Practical Pose Trajectory Splines With Explicit Regularization

We investigate spline-based continuous-time pose trajectory estimation using non-linear explicit motion priors. Current regularization priors either linearize the orientation, rely on the implicit regularization obtained from the used spline basis function, or use sampling based regularization schemes. The latter is a special case of a Riemann sum approximation, and we demonstrate when and why this can fail, and propose a way to avoid these issues. In addition we provide a number of novel practically useful theoretical contributions, including requirements on knot spacing for orientation splines, new basis functions for constant velocity extrapolation, and a generalization of the popular P-Spline penalty to orientation. We analyze the properties of the proposed approach using synthetic data. We validate our system using the standard task of visual-inertial calibration, and apply it to stereo visual odometry where we demonstrate real-time performance on KITTI.