LIO-MARS: Non-uniform Continuous-time Trajectories for Real-time LiDAR-Inertial-Odometry

Abstract--Autonomous robotic systems heavily rely on environment knowledge to safely navigate. For search & rescue, a flying robot requires robust real-time perception, enabled by complementary sensors. IMU data constrains acceleration and rotation, whereas LiDAR measures accurate distances around the robot. Our new scan window uses non-uniform temporal knot placement to ensure continuity over the whole trajectory without additional scan delay. Moreover, we accelerate essential covariance and GMM computations with Kronecker sums and products by a factor of 3.3. An unscented transform de-skews surfels, while a splitting into intra-scan segments facilitates motion compensation during spline optimization. Complementary soft constraints on relative poses and preintegrated IMU pseudo-measurements further improve robustness and accuracy. ELIABLE real-time perception is essential for robotic autonomy. In particular, accurate mapping and ego-motion estimation are key components for safe interaction in complex and unstructured environments. Due to their precision and measurement density, modern LiDARs are often used in these scenarios, e.g., in the DARP A Subterranean Challenge [1], [2]. Sensor motion during scanning distorts the point cloud and degrades the quality of the map. This intra-scan motion is either compensated by de-skewing prior to registration [3], [4], [5], [6] or by modeling it with a continuous-time trajectory [7], [8], [9]. The former uses the previous state estimate and, optionally, an IMU to predict the motion and transform points to a common reference time. However, this comes at the cost of reduced real-time capability and requires either costly reintegration of surfels [9] or a limited number of selected pointwise features [e.g., CT -ICP [7], CLINS [8]]. To overcome these limitations of continuous-time methods, our novel real-time LiDAR-inertial odometry (LIO) jointly optimizes temporally partitioned scan segments (Figure 1) by registering multi-resolution surfel maps while an unscented transform (UT) compensates the intra-surfel motion. Manuscript received October XX, 2025; revised XX, 2025.