Differential evolution solution to the SLAM problem

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Abstract

A new solution to the Simultaneous Localization and Modelling problem is presented in this paper. The algorithm is based on the stochastic search for solutions in the state space to the global localization problem by means of a differential evolution algorithm. This non linear evolutive filter, called Evolutive Localization Filter (ELF), searches stochastically along the state space for the best robot pose estimate. The set of pose solutions (the population) focuses on the most likely areas according to the perception and up to date motion information. The population evolves using the log-likelihood of each candidate pose according to the observation and the motion errors derived from the comparison between observed and predicted data obtained from the probabilistic perception and motion model.

The proposed SLAM algorithm operates in two steps: in the first step the ELF filter is used at 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 the second step, the aligned laser measures and the corrected robot poses are used to detect whether the robot is revisiting a previously crossed area (i.e., a cycle in the robot trajectory exists). Once a cycle is detected, the Evolutive Localization Filter is used again to estimate the accumulated residual drift in the detected loop and then 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.

Introduction

Localization and map building are closely linked problems, and learning maps need to simultaneously solve both problems. These problems are often referred to as simultaneous localization and mapping(SLAM). Building maps when robot poses are known is a tractable problem with limited computational complexity, because it is only necessary to manage the error associated with each individual sensor measurement at the time of modelling. However, in the SLAM case, uncertainty in measurements, uncertainty in robot pose estimates and a partially learned map, which contains the residual errors (the difference between the true pose value and the pose estimate) remaining after the localization process make the SLAM problem complex.

Two main approaches to effectively solve the simultaneous localization and mapping problem have emerged in the last decade. The first approach uses a feature-based model of the environment and the extended Kalman filter 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 linearisation of the motion and perception models which causes problems in the long term. Moreover, the technique has difficulties modelling many environments due to the limited set of feature models used (e.g., cluttered laboratories or offices).

The second group of solutions uses particle filters to obtain a solution to the SLAM problem. This group of solutions can use certainty grid map models, or a feature map to represent the environment [27], and sequential Monte Carlo methods [7] 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 computational cost, and the algorithm robustness is heavily dependent on this because each particle has a statistical significance associated with it.

In spite of the advances in stochastic search optimization methods in the last decade, they have received limited attention in the field of localization and SLAM problems. 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 [24] 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 a 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 errors 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 validated on a set of data obtained from our experiments, and data extracted from the Radish repository. The results show that the proposed method is able to satisfactorily close environment cycles, to generate accurate metric maps.

The paper is organized as follows. A global evolutive localization filter (ELF) is formulated and explained in Section 3. Next, Section 4 introduces the ELF algorithm details, Section 5 deals with the key aspects of the ELF algorithm application to the SLAM problem and the SLAM algorithm proposed. The following sections present the experimental results, and discuss the advantages and disadvantages of the algorithm.

Section snippets

State of the art

The SLAM problem has been one of the most interesting theoretical problems in mobile robotics since 1986 when the seminal work of Smith, Self and Cheeseman [23], [22] introduced the concept of a stochastic map to establish uncertain spatial relationships between features detected in the environment. They use a covariance matrix to encode the correlations between all pairs of landmarks included in the map, and the Extended Kalman filter provides the mechanism for integrating and updating new

Localization problem formulation and solution

The SLAM solution we propose is based on the application at local or global scale of a differential evolution search method to obtain optimal solutions to the localization problem. In this section, the localization problem is formulated as an optimization problem, and the stochastic search method called Evolutionary Localization Filter (ELF) is developed.

From a Bayesian point of view, the localization problem can be formulated as a probability density estimation problem where the robot seeks to

Evolutive localization filter algorithm

The algorithm proposed to implement the evolutive localization filter is based on the Differential Evolution (DE) method proposed by Storn and Price [24] for global optimization problems over continuous spaces, and the Evolutive Localization Filter (ELF) proposed by Moreno [20] to solve the global localization problem. The Evolutive Localization Filter uses a parallel direct stochastic search method which utilizes n dimensional parameter vectors xik=(xi,1k,,xi,nk)T to point each candidate

Differential evolution approach to SLAM problem

In the simultaneous localization and mapping problem case, the map needs to be estimated concurrently with the pose to generate the expected measurements. In Fig. 2, the data flow in SLAM is shown. Note how the SLAM problem solution depends on the data association problem at local and global level.

The most extended Bayesian formulation for the SLAM problem is to estimate the posterior probability of the trajectories, the map associated to it given the observations z1:t and the odometry

Experimental results

To demonstrate the algorithm, two different test environments have been used. The data for the first test environment have been obtained from the Robotics Data Set Repository (Radish) [3] and they are part of the Intel Jones Farms Campus (Oregon). We thank M. Batalin for providing this data. This environment is an excellent test to show the cycle resolution capability of the mapping algorithm due to the presence of different cycles in the environment.

Fig. 4 shows the pose at the end of the

Conclusion

The differential evolution-based solution to the grid-based SLAM problem presented in this article introduces a new possibility to accurately solve the SLAM problem. At a local scale, the ELF localisation algorithm provides a fast and accurate maximum likelihood estimate with results equivalent to other re-localisation methods like scan matching approaches. And at a global scale, the algorithm only incurs substantial cost at cycle closing detection time and the cost increases linearly with the

Acknowledgements

The authors gratefully acknowledge the funds provided by the Spanish Government through the MCYT project DPI2004-0594.

Luis Moreno received the Degree in Automation and Electronics Engineering in 1984 and the Ph.D. degree in 1988 from the Universidad Politécnica de Madrid, Madrid, Spain. From 1988 to 1994, he was an associate professor at the Universidad Politécnica de Madrid. In 1994 he joined the Dpt of Systems Engineering and Automation, Universidad Carlos III de Madrid, Madrid, Spain, where he has been involved in several mobile robotics projects. His research interests are in the areas of mobile robotics,

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    Luis Moreno received the Degree in Automation and Electronics Engineering in 1984 and the Ph.D. degree in 1988 from the Universidad Politécnica de Madrid, Madrid, Spain. From 1988 to 1994, he was an associate professor at the Universidad Politécnica de Madrid. In 1994 he joined the Dpt of Systems Engineering and Automation, Universidad Carlos III de Madrid, Madrid, Spain, where he has been involved in several mobile robotics projects. His research interests are in the areas of mobile robotics, mobile manipulators, environment modelling, path planning and mobile robot global localization problems.

    Santiago Garrido received the Degree in Mathematics in 1979 from the Complutense University of Madrid, the Degree in Physics science in 1985 and the Ph.D. degree in 2000 from the Universidad Carlos III de Madrid, Spain. In 1997 he joined the Dpt of Systems Engineering and Automation, Universidad Carlos III de Madrid, Madrid, Spain, where he has been involved in several mobile robotics projects. His research interests are in the areas of mobile robotics, mobile manipulators, environment modelling, path planning and mobile robot global localization problems.

    Dolores Blanco received the B.S. degree in Physics from the University Complutense of Madrid, Spain in 1992. She received the Ph.D. degree in Mecatronics from University Carlos III of Madrid (UC3M) in 2002. From 1996 to 1999, she was a fellowship student at the Department of Systems Engineering and Automation of UC3M. Since 1999, she is assistant professor in the same Department. Member of Mobile Manipulator Group at UC3M. Her current research includes sensor based path planning, localization and control for mobile manipulators.

    M. Luisa Muñoz was born in Madrid, Spain. She graduated in physics science from the Complutense University of Madrid and received the Ph.D. degree in 1988. During her predoctoral period she colaborated as a researcher at the Scientific Research Council (CSIC), Spain. Since 1990, she is currently an Associate Professor of Computer Technology and Architecture at the Polytechnic University of Madrid, Spain. She has been researching in a broad range of topics that covering signal processing, neural network algorithms, image processing and computational vision. Nowaday, her main research interests include evolutionary algorithm applications to mobile robotics.

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