Galilean Robots, Aristotelian Sensors: Joint Spatiotemporal Trajectory Estimation and Extrinsic Calibration

This paper introduces a new method for multi-sensor state estimation that uses the Galilean group to represent robot trajectories and the Aristotelian subgroup for sensor extrinsics. By coupling motion and temporal offset directly within the group structure, the approach eliminates the need for separate continuous-time trajectory representations or motion compensation. The authors develop priors driven by twists and IMUs, accommodate non-ideal clocks, and validate the framework using camera, position, and range measurements in both simulated and real experiments. Results show performance comparable to established methods across various heterogeneous sensor configurations, offering a simplified quality-of-life improvement without compromising accuracy.