Abstract Using Multiple Gaussian Hypotheses to Represent Probability Distributions for Mobi
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quirement for independent measurement data. This is significant as it is not clear that statistical independence can be guaranteed for most robotic applications. 2 System Model
Mobile robot localization is one area of particular interest where the representation of arbitrary probability distributions is required. Here we consider the problem of global localization which is to determine the position of the robot in an environment by observations of features in the environment with known locations (stored in a map). A probabilistic approach is required for global localization as the observation of the features is a highly uncertain process, depending upon real sensors and signal processing. However, the features observed by the robot are generally not unique and may occur multiple times in the map. As a result, the probability distribution over the robots location will be, in general, multi-modal. Many localization schemes have neglected this and used singlemode representations, of which the Kalman filter is by far the most common (e.g. [5, 6, 7]). In this paper, we present a method for representing the probability distribution by a number (or a mixture) of Gaussian hypotheses. Multiple Gaussian hypotheses have been previously applied to the problem of mobile robot localization by Jensfelt and Kristensen [8]. However, this method assumed a solution to the "data association" problem. That is, it was assumed that measurements could be matched against the existing set of hypotheses and only matching measurements were used to update the hypotheses. On the other hand, the method presented here delays the data association step by forming all possible matches and only then removing the least likely of them (if necessary). A further enhancement presented here is the use of "covariance intersection" [9] to intersect Gaussian hypotheses. This technique does not depend on the assumption of statistical independence and hence, the robot localization method presented here has no re-
David J. Austin d. aust in@comput er. org
Patric Jensfelt p a t r i c O s 3 , k t h . se
C e n t r e for A u t o n o m o u s S y s t e m s , R o y a l I n s t i t u t e of T e c h n o l o g y , S t o c k h o l m S E - 1 0 0 44, S w e d e n .
Proceedings of the 2000 IEEE International Conference on Robotics & Automation San Francisco, CA • April 2000
Using Multiple Gaussian Hypotheses to Represent Probability Distributions for Mobile Robot Localization
As discussed above, due to the highly uncertain nature of real-world sensors and signal processing, we use a probabilistic framework for mobile robot localization. T h a t is, we maintain a probability distribution over the space of possible robot locations. For this paper we will consider the space of robot poses (both position and orientation in the plane). We denote the true robot pose at time t as x(t) = (x(t),y(t),a(t)) and the estimate at time t as :~(t) = (2(t), ~)(t), &(t)). For the mobile robot, we assume t h a t the system evolves as: x(t + 1) = f ( x ( t ) , u ( t ) ) + v(t) (1)
where g is a nonlinear feature extraction function and w(t) is the process noise, assumed zero-mean and Gaussian with covariance matrix R ( t ) . It is further assumed that v(t) and w(t) are independent. Given this general framework we must update an a priori probability distribution with the information in the feature hypotheses to give a new, posterior distribution, which reflects the u p d a t e d knowledge of the robot pose. However, before we can apply the new information, we must decide upon a representation for the probability distributions.
Abstract
A new mobile robot localization technique is presented which uses multiple Gaussian hypotheses to represent the probability distribution of the robots location in the environment. Sensor data is assumed to be provided in the form of a Gaussian distribution over the space of robot poses. A tree of hypotheses is built, representing the possible data association histories for the system. Covariance intersection is used for the fusion o/the Gaussians whenever a data association decision is taken. However, such a tree can grow without bound and so rules are introduced for the elimination o / t h e least likely hypotheses from the tree and for the proper re-distribution of their probabilities. This technique is applied to a feature-based mobile robot localization scheme and experimental results are given demonstrating the effectiveness of the scheme.