Warped Hypertime Representations for Long-term Autonomy of Mobile Robots

Abstract

This paper presents a novel method for introducing time into discrete and continuous spatial representations used in mobile robotics, by modelling long-term, pseudo-periodic variations caused by human activities. Unlike previous approaches, the proposed method does not treat time and space separately, and its continuous nature respects both the temporal and spatial continuity of the modeled phenomena. The method extends the given spatial model with a set of wrapped dimensions that represent the periodicities of observed changes. By performing clustering over this extended representation, we obtain a model that allows us to predict future states of both discrete and continuous spatial representations. We apply the proposed algorithm to several long-term datasets and show that the method enables a robot to predict future states of representations with different dimensions. The experiments further show that the method achieves more accurate predictions than the previous state of the art.

Figures (5)

• Figure 1: Method overview: The data points (a,t) observed over time (top, black) are first processed by frequency analysis fremen to determine a dominant periodicity $T$. Then, the time $t$ is projected onto a 2d space (called hypertime) and the vectors $(a,t)$ become $(a,cos(2\pi\,t/T),sin(2\pi\,t/T))$ (bottom, left). The projected data are then clustered (bottom, center, blue) to estimate the distribution of $a$ over the hypertime space (green). Projection of the distribution back to the uni-dimensional time domain allows to calculate the probabilistic distribution of $a$ for any past or future time.
• Figure 2: Door state prediction error. The left figure shows the MSE for the training (week 0) and testing (weeks 1-9) datasets. An arrow from model A to model B in the right figure indicates that A's prediction error is statistically significantly lower than prediction error of model B.
• Figure 3: Temporal model performance for feature-based topological localisation. The left figure shows the dependence of localisation error rate on the number of features predicted by a given temporal model. An arrow from A to B in the right indicates that A's localisation error rate is statistically significantly lower than localisation error rate of model B.
• Figure 4: Navigation velocity reconstruction and prediction errors. The left figure shows the MSE for the training and testing sets. An arrow from A to B in the right indicates that A's prediction error is statistically significantly lower than velocity prediction error of model B.
• Figure 5: Human presence prediction results. The left figure shows how the mean squared error reduced for a particular model granularity compared to the Mean model. An arrow from A to B in the right indicates that A's prediction error is statistically significantly lower than velocity prediction error of model B.