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Energy consumption of memory accesses dominates the compute energy in energy-constrained robots, which require a compact 3-D map of the environment to achieve autonomy. Recent mapping frameworks only focused on reducing the map size while incurring significant memory usage during map construction due to the multipass processing of each depth image. In this work, we present a memory-efficient continuous occupancy map, named GMMap, that accurately models the 3-D environment using a Gaussian mixture model (GMM). Memory efficient GMMap construction is enabled by the single-pass compression of depth images into local GMMs, which are directly fused together into a globally-consistent map. By extending Gaussian Mixture Regression (GMR) to model unexplored regions, occupancy probability is directly computed from Gaussians. Using a low power ARM Cortex A57 CPU, GMMap can be constructed in real time at up to 60 images/s. Compared with prior works, GMMap maintains high accuracy while reducing the map size by at least 56%, memory overhead by at least 88%, dynamic random-access memory (DRAM) access by at least 78%, and energy consumption by at least 69%. Thus, GMMap enables real-time 3-D mapping on energy-constrained robots. 

Exploration tasks are embedded in many robotics applications, such as search and rescue and space exploration. Information-based exploration algorithms aim to find the most informative trajectories by maximizing an information-theoretic metric, such as the mutual information between the map and potential future measurements. Unfortunately, most existing information-based exploration algorithms are plagued by the computational difficulty of evaluating the Shannon mutual information metric. In this article, we consider the fundamental problem of evaluating Shannon mutual information between the map and a range measurement. First, we consider 2D environments. We propose a novel algorithm, called the fast Shannon mutual information (FSMI). The key insight behind the algorithm is that a certain integral can be computed analytically, leading to substantial computational savings. Second, we consider 3D environments, represented by efficient data structures, e.g., an OctoMap, such that the measurements are compressed by run-length encoding (RLE). We propose a novel algorithm, called FSMI-RLE, that efficiently evaluates the Shannon mutual information when the measurements are compressed using RLE. For both the FSMI and the FSMI-RLE, we also propose variants that make different assumptions on the sensor noise distribution for the purpose of further computational savings. We evaluate the proposed algorithms in extensive experiments. In particular, we show that the proposed algorithms outperform existing algorithms that compute Shannon mutual information as well as other algorithms that compute the Cauchy–Schwarz quadratic mutual information (CSQMI). In addition, we demonstrate the computation of Shannon mutual information on a 3D map for the first time.