Mathematical Problems in Engineering

Volume 2018, Article ID 1596080, 11 pages

https://doi.org/10.1155/2018/1596080

## A Robot SLAM Improved by Quantum-Behaved Particles Swarm Optimization

^{1}College of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China^{2}Engineering Research Center for Metallurgical Automation and Detecting Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China

Correspondence should be addressed to Tao Zuo; moc.361@666umouz

Received 23 January 2018; Revised 28 March 2018; Accepted 4 April 2018; Published 10 May 2018

Academic Editor: Oscar Reinoso

Copyright © 2018 Tao Zuo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We propose a new SLAM method based on fast simultaneous localization and mapping (FastSLAM). The technique presented uses an improved quantum-behaved particles swarm optimization (QPSO) to improve the proposal distribution of particles and optimize the estimated particles. This method makes the sampled particles closer to the true pose of the robot and improves the estimation accuracy of robot poses and landmarks. In the QPSO algorithm, the Gaussian disturbance is added to increase the diversity of the particles. By using this technique the premature convergence of particles swarm is overcome. In the resample step, the threshold value is used to evaluate the particle diversity. When the particle diversity is below the threshold value, the linear optimization is used to produce new sample particles, which increases the particle diversity and eliminates the loss of diversity. Simulations and experiments show that the proposed approach improves the accuracy of SLAM. The accuracy of estimated poses and landmarks with the proposed method is better than that with the traditional SLAM method.

#### 1. Introduction

Simultaneous and localization and mapping (SLAM) is an active research area in mobile robotics [1, 2]. The task of SLAM is to build a map while estimating the robot pose relative to the map. In SLAM, the robot paths and maps are both unknown and the errors of robot path estimates correlate the errors in the maps.

The Extended Kalman Filter based SLAM (EKF-SLAM) approach was the most successful method in the early stage [3, 4]. However, the errors of state estimation are large when the EKF-SLAM is used in nonlinear systems, and the calculated amount increases exponentially along with the enlargement of maps.

Michael Montemerlo proposed FastSLAM to solve the SLAM problem, which had been proved to be an effective method [5, 6]. In FastSLAM, the particle filter is used to estimate the mobile robot poses and the EKF is used to estimate the features.

However, there exist drawbacks on FastSLAM. Several studies have demonstrated that the RBPF (Rao-Blackwellized particle filter) used in FastSLAM present particle depletion problems. Minority high-weighted particles are duplicated many times after frequent resamples, which will result in loss of diversity and decrease of estimation accuracy. Moreover, the proposal distribution of sample particles influences the estimation accuracy in FastSLAM. It can improve position accuracy to a certain extent to increase the number of sample particles, but it will increase the computing time.

Some researches tried to improve the performance of FastSLAM and solve the sample impoverishment problem. Grisetti et al. [7] proposed an approach to compute an accurate proposal distribution taking into account not only the movement of the robot but also the most recent observation. Furthermore, resampling operations were carried out selectively which seriously reduced the problem of particle depletion. Lee et al. [8] proposed an approach to prevent the degeneracy by particle cooperation. The PSO is performed to update the robot position by means of particle cooperation. Zhao et al. [9] and Baifan et al. [10] applied PSO to driver all the particles to the regions with high likelihoods in the nonlinear area. The number of particles was decreased and the computational complexity was reduced. Jia-cheng et al. [11] used PSO to acquire the proposal distribution of mobile robot’s poses. The new distribution of particles maintained the diversity of mobile robot in a particular environment. Erliang et al. [12] proposed a RBPF SLAM algorithm based on PSO. Particles in high likelihood sampling set moved to the region with the maximum value of posterior probability distribution; meanwhile the algorithm maintained the multiplicity of the low likelihood particles. Kim et al. [13] provided a robust new algorithm based on the scaled unscented transformation called unscented FastSLAM (UFastSLAM). This approach improved the filter consistency and state estimation accuracy. Hanvangi et al. [14] proposed a square root unscented FastSLAM with improved proposal distribution and resampling. PSO was used to optimize the proposal distribution. Liu et al. [15] proposed a FastSLAM method based on PSO and unscented particle filter. The number of particles was seriously reduced and the computational time decreased.

These researches could improve the performance of FastSLAM to some extent, but the loss of diversity of particles was not solved. The PSO used in these researches could optimize the proposal distribution of particles, but PSO also had the premature convergence problem.

To overcome these problems, in this paper, we propose a new FastSLAM approach improved by Quantum-behaved particles swarm optimization (QPSO-FastSLAM). Compared with the PSO [16, 17], QPSO can search the globally optimal solution in the whole feasible solution spaces and has better global searching ability [18–20]. When QPSO is used to optimize the proposal distribution of the particles, the estimated particle pose is closer to the true pose. To overcome the depletion problem of particles, the threshold value is used to judge the particle diversity. When the particle diversity is below the threshold value, the linear optimization is used to produce new sample particles, which increase the particle diversity and eliminate the loss of diversity.

The rest of this paper is organized as follows. Section 2 describes the SLAM problem and the framework of FastSLAM. Section 3 presents the QPSO algorithm. Section 4 presents the framework of QPSO-FastSLAM. Section 5 gives the evaluation of diversity and Gaussian random disturbance approach for QPSO. Section 6 presents the linear optimization based resample method. Section 7 presents the steps of the proposed QPSO-FastSLAM approach. Section 8 shows the simulation and experiment results of the proposed method. Finally, Section 9 gives conclusions.

#### 2. FastSLAM

##### 2.1. FastSLAM Framework

In SLAM both the trajectory of the robot and the positions of landmarks are estimated simultaneously without any a priori knowledge of environments. The true positions of robots and landmarks are never known or measured directly. The estimations of the map and the trajectory rely on the observations between true robots and true landmarks.

The FastSLAM proposed by Michael Montemerlo has now developed to FastSLAM 2.0 version. In FastSLAM, the state estimations of landmarks are considered mutually independent when the robot path is known. Then the estimations of poses and maps are separated. The robot poses are estimated by Rao-Blackwellized particle filters and the maps are estimated by EKF [1, 2, 21, 22]. The joint posterior probability distribution of FastSLAM is decomposed into where is the robot pose, denotes the th landmark in environmental maps, is the control input, and is the data association; that is, the correspondence between known landmarks in the maps and observed information. is the number of landmarks in each of the maps of the environment. In FastSLAM, the first part of (1) is estimated by the Rao-Blackwellized particle filter to get robot poses. Each particle carries pose information and saves a map, and each map is composed of independent landmark features. In the second part of (1), the environmental maps are estimated by EKF with each landmark feature.

The structure of each particle in FastSLAM is shown in Figure 1. Each particle consists of its pose and landmark estimates described by the mean *μ* and covariance Σ.