A Properly Designed Extended Kalman Filtering Approach for Robot Localization by Sensors with Different Degree of Accuracy G. Ippoliti, L. Jetto, S. Longhi and A. Monteri` u Universit`a Politecnica delle Marche, Dipartimento di Ingegneria Informatica, Gestionale e dell’Automazione, Via Brecce Bianche, 60131 Ancona, Italy. Tel.: +39 071 220 4451, Fax: +39 071 220 4474, Email: g.ippoliti@diiga.univpm.it {l.jetto, sauro.longhi, a.monteriu}@univpm.it Abstract — A basic requirement for an autonomous mobile robot is to localize itself with respect to a given coordinate system. In this regard two different op- erating conditions exist: structured and unstructured environment. The relative methods and algorithms are strongly influenced by the a priori knowledge on the environment where the robot operates. If the environ- ment is only partially known the localization algorithm needs a preliminary definition of a suitable environ- ment map. In this paper the localization problem is formulated in a stochastic setting and an Extended Kalman Filtering (EKF) approach is proposed for the integration of odometric, gyroscope and laser scanner measures. As gyroscopic measures are much more re- liable than the other ones, the localization algorithm gives rise to a nearly singular EKF. This problem is dealt with defining a lower order non singular EKF. I. INTRODUCTION Two different kinds of mobile robot localization exist: relative and absolute. The first one is based on the data provided by sensors measuring the dynamics of variables internal to the vehicle; absolute localization requires sen- sors measuring some parameters of the environment where the robot is operating. The actual trend is to exploit the complementary nature of these two kinds of sensorial information to improve the precision of the localization procedure (see e.g. [1]–[6]) at expense of an increased cost and computational complexity. The aim is to improve the mobile robot autonomy by enhancing its capability of localization with respect to the surrounding environment. In this framework the re- search interests have been focused on multi-sensor systems because of the limitations inherent any single sensory device, that can only supply a partial information on the environment, thus limiting the ability of the robot to localize itself. The methods and algorithms proposed in the literature for an efficient integration of multiple-sensor information differ according to the a priori information on the environment, which may be almost known and static, or almost unknown and dynamic. If the environment is only partially known the localiza- tion algorithm needs a preliminary definition of a suitable environment map. Recently, the Simultaneous Localization and Map Build- ing problem (SLAM problem) has been deeply investigated for increasing the autonomy of navigation of mobile robots (see e.g. [7]–[23]). The idea is to develop a localization algorithm that can build a map of the environment while simultaneously using the same map to localize the mobile robot. This approach promises to allow these vehicles to really operate autonomously for long period of time in unknown environments. The purpose of this paper is to propose and to ex- perimentally evaluate a localization algorithm based on a measure apparatus composed of a set of sensors of a different nature and characterized by a highly different degree of accuracy. The sensor equipment includes odo- metric, gyroscopic and laser measures. In particular, the interest of this paper focuses on the emerging area of assistive technologies where powered wheelchairs can be used to strengthen the residual abilities of users with motor disabilities [24]–[26]. The proposed algorithm results in a computationally efficient solution of the localization problem and may really represent a first basic step towards the proper design of a navigation system aimed at enhancing the efficiency and the security of commercial powered wheelchairs. The main technical novelties of this paper are: i) both the information carried by the kinematic model of the robot and that carried by the dynamic equations of the odometry are exploited. The first kind of information is inglobed in the dynamical equation of the state-space model of the vehicle, the second one is properly inglobed in a measure equation through the definition of an extended state; ii) the nearly singular filtering problem arising from the very high accuracy of a measure has been explicitly taken into account. The experimental tests, performed on the TGR Explorer