Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through Sparse Gaussian Process

TL;DR

A multi-LiDAR multi-IMU state estimator that takes advantage of Gaussian Process that predicts a non-parametric continuous-time trajectory to capture sensors' spatial-temporal movement with limited control states and is capable of handling different sensor configurations and resilient to sensor failures is introduced.

Abstract

Nowadays, sensor suits have been equipped with redundant LiDARs and IMUs to mitigate the risks associated with sensor failure. It is challenging for the previous discrete-time and IMU-driven kinematic systems to incorporate multiple asynchronized sensors, which are susceptible to abnormal IMU data. To address these limitations, we introduce a multi-LiDAR multi-IMU state estimator by taking advantage of Gaussian Process (GP) that predicts a non-parametric continuous-time trajectory to capture sensors' spatial-temporal movement with limited control states. Since the kinematic model driven by three types of linear time-invariant stochastic differential equations are independent of external sensor measurements, our proposed approach is capable of handling different sensor configurations and resilient to sensor failures. Moreover, we replace the conventional $\mathrm{SE}(3)$ state representation with the combination of $\mathrm{SO}(3)$ and vector space, which enables GP-based LiDAR-inertial system to fulfill the real-time requirement. Extensive experiments on the public datasets demonstrate the versatility and resilience of our proposed multi-LiDAR multi-IMU state estimator. To contribute to the community, we will make our source code publicly available.

Figures (6)

• Figure 1: The schematic of continuous-time self-driven estimator vs discrete-time IMU-driven scheme. In the discrete-time estimator, continuously captured LiDAR points must be transferred to a specific state, while our continuous-time estimator can query any state through GP interpolation. Besides, the IMU-driven estimator relies on IMU data for state propagation, while the kinematics of our estimator is driven by GP prior.
• Figure 2: An illustration of sliding window optimization, including three kinds of constraints from external observation, internal kinematics, and marginalization prior. The global state $\mathbf{x}(t)$ of this sliding window consists of three segments, while the state $\mathbf{x}_{k}(t)$ in each segment is driven by the hybrid GP prior. Upon the arrival of measurements within $[t_{3},t_{4})$, the oldest states $\mathbf{x}_{0}$ along with all measurements within $[t_{0},t_{1})$ will be marginalized.
• Figure 3: The mapping result of our proposed Traj-LIO on sequence eee 03 in NTU VIRAL dataset.
• Figure 4: The estimated angular velocity is compared with the measured gyroscope values across three axes. The right side shows the results obtained by our method using IMU information, while the left only uses LiDAR information.
• Figure 5: Mapping result of our method only using LiDAR information when the gyroscope exceeds its range. (a) Point-LIO fails in this scenario without IMU. (b) and (c) delve into the details of our results.