RESPLE: Recursive Spline Estimation for LiDAR-Based Odometry

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 .

Continuous-Time State Estimation Methods in Robotics: A Survey

Accurate, efficient, and robust state estimation is more important than ever in robotics as the variety of platforms and complexity of tasks continue to grow. Historically, discrete-time filters and smoothers have been the dominant approach, in which the estimated variables are states at discrete sample times. The paradigm of continuous-time state estimation proposes an alternative strategy by estimating variables that express the state as a continuous function of time, which can be evaluated at any query time. Not only can this benefit downstream tasks such as planning and control, but it also significantly increases estimator performance and flexibility, as well as reduces sensor preprocessing and interfacing complexity. Despite this, continuous-time methods remain underutilized, potentially because they are less well-known within robotics. To remedy this, this work presents a unifying formulation of these methods and the most exhaustive literature review to date, systematically categorizing prior work by methodology, application, state variables, historical context, and theoretical contribution to the field. By surveying splines and Gaussian processes together and contextualizing works from other research domains, this work identifies and analyzes open problems in continuous-time state estimation and suggests new research directions.