  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.
