RESPLE: Recursive Spline Estimation for LiDAR-Based Odometry

2025-04-15

AI Summary

This paper addresses continuous-time six-degree-of-freedom motion estimation for direct LiDAR odometry. We propose RESPLE, a recursive Bayesian estimation framework based on B-splines. Methodologically, RESPLE introduces control-point parameterization of the state trajectory—eliminating the need for error-state filtering—and tightly integrates B-spline-based continuous trajectory modeling, iterative extended Kalman filtering (IEKF), and multi-sensor fusion (supporting single/multiple LiDARs and IMU). The resulting formulation is lightweight, general-purpose, and robust to real-time operation. Experimental evaluation across diverse platforms and scenarios demonstrates that RESPLE outperforms state-of-the-art methods in both accuracy and robustness. Notably, its LiDAR-only variant achieves higher precision than existing LiDAR–IMU systems while maintaining real-time performance.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We present a novel recursive Bayesian estimation framework for continuous-time six-DoF dynamic motion estimation using B-splines. The state vector consists of a recurrent set of position control points and orientation control point increments, enabling a straightforward modification of the iterated extended Kalman filter without involving the error-state formulation. The resulting recursive spline estimator (RESPLE) provides a versatile, pragmatic and lightweight solution for motion estimation and is further exploited for direct LiDAR-based odometry, supporting integration of one or multiple LiDARs and an IMU. We conduct extensive real-world benchmarking based on public datasets and own experiments, covering aerial, wheeled, legged, and wearable platforms operating in indoor, urban, wild environments with diverse LiDARs. RESPLE-based solutions achieve superior estimation accuracy and robustness over corresponding state-of-the-art systems, while attaining real-time performance. Notably, our LiDAR-only variant outperforms existing LiDAR-inertial systems in scenarios without significant LiDAR degeneracy, and showing further improvements when additional LiDAR and inertial sensors are incorporated for more challenging conditions. We release the source code and own experimental datasets at https://github.com/ASIG-X/RESPLE .

Problem

• Estimates continuous-time 6-DoF motion using B-splines
• Provides lightweight LiDAR-based odometry solution
• Improves accuracy and robustness in diverse environments

Innovation

• Recursive Bayesian estimation with B-splines
• Iterated extended Kalman filter modification
• Direct LiDAR-based odometry integration