436 JESA. Volume 50 – n° 4-6/2017
1. Introduction
Mobile robots generally rely on the localization results to follow the planned path.
Uncertainty in localization may negatively affect the path planning and path following.
However, there is little report on the impact of localization uncertainty on path
planning.
The existing studies often describe localization uncertainty by the distribution
covariance of locations and treat it the same as localizability. Roy et al. (1999) were
the first to study the uncertainty in localization and localizability. Li and Franck
measured the confidence of the information from the positioning system using map-
aided horizontal uncertainty level meter. References (Yang et al., 2015) explore the
localization uncertainty and localizability in wireless network localization.
The localization uncertainty and localizability have been extensively investigated
in the map-based localization methods, in which the robot localizes itself by matching
its perception with the given map through dead-reckoning (Qian et al., 2016).
Assuming that the map is binary and the obstacle is differentiable, Censi (2007)
determined the theoretical precision limit of map-based localization methods based
on Cramér–Rao bound, defined localizability as the low bound of the localization
uncertainty of the robot, and proposed a series of localizability estimation methods.
Qian et al. (2016) introduced the influence factor of dynamic obstacles to estimate the
localizability. Wang et al. (2015) developed a localizability-based action selection
mechanism for mobile robots to speed up the convergence of global localization, in
which the possible observation distinctness after a given action is predicted by a utility
function. Ruiz-Mayor et al. proposed a new approach to estimate the perceptual
ambiguity associated with localization uncertainty, and created a new probabilistic
model of indistinguishability for perception with different kinds of range sensors
(Murtra et al., 2008).
The localization uncertainty has been taken into account in many recent studies on
path or motion planning. For instance, Gonzalez and Stentz (2007) pursued the lowest
expected cost, taking the localization uncertainty as a threat to the target reachability.
Hu et al. (2012) presented a path planning algorithm for a mobile manipulator based
on localizability, evaluated the localizability of a given path by adding up the fisher
matrix along the path, and selected the path with the best localizability. Considering
the localization uncertainty of the path, Robert et al. put forward a path planning
algorithm after evaluating the uncertainties along the path and taking the localization
uncertainty as a negative issue.
To sum up, the previous research has shown that the localization uncertainty has
a negative impact to path or motion planning. However, more analysis is needed to
identify and evaluate the exact impact. Hence, this paper attempts to disclose the
impact of uncertain localization on path planning and develop evaluation functions
for the impact (Zhao et al., 2000).
The remainder of this paper is organized as follows: Section 2 discusses the impact
of localization uncertainty on path planning and path following; Section 3 puts
forward the evaluation functions for this impact; Section 4 verifies the performance