A White-Noise-on-Jerk Motion Prior for Continuous-Time Trajectory Estimation on <italic>SE(3)</italic>

Abstract

Simultaneous trajectory estimation and mapping (STEAM) offers an efficient approach to continuous-time trajectory estimation, by representing the trajectory as a Gaussian process (GP). Previous formulations of the STEAM framework use a GP prior that assumes white-noise-on-acceleration, with the prior mean encouraging constant body-centric velocity. We show that such a prior cannot sufficiently represent trajectory sections with non-zero acceleration, resulting in a bias to the posterior estimates.This paper derives a novel motion prior that assumes whitenoise-on-jerk, where the prior mean encourages constant bodycentric acceleration. With the new prior, we formulate a variation of STEAM that estimates the pose, body-centric velocity, and body-centric acceleration. By evaluating across several datasets, we show that the new prior greatly outperforms the white-noiseon-acceleration prior in terms of solution accuracy.

The Oxford Multimotion Dataset: Multiple SE(3) Motions With Ground Truth

“…To improve performance, the trajectory estimate can be retrospectively interpolated through the occlusion when the object is detected again by using linear interpolation in se (3) algebra space. More accurate motion priors [25,26] may be able to better estimate this more complicated motion. This shows there is significant room for further work in estimating motion through occlusion, and this dataset includes a useful gradient of difficulties to measure that progress.…”

Occlusion-Robust MVO: Multimotion Estimation Through Occlusion Via Motion Closure

“…Few objects move with truly constant velocity, but these results illustrate that it is robust to small changes in velocity and allows velocities to evolve over time. Future work will consider a white-noise-on-jerk prior [35] to better model smoothly varying accelerations, and more expressive priors can be used to address complex dynamic motions, such as when the swinging block changed direction at the end of the segment in Fig. 5c.…”

“…The applicability of the white-noise-on-acceleration motion prior is limited in scenes where objects change direction or speed. Future work will focus on introducing a white-noiseon-jerk prior [31], which is more applicable to motions with smoothly varying velocities.…”

Unsupervised Learning of Lidar Features for Use in a Probabilistic Trajectory Estimator

“…Using the KITTI odometry benchmark metric [4], the average translation (%) and orientation ( the focus of this work, and the faster spin-rate alleviates this problem to some degree. We demonstrated motion compensation in past work with the same estimator [33], [34], and note that it is applicable to this work as well. We follow the KITTI odometry evaluation metric for all datasets, which averages the relative position and orientation errors over trajectory segments of 100 m to 800 m. We implemented the network using a KPConv implementation in PyTorch 5 .…”