Supervised Linear Feature Extraction for Mobile Robot Localization

We are seeking linear projections of supervised highdimensional robot observations and an appropriate environment model that optimize the robot localization task. V~b show that an appropriate risk function to minimize is the conditional entropy of the robot positions given the projected observations. We propose a method of iterative optimization through a probabilistic model based on kernel smoothing. To obtain good starting optimization solutions we use canonical correlation analysis. We apply our method on a real experiment involving a mobile robot equipped with an omnidirectional camera in an otfice setup. 1 I n t r o d u c t i o n Current trend in mobile robot technology is towards building fully autonomous mobile robots, i.e., robots that can operate without external guidance in unstructured or natural environments. To localize themselves accurately and then plan paths in their workspace the robots must use their perception mechanism, e.g., vision, often in combination with a dead-reckoning device, e.g., an odometer. From a statistical viewpoint the robot localization task can be regarded as a prediction problem. Given an a priori model of the environment and a new sensor observation the task is to predict the position of the robot as accurately as possibly. Such a model, called map, is often built through supervised learning from a set of known robot positions-sensor observations [7, 11, 5, 12]. Sensor technology provides high-dimensional data -7803-5886-4100 /$ 10 .00© 2000 IEEE 2979 l e-mai l : m o t o m u r a @ e t l . g o . j p such as images or range profiles. To deal with the abundance and the inherent redundancy in the data (e.g., too many correlated measurements) an appropriate feature extraction scheme should precede the modeling step. The extracted features can be natural landmarks, i.e., distinctive features of the environment [1] or landmarks formed by some mathematical transformation on the original observations [11, 5, 12]. In this paper we deal with the latter case, specifically the extraction of linear features from omnidirectional image data to be used for map building and localization. Previous work in our group has investigated the use of principal component analysis (PCA) for this purpose [5, 12]. However, PCA is an unsupervised method which optimizes a reconstruction error and may not be necessarily good for localization. In this paper we look for supervised linear projections of the robot observations and an appropriate environment model so that the localization performance of the robot is optimized. In the following we describe the proposed model, the localization criterion to optimize, and the optimization method we use to get the optimal features. We demonstrate our method on a real robot equipped with an omnidirectional camera in an office environment. The results show that our method outperforms PCA as a linear feature extraction method for robot localization. 2 T h e r o b o t l o c a l i z a t i o n p r o b l e m Imagine a (point) robot at an unknown position x* E ]R 2 of its two-dimensional workspace, observing a ddimensional vector 1 z*, e.g., an image. The robot localization problem concerns the prediction of x* given