Differential Evolution approach to the grid-based Localization and Mapping problem Luis Moreno, Santiago Garrido, Fernando Mart´ ın and M. Luisa Mu˜ noz Abstract— A new solution to the Simultaneous Localization and Modelling problem is presented. It is based on the stochastic search of solutions in the state space to the global localization problem by means of a differential evolution algorithm. A non linear evolutive filter, called Evolutive Localization Filter (ELF), searches stochastically along the state space for the best robot pose estimate. The proposed SLAM algorithm operates in two steps: in the first step the ELF filter is used at a local level to re-localize the robot based on the robot odometry, the laser scan at a given position and a local map where only a low number of the last scans have been integrated. In a second step the aligned laser measures together with the corrected robot poses are use to detect when the robot is revisiting a previously crossed area. Once a cycle is detected, the Evolutive Localization Filter is used again to re-estimate the robot poses in order to integrate the sensor measures in the global map of the environment. The algorithm has been tested in different environments to demonstrate the effectiveness, robustness and computational efficiency of the proposed approach. Index Terms— SLAM, Local Positioning Systems, Mobile robots, Differential Evolution Algorithm I. INTRODUCTION Localization and map building are key components in robot navigation and are required to successfully execute a path generated by a global planner. Both problems are closely linked, and learning maps required to solve simultaneously both problems. These simultaneous problems are often re- ferred as simultaneous localization and mapping (SLAM). In the SLAM case, uncertainty in measures, uncertainty in robot pose estimates and a partially learned map which contains the residual errors unsolved at integration or re-localization processes makes the SLAM problem complex. The two main approaches to effectively solve the si- multaneous localization and mapping problem have been consolidates in the last decade. The first approach uses a feature-based model of the environment and the extended Kalman filter (EKF) to manage the associated uncertainty. This approach is extremely compact, and its computational cost has been considerably improved in the most recent work. On the other hand, however, the linear nature of the basic method requires linearization of the motion and perception models which causes problems in the long term. Moreover, the technique has difficulties modelling many environment areas due to the limited set of feature models used. The second group of solutions use particle filters to obtain a solution to the SLAM problem. This group of Luis Moreno, Santiago Garrido, Fernando Mart´ ın are with the Robotics Lab., Carlos III University, Madrid, Spain. moreno@ing.uc3m.es M. Luisa Mu˜ noz is with the Facultad de Inform´ atica, Polytechnical University of Madrid, Madrid, Spain. solutions can use certainty grid map models or a feature map to represent the environment [12], and the sequential Monte Carlo methods to estimate the posterior probability distribution functions. This approach has proved to be very robust from a statistical point of view in the management of the uncertainties present in the problem. Its disadvantage is that the number of particles required increases the computa- tional cost and the algorithm robustness is heavily dependent on this because each particle has a statistical significance associated with it. In this work we present a new solution to the grid-based SLAM problem based on the stochastic search of the best pose estimate. This approach uses a differential evolution method [9] to perturb the possible pose estimates contained in a given set until the optimum is obtained. By properly choosing the cost function, a maximum a posteriori estimate is obtained. This method is applied at local level to re- localize the robot and at global level to solve the data association problem. The method proposed integrates sensor information in the map only when cycles are detected and the residual error are eliminated, avoiding a high number of modifications in the map or the existence of multiple maps, thus decreasing the computational cost compared to other solutions. Our approach has been validate on a set of data obtained from our experiments and data extracted from the Radish repository data. The results show the proposed method is able to satisfactorily close environment cycles to generate accurate metric maps. II. STATE OF THE ART The SLAM problem has been one of the most interest- ing theoretical problems in mobile robotics since the 90’s when the seminal work of Smith, Self and Cheeseman [8] introduced the concept of a stochastic map to establish uncertain spatial relationship between features detected in the environment. The Kalman filter provides the mechanism for integrating and updating the map. Julier and Uhlmann [3] have shown important conclusions derived from the fact that the linearization problem is structural and cannot be avoided. Castellanos et al. have also shown [1] that linearization errors produce inconsistency problems in the standard EKF solution for SLAM. A widely investigated aspect is the scaling properties of the stochastic map solution to the SLAM problem. The O(n 2 ) complexity of the basic solution (where n is the number of features in the map) has been a serious bottleneck. Several researchers have developed techniques