Event-Based Visual Odometry on Non-Holonomic Ground Vehicles

TL;DR

The paper tackles robust monocular, purely event-based visual odometry for non-holonomic ground vehicles by embedding the Ackermann motion model into a continuous-time, event-driven solver. It derives a continuous-time incidence relation for tracked event corners and transforms it into a tractable univariate polynomial via Taylor expansions of $\sin$ and $\cos$, solved through rank minimisation with Sturm root bracketing and histogram voting. The approach offers three expansion regimes (s3c2, s5c4, s7c6), enabling real-time estimates of the rotational velocity $\omega$ and demonstrating competitive accuracy with frame-based delta rotations while outperforming them under challenging illumination. The work advances purely event-based ego-motion estimation for ground vehicles and provides open-source code to facilitate adoption and further research.

Abstract

Despite the promise of superior performance under challenging conditions, event-based motion estimation remains a hard problem owing to the difficulty of extracting and tracking stable features from event streams. In order to robustify the estimation, it is generally believed that fusion with other sensors is a requirement. In this work, we demonstrate reliable, purely event-based visual odometry on planar ground vehicles by employing the constrained non-holonomic motion model of Ackermann steering platforms. We extend single feature n-linearities for regular frame-based cameras to the case of quasi time-continuous event-tracks, and achieve a polynomial form via variable degree Taylor expansions. Robust averaging over multiple event tracks is simply achieved via histogram voting. As demonstrated on both simulated and real data, our algorithm achieves accurate and robust estimates of the vehicle's instantaneous rotational velocity, and thus results that are comparable to the delta rotations obtained by frame-based sensors under normal conditions. We furthermore significantly outperform the more traditional alternatives in challenging illumination scenarios. The code is available at \url{https://github.com/gowanting/NHEVO}.

Figures (7)

• Figure 1: We consider visual odometry with a forward-facing event camera mounted on an Ackermann steering vehicle for which motion can be locally approximated by an arc of a circle about an Instantaneous Centre of Rotation (ICR). We assume constant rotational velocity during the time interval for which events are considered.
• Figure 2: The model used in the derivation, where the coordinate system $C_i$ is consistent with the event $\mathbf{e}_i$. Please see text for detailed explanations.
• Figure 3: The Taylor series expansion approximations for $\sin$ and $\cos$, the corresponding highest orders are 3, 5, 7 and 2, 4, 6 respectively.
• Figure 4: Impact of different factors on the accuracy of the recovered rotational velocity. sacb means that the highest order of the Taylor series expansions for $\sin$ is a and the highest order of the Taylor series expansion for $\cos$ is b.
• Figure 5: Example images and events with tracked corners used in our real-data experiments. (a), (b), and (c) represent a raw image, a cropped image, and a dark-filtered night image for KITTI, respectively. (d) shows the events generated using vid2e gehrig2020video and demonstrates the corner tracking result. (e) is an example image from our self-collected data at nighttime, on which again almost no features can be extracted.