A Spline-Based Trajectory Representation for Sensor Fusion and Rolling Shutter Cameras

The use of multiple sensors for ego-motion estimation is an approach often used to provide more accurate and robust results. However, when representing ego-motion as a discrete series of poses, fusing information of unsynchronized sensors is not straightforward. The framework described in this paper aims to provide a unified solution for solving ego-motion estimation problems involving high-rate unsynchronized devices. Instead of a discrete-time pose representation, we present a continuous-time formulation that makes use of cumulative cubic B-Splines parameterized in the Lie Algebra of the group \(\mathbb {SE}3\). This trajectory representation has several advantages for sensor fusion: (1) it has local control, which enables sliding window implementations; (2) it is \(C^2\) continuous, allowing predictions of inertial measurements; (3) it closely matches torque-minimal motions; (4) it has no singularities when representing rotations; (5) it easily handles measurements from multiple sensors arriving a different times when timestamps are available; and (6) it deals with rolling shutter cameras naturally. We apply this continuous-time framework to visual–inertial simultaneous localization and mapping and show that it can also be used to calibrate the entire system.