  Sensor calibration, which can be intrinsic or extrinsic, is an essential step
to achieve the measurement accuracy required for modern perception and
navigation systems deployed on autonomous robots. To date, intrinsic
calibration models for spinning LiDARs have been based on hypothesized based on
their physical mechanisms, resulting in anywhere from three to ten parameters
to be estimated from data, while no phenomenological models have yet been
proposed for solid-state LiDARs. Instead of going down that road, we propose to
abstract away from the physics of a LiDAR type (spinning vs solid-state, for
example), and focus on the spatial geometry of the point cloud generated by the
sensor. By modeling the calibration parameters as an element of a special
matrix Lie Group, we achieve a unifying view of calibration for different types
of LiDARs. We further prove mathematically that the proposed model is
well-constrained (has a unique answer) given four appropriately orientated
targets. The proof provides a guideline for target positioning in the form of a
tetrahedron. Moreover, an existing Semidefinite programming global solver for
SE(3) can be modified to compute efficiently the optimal calibration
parameters. For solid state LiDARs, we illustrate how the method works in
simulation. For spinning LiDARs, we show with experimental data that the
proposed matrix Lie Group model performs equally well as physics-based models
in terms of reducing the P2P distance, while being more robust to noise.
