  Aggressive motions from agile flights or traversing irregular terrain induce
motion distortion in LiDAR scans that can degrade state estimation and mapping.
Some methods exist to mitigate this effect, but they are still too simplistic
or computationally costly for resource-constrained mobile robots. To this end,
this paper presents Direct LiDAR-Inertial Odometry (DLIO), a lightweight
LiDAR-inertial odometry algorithm with a new coarse-to-fine approach in
constructing continuous-time trajectories for precise motion correction. The
key to our method lies in the construction of a set of analytical equations
which are parameterized solely by time, enabling fast and parallelizable
point-wise deskewing. This method is feasible only because of the strong
convergence properties in our nonlinear geometric observer, which provides
provably correct state estimates for initializing the sensitive IMU integration
step. Moreover, by simultaneously performing motion correction and prior
generation, and by directly registering each scan to the map and bypassing
scan-to-scan, DLIO's condensed architecture is nearly 20% more computationally
efficient than the current state-of-the-art with a 12% increase in accuracy. We
demonstrate DLIO's superior localization accuracy, map quality, and lower
computational overhead as compared to four state-of-the-art algorithms through
extensive tests using multiple public benchmark and self-collected datasets.
