Abstract
The ability to generate accurate terrain models is of key importance in a wide variety of robotics tasks, ranging from path planning and trajectory optimization to environment exploration and mining applications. This paper introduces a novel regression methodology for terrain modeling that takes place in a Reproducing Kernel Hilbert Space, and can approximate arbitrarily complex functions using Variational Bayesian inference. A sparse kernel is used to efficiently project input points into a high-dimensional feature vector, based on cluster information generated automatically from training data. Each kernel maintains its own regression model, and the entire set is simultaneously optimized in an iterative fashion as more data is collected, to maximize a global variational bound. Additionally, we show how kernel parameters can be jointly learned alongside the regression model parameters, to achieve a better approximation of the underlying function. Experimental results show that the proposed methodology consistently outperforms current state-of-the-art techniques, while maintaining a fully probabilistic treatment of uncertainties and high scalability to large-scale datasets.
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Notes
- 1.
The proposed framework can be trivially extended to support different regression models for each cluster, including the learning of which regression models should be used, however this was not explored in this paper.
- 2.
All computations were performed on a i7/2.60 x 8 GHz notebook, with multi-threading enabled wherever possible. Due to lack of memory, training data was downsampled by 5 in the Rover dataset and by 25 in the Aerial dataset for tests using the SGP framework.
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Acknowledgements
This research was supported by funding from the Faculty of Engineering and Information Technologies, The University of Sydney, under the Faculty Research Cluster Program.
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Guizilini, V.C., Ramos, F.T. (2020). Variational Hilbert Regression with Applications to Terrain Modeling. In: Amato, N., Hager, G., Thomas, S., Torres-Torriti, M. (eds) Robotics Research. Springer Proceedings in Advanced Robotics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-28619-4_33
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