Tell me about dynamics! Mapping velocity fields from sparse samples with Semi-Wrapped Gaussian Mixture Models

Abstract

Autonomous mobile robots often require information about the environment beyond merely the shape of the work-space. In this work we present a probabilistic method for mapping dynamics, in the sense of learning and representing statistics about the flow of discrete objects (e.g., vehicles, people) as well as continuous media (e.g., air flow).

We also demonstrate the capabilities of the proposed method with two use cases. One relates to motion planning in populated environments, where information about the flow of people can help robots to follow social norms and to learn implicit traffic rules by observing the movements of other agents. The second use case relates to Mobile Robot Olfaction (MRO), where information about wind flow is crucial for most tasks, including e.g. sensor planning, gas detection, gas distribution mapping and gas source localisation. We represent the underlying velocity field as a set of Semi-Wrapped Gaussian Mixture Models (SWGMM) representing the learnt local PDF of velocities. To estimate the parameters of the PDF we employ a formulation of Expectation Maximisation (EM) algorithm specific for SWGMM. We also describe a data augmentation method which allows to build a dense dynamic map based on a sparse set of measurements. In case only a small set of observations is available we employ a hierarchical sampling method to generate virtual observations from existing mixtures.