Prism-based LiDARs are more compact and cheaper than the conventional mechanical multi-line spinning LiDARs, which have become increasingly popular in robotics, recently. However, there are several challenges for these new LiDAR sensors, including small field of view, severe motion distortions, and irregular patterns, which hinder them from being widely used in LiDAR odometry, practically. To tackle these problems, we present an effective continuous-time LiDAR odometry (ECTLO) method for the Risley-prism-based LiDARs with non-repetitive scanning patterns. A single range image covering historical points in LiDAR's small FoV is adopted for efficient map representation. To account for the noisy data from occlusions after map updating, a filter-based point-to-plane Gaussian Mixture Model is used for robust registration. Moreover, a LiDAR-only continuous-time motion model is employed to relieve the inevitable distortions. Extensive experiments have been conducted on various testbeds using the prism-based LiDARs with different scanning patterns, whose promising results demonstrate the efficacy of our proposed approach.

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