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

TL;DR

LIO-MARS advances real-time LiDAR-Inertial-Odometry by integrating a non-uniform continuous-time trajectory with a sliding window, enabling tight LiDAR-IMU coupling without scan delay. It enhances surfel-map registration through a Gaussian Mixture Model with robust motion compensation via an unscented transform and segment-wise intra-scan handling, while accelerating computations with Kronecker-based covariances and symmetry exploitation. The framework introduces learned robustness via relative motion constraints and gravity modeling on the unit sphere, plus non-uniform knot placement to maintain numerical stability. Extensive experiments across handheld, ground, and aerial datasets demonstrate state-of-the-art performance among recent LIO systems with real-time capabilities and robust behavior in challenging scenarios.

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. Building upon the LiDAR odometry MARS, our LiDAR-inertial odometry (LIO) jointly aligns multi-resolution surfel maps with a Gaussian mixture model (GMM) using a continuous-time B-spline trajectory. 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. Extensive evaluation showcases the state-of-the-art quality of our LIO-MARS w.r.t. recent LIO systems on various handheld, ground and aerial vehicle-based datasets.

Figures (9)

• Figure 1: Joint registration of LiDAR scans embedded in multi-resolution surfel maps (colored by relative scan time) optimizes a non-uniform continuous-time B-spline trajectory. An UT compensates motion within a surfel, while a temporal partitioning into segments enables optimization of motion distortion between surfel intrinsically. Inclusion of relative ($\Delta R,\Delta \bm{v},\Delta\bm{p},\Delta T$) and absolute ($\bm{\alpha}_0,\bm{\alpha},\bm{\omega}$) soft-constraints further improves robustness in challenging situations.
• Figure 2: System overview: A non-uniform continuous-time spline trajectory defined by knots $\mathcal{X}$ describes the sensor motion. A new raw scan $\mathcal{P}_l$ is preoriented with IMU before lattice embedding into a multi-resolution surfel map $\mathcal{S}_l$. Motion priors ($\Delta T,\Delta_{pre}$) aid the spline initialization of the sliding registration window $\mathcal{W}_l$. Sensor motion within surfel is compensated prior to alignment against a keyframe-based local surfel map $\mathcal{M}$ under motion constraints. After spline registration, a new pointwise undistorted keyframe is added to the storage if necessary; or the local map is updated with the closest keyframes.
• Figure 3: Influence of knot placement: a) Knots $X_k$ influence the time (black/blue) between $t_{X_0}$ and $t_{X_1}$. MARS quenzel2021mars necessitates reinitialization of its knots at every timestep since the uniform spline requires a constant $\Delta t$ (black) between knots while the knot times $t_{X}$ move forward with variable $\Delta t_l$. b) Uniform knot placement with fixed $\Delta t$ , e.g., as in CLINS lv2021clins and SLICT nguyen2023slict, may enforce continuity by appending new and fixing previous knots. The difference between scan time $t_l$ and furthest knot $X_{k+1}$ [red in b)] impairs constraints on $X_{l-1}$. c) Coco-LIC lang2023cocolic varies the number of knots under variable acceleration, but retains uniform knot placement under uniform motion as in b. d) Our non-uniform window has minimal difference and thus constrains the furthest knot better.
• Figure 4: Spline window: a) MARS quenzel2021mars only optimizes a $N$th order spline for $L$ scans (e.g., $N=L=3$) for a single interval $\Delta t$ from scan $j-L$ until $j$ allowing discontinuity between $j-L$ and $j-L+1$ (left, red dashed). b) Our method enforces continuity and keeps previous intervals fixed while optimizing one interval per scan.
• Figure 5: Ill-conditioning of uniform B-spline w.r.t. the last constraint. The condition number $\kappa_l$ improves for $t_l$ approaching $t_{k+1}$ [a)] since the weight $\lambda$ [b)] increases for the newest knot ($k+1$).