFs, etc.)

July 17, 2015 11:49 ,

Bratieres, S.; Quadrianto, N.; Ghahramani, Z., GPstruct: Bayesian Structured Prediction Using Gaussian Processes, Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.37, no.7, pp.1514,1520, July 1 2015, DOI: 10.1109/TPAMI.2014.2366151.

We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M ^3 N), and structured support vector machines (SVMstruct), which embody only a subset of its properties. We present an inference procedure based on Markov Chain Monte Carlo. The framework can be instantiated for a wide range of structured objects such as linear chains, trees, grids, and other general graphs. As a proof of concept, the model is benchmarked on several natural language processing tasks and a video gesture segmentation task involving a linear chain structure. We show prediction accuracies for GPstruct which are comparable to or exceeding those of CRFs and SVMstruct.

Posted in: Computer vision , Tagged: , , , ,