Evaluation of compressive sensing methods for robot mapping with reduced sensor input
Sathishchandra, Harish N.
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Robotic mapping has been a highly active research area in robotics and AI for at least two decades. Robot mapping addresses the problem of acquiring spatial models of physical environments through mobile robots. The mapping problem is generally regarded as one of the most important problems in the pursuit of building truly autonomous mobile robots. The effectiveness of current algorithms is driven in large part by the sheer volume of data available, acquired at high sample rates using sensors such as high-resolution laser rangefinders or cameras. Storing and operating on such large volumes of data can be costly in terms of storage space and computational power. While this may not be an issue for many robots, recently, there has been a surge of interest in micro aerial vehicles with limited onboard resources and payload capacity. It is not feasible for these systems to carry the high powered sensors that are typically needed for mapping or to store the large volumes of data algorithms currently need. The goal of this thesis is to study and evaluate compressive sensing methods to enable low resolution, lightweight sensors to create maps of sufficient quality for robot navigation tasks. The first part of this work focuses on two Compressive Sensing (CS)-based approaches for producing maps from highly sub-sampled data: 1) A total-variation minimization and 2) A basis pursuit problem. The total variation reconstruction is shown to provide high quality reconstruction of the map, but suffers from the fact that the regularization parameter is highly dependent on the structure of the mapped environment. The basis pursuit reconstruction, however, is more robust to the environment. The algorithm, previously introduced in the literature, uses a re-weighted basis pursuit algorithm to reconstruct a full lidar scan from a sub-sampled set of points. This reconstruction is then passed on to any standard mapping algorithm to produce a map of the environment. The re-weighting is done based on the slope of the depth profile around each sampled point. The second part of this work focuses on empirically evaluating the maps obtained by simulated experiments from the re-weighted basis pursuit algorithm and that obtained from linear interpolation as a function of the amount of sub-sampling. We considered three different subsampling approaches: subsampling in space (i.e., subsampling an individual lidar scan that in an ideal case would be comprised of 180 individual beams), and subsampling in time (i.e., using a reduced number of measurement locations in the environment), and a combination of both. For the evaluation metric, we picked 150 random pairs of points and constructed optimal paths between them using the A-star graph search algorithm, and compared how ``close'' the lengths of these paths were to the paths constructed on the ground truth map. The sum of squared error metric was used to measure this ``closeness''. In essence, if a reconstructed map contains too many false walls or randomly filled locations, the A-star paths should be longer than on the true map while if the reconstruction fails to produce complete walls, the paths should be shorter. The simulated experiments show that the re-weighted basis pursuit algorithm outperforms linear interpolation in severely under sampled datasets. The experiment also shows that the best trajectory for optimal reconstruction is if the robot stays close to the walls of the environment.