LiDAR Odometry is an essential component in many robotic applications. Unlike
the mainstreamed approaches that focus on improving the accuracy by the
additional inertial sensors, this letter explores the capability of LiDAR-only
odometry through a continuous-time perspective. Firstly, the measurements of
LiDAR are regarded as streaming points continuously captured at high frequency.
Secondly, the LiDAR movement is parameterized by a simple yet effective
continuous-time trajectory. Therefore, our proposed Traj-LO approach tries to
recover the spatial-temporal consistent movement of LiDAR by tightly coupling
the geometric information from LiDAR points and kinematic constraints from
trajectory smoothness. This framework is generalized for different kinds of
LiDAR as well as multi-LiDAR systems. Extensive experiments on the public
datasets demonstrate the robustness and effectiveness of our proposed
LiDAR-only approach, even in scenarios where the kinematic state exceeds the
IMU's measuring range. Our implementation is open-sourced on GitHub.

通过连续时间视角探索 LiDAR 单独里程计的能力，我们提出的 Traj-LO 方法通过紧密地结合 LiDAR 点的几何信息和轨迹平滑度的运动约束，恢复了 LiDAR 的时空一致性移动。该方法在不同种类的 LiDAR 以及多 LiDAR 系统中都具有广泛的实验验证，即使在运动状态超出 IMU 测量范围的情况下也展现了鲁棒性和有效性。我们的实现已在 GitHub 上开源。

Traj-LO: 高效连续时间轨迹的仅激光雷达导航定位

Traj-LO: In Defense of LiDAR-Only Odometry Using an Effective  Continuous-Time Trajectory

Accelerated gradient methods play a central role in optimization, achieving
optimal rates in many settings. While many generalizations and extensions of
Nesterov's original acceleration method have been proposed, it is not yet clear
what is the natural scope of the acceleration concept. In this paper, we study
accelerated methods from a continuous-time perspective. We show that there is a
Lagrangian functional that we call the \emph{Bregman Lagrangian} which
generates a large class of accelerated methods in continuous time, including
(but not limited to) accelerated gradient descent, its non-Euclidean extension,
and accelerated higher-order gradient methods. We show that the continuous-time
limit of all of these methods correspond to traveling the same curve in
spacetime at different speeds. From this perspective, Nesterov's technique and
many of its generalizations can be viewed as a systematic way to go from the
continuous-time curves generated by the Bregman Lagrangian to a family of
discrete-time accelerated algorithms.

本文从连续时间的角度研究了加速方法，发现 Bregman Lagrangian 是一种生成各种加速方法的拉格朗日函数，其中包括 Nesterov 成果的系统方法。