A Hierarchical Wavelet Decomposition for Continuous-Time SLAM

This paper proposes using hierarchical wavelets as a basis in parametric continuous-time batch estimation. The need for a continuous-time robot pose in the simultaneous localization and mapping (SLAM) problem has arisen as stateof-the-art batch SLAM algorithms attempt to handle more challenging hardware; specifically, the continuous-time framework is particularly beneficial when using high-rate sensors, multiple unsynchronized sensors, or scanning sensors, such as lidar and rolling-shutter cameras, during motion. Although the traditional discrete-time SLAM formulation can be adapted by using temporal pose interpolation, approaches using the continuous-time framework are able to generate smooth robot trajectories with less state variables. In this paper, we focus on the parametric approach using temporal basis functions to develop a finite-element representation of the continuous-time robot trajectory. While the majority of current implementations have utilized a uniformly spaced B-spline basis, we note that trajectory richness is often quite variable; in this paper, we show how a hierarchical system of wavelet basis functions can be used to increase the resolution of the solution only in the temporally local regions of the trajectory that require additional detail. We validate our approach by contrasting uniform Bsplines and wavelets in a six-dimensional pose-graph SLAM experiment, using both simulated and real data.