Mapping the surrounding environment is essential for the successful operation of autonomous robots. While extensive research has focused on mapping geometric structures and static objects, the environment is also influenced by the movement of dynamic objects. Incorporating information about spatial motion patterns can allow mobile robots to navigate and operate successfully in populated areas. In this paper, we propose a deep state-space model that learns the map representations of spatial motion patterns and how they change over time at a certain place. To evaluate our methods, we use two different datasets: one generated dataset with specific motion patterns and another with real-world pedestrian data. We test the performance of our model by evaluating its learning ability, mapping quality, and application to downstream tasks. The results demonstrate that our model can effectively learn the corresponding motion pattern, and has the potential to be applied to robotic application tasks.

Philip Becker-Ehmck philip.becker-ehmck@argmax.ai Patrick van der Smagt Disclosure: Parts of this work have been submitted in form of a Master's Thesis towards partial fulfillment of the requirements for a Masters program at the Technical University of Munich [4] Abstract Learning a model of dynamics from high-dimensional images can be a core ingredient for success in many applications across different domains, especially in sequential decision making. However, currently prevailing methods based on latent-variable models are limited to working with low resolution images only. In this work, we show that some of the issues with using high-dimensional observations arise from the discrepancy between the dimensionality of the latent and observable space, and propose solutions to overcome them. 1 Introduction Learning a probabilistic model for sequential data is a key step towards solving a lot of interesting problems, including analysis and deconstruction of auditory sequences [18], predicting the next piece of information given previously recorded data such as video frames [9] and text [20], and controlling an agent to perform specific tasks (model-based reinforcement learning [5]). While in this paper, we consider probabilistic models especially tuned for the needs of the last, i.e with control inputs, the approaches we discuss can be applied to control-less environments as well. A key feature required in control-based models is that they should be able to generate a feasible trajectory distribution given a control policy. To this end, one of the more successful solutions proposed in the past for modeling dynamical systems is Deep V ariational Bayes Filter ( DVBF) [10] - a framework for learning a State-Space Model given sequential observations from the environment in an unsupervised manner.