GP-SUM. Gaussian Process Filtering of non-Gaussian Beliefs

Abstract

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted Sum of Gaussians. The key attribute of GP-SUM is that it does not rely on linearizations of the dynamic or observation models, or on unimodal Gaussian approximations of the belief, hence enables tracking complex state distributions. The algorithm can be seen as a combination of a sampling-based filter with a probabilistic Bayes filter. On the one hand, GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. On the other hand, it achieves effective sampling and accurate probabilistic propagation by relying on the GP form of the system, and the sum-of-Gaussian form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also demonstrate its use in a pushing task, predicting with experimental accuracy the naturally occurring non-Gaussian distributions.

Augmenting Physical Simulators with Stochastic Neural Networks: Case Study of Planar Pushing and Bouncing

“…Reasoning about the uncertainty in actions and motions is a powerful tool in planning and control [17], [18], [19], [20]. In the context of planar manipulation, Bauza and Rodriguez [20] used Gaussian processes to learn the motion model of planar shapes and to propagate uncertainty using the GP-SUM algorithm. The GP-SUM algorithm is a hybrid Bayes and particle filter; it exploits the Gaussian structure of the motion model to efficiently approximate the distribution over outcomes as a mixture of Gaussians.…”

“…The GP-SUM algorithm is a hybrid Bayes and particle filter; it exploits the Gaussian structure of the motion model to efficiently approximate the distribution over outcomes as a mixture of Gaussians. Bauza and Rodriguez [20] showed that pushing can exhibit multimodality and their approach is able to capture it. We use the model and algorithm from [20] as benchmarks for our approach and compare the two on the MIT push dataset [5].…”

“…Bauza and Rodriguez [20] showed that pushing can exhibit multimodality and their approach is able to capture it. We use the model and algorithm from [20] as benchmarks for our approach and compare the two on the MIT push dataset [5].…”

“…To evaluate this, from the repeated pushes, we collect the ground truth distribution of the position of the object (rect1) after being pushed for one second. We then sample 2,000 points from the state-of-the-art stochastic motion modeling approach-GP-SUM [20]. We also sample 2,000 trajectories from our Hybrid model.…”

Omnipush: accurate, diverse, real-world dataset of pushing dynamics with RGB-D video

“…Since we presented our earlier dataset on planar pushing [1], it has been directly used for: 1) Stochastic modeling: [23,10,17] 2) Modeling from rendered images: [16] 3) Model identification: [24] 4) Learning models for control: [25,26] 5) Filtering: [27] 6) Meta-learning: [28] With this new dataset we hope to further facilitate research in learning models and control.…”