Occupancy mapping has been widely utilized to represent the surroundings for autonomous robots to perform tasks such as navigation and manipulation. While occupancy mapping in 2-D environments has been well-studied, there have been few approaches suitable for 3-D dynamic occupancy mapping which is essential for aerial robots. This paper presents a novel 3-D dynamic occupancy mapping algorithm called DS-K3DOM. We first establish a Bayesian method to sequentially update occupancy maps for a stream of measurements based on the random finite set theory. Then, we approximate it with particles in the Dempster-Shafer domain to enable real-time computation. Moreover, the algorithm applies kernel-based inference with Dirichlet basic belief assignment to enable dense mapping from sparse measurements. The efficacy of the proposed algorithm is demonstrated through simulations and real experimentsiiThe code is available at: https://github.com/JuyeopHan/dsk3dom_public.

Mapping three-dimensional (3-D) dynamic environments is essential for aerial robots but challenging to consider the increased dimensions in both space and time compared to 2-D static mapping. This paper presents a kernel-based 3-D dynamic occupancy mapping algorithm, K3DOM, that distinguishes between static and dynamic objects while estimating the velocities of dynamic cells via particle tracking. The proposed algorithm brings the benefits of kernel inference such as its simple computation, consideration of spatial correlation, and natural measure of uncertainty to the domain of dynamic mapping. We formulate the dynamic occupancy mapping problem in a Bayesian framework and represent the map through Dirichlet distribution to update posteriors in a recursive way with intuitive heuristics. The proposed algorithm demonstrates its promising performance compared to baseline in diverse scenarios simulated in ROS environments.

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separability condition in this work is more relaxed than the widely used linear separability. Moreover, the constructed neural network guarantees perfect classification for any datasets sampled from a separable probability distribution. This generalization capability comes from the saturation of sigmoid function that exploits small margins near the boundaries of intervals formed by the separable probability distribution1.