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# 0 Introduction

At present, the traditional location and environment map acquisition still need a lot of manpower to accurately measure the surrounding environment, the process is time-consuming and laborious, the method of simultaneous location and map building (SLAM) is the current research hotspot of mobile robots. The traditional slam method adopts the kinematic model of differential drive, but the application field of differential drive AGV (automatic guided vehicle) is limited. In the mainstream industrial mobile robot field, a large number of applications are single steering wheel AGV, and the picture of single steering wheel AGV in the actual application project is shown in Figure 1. Therefore, this paper focuses on the single steering wheel AGV's gmapping Slam navigation algorithm is studied, the main contents are as follows.

# 1 gmapping algorithm

Gmapping algorithm aims at the shortcomings of traditional RBPF algorithm, which needs a large number of particles to fit the target distribution and leads to particle dissipation due to heavy frequency sampling operation. It realizes the improvement of proposed distribution and adaptive resampling to limit the number of resampling.

## 1.1 conventional RBPF SLAM algorithm

In the conventional RBPF SLAM algorithm, particle filter is used to approximate the distribution information of robot pose confidence. Each particle contains a separate map information. It uses the given robot observation data Z_{1: T}and odometer measurement sequence U_{1: T-1}in this time period to estimate the robot trajectory distribution x_{1: T}and map m, and obtains the joint posterior probability estimation of the robot's pose x_{1: T}and environment map M. The algorithm separates the state estimation of map from the state estimation of pose, which allows to estimate the trajectory of robot first, then calculate the trajectory map based on the given trajectory, and express the realization principle by the following formula.

Every grain Sub represents a potential trajectory information of mobile robot. The core idea of particle filter algorithm is to use the weighted sum of random samples to approximate the posterior probability density function, and then approximate the integration operation by summing. Therefore, in the filtering algorithm, the probability is represented by sampling variables, and the probability density function is approximately described by a large number of samples and solving their corresponding weights. The process steps of particle filter algorithm are as follows:

1) Sampling stage: firstly, particle filter samples the next generation of particles {x_{T}^{I}} from the proposed distribution π (x_{T}│ Z_{1: T}, U_{0: T}), and uses the weighted sum of particles to approach the posterior probability density;

2) Particle importance sampling: the motion model of odometer is selected as the function of proposed distribution, and the importance weight Wx_{T}^{I} of current particle set and each particle evaluation is calculated;

3) Particle resampling stage: redistribute the sampled particles according to the weight scale. Some particles with low weight are discarded, and the same number of particles with high weight are duplicated. In the next round of filtering, the new predicted particles can be obtained by inputting the resampled particle set into the state transition equation;

4) Incremental map update: for each sample particle x x _{ T}^{(I)}, the corresponding map information estimate m_{T}^{I}is calculated according to the current trajectory x^{(I)}_{1: T} of the robot and the observation data Z_{1: T} of the sensor.

## 1.2 distribution of improvement proposals

Traditional particle filter motion model only relies on odometer motion model as its importance probability density function. At the same time, its weight is only updated according to the odometer model information. But the accuracy of the model is not very good, AGV

The measurement data obtained by the assembled lidar (such as the R2000 of doublefour) is much more accurate than the odometer data, so the latest observation data Z_{T} is taken into account when generating the next particle. By integrating it into the probability distribution, the sampling can be focused on the areas where the observation likelihood is significant. The improvement suggestions are distributed as follows:

When using the proposed distribution to calculate the weight, the formula is:

Based on the original robot odometer data U_{T-1} and the latest observation data Z_{T}, the above formula can obtain sampling particles more accurately and greatly reduce the number of particles needed.

## 1.3 adaptive resampling

For the resampling step that has an important influence on particle filter algorithm, the resampling step is to use low weight particle sampling instead of high weight particle sampling. At the same time, the resampling step also has the possibility of filtering out the particles with high weight. Because the number of particles used to approximate the target distribution is limited, with the resampling step, the diversity of particles gradually decreases, and the final particle consumption is reduced As a result, the algorithm fails. Therefore, an effective number of particles is needed to evaluate the degree of weight degradation of particles, namely:

Among them,^{~ I}_{W} is the normalized weight of particle x IUI, M is the number of particles, n_{eff} is the parameter to evaluate the dispersion degree of particle weight, and the diversity of particle set is directly proportional to it, operation is required when n_{eff}<n/2.

# 2 motion model of single steering wheel

The data information of single steering wheel odometer of mobile robot is as follows:

1) Position (position coordinates (x, y) and angle z).

2) Speed (the linear velocity V of the forward speed of the mobile robot and the angular velocity ω of the steering speed of the mobile robot).

The single steering wheel AGV is composed of one steering wheel and two fixed driven wheels. The steering wheel has two functions of walking and turning at the same time. Therefore, the single steering wheel AGV has two kinematic degrees of freedom, that is, the linear speed of the steering wheel VF and the angle of the steering wheel α. The wheel system layout is shown in Figure 2.

B is the wheelbase;

D is the track width.

According to the geometric operation, the speedometer data of O_{1} point is as follows:

Set the initial pose of the mobile robot in the coordinate system as Q (x_{0},

Y_{0}, Z_{0}), as shown in Figure 3, then the next position W can be calculated

(x_{1}, y_{1}, Z_{1}) position and attitude data of odometer:

Among them, VF and α of steering wheel can be solved by walking encoder and turning encoder. B and D are model parameters of single steering wheel AGV, DT is program running cycle.

# 3 single wheel SLAM Based on ROS

## 3.1 model construction of single steering wheel robot

URDF is an XML language for describing robot simulation model. Xacro is the evolution version of URDF. Xacro can simplify the code of URDF simulation model and provide programmable interface to modify and calculate parameters. It mainly defines joint and link, in which link includes rigid body appearance, inertia parameters, collision attributes and other information, and joint includes information describing robot joint kinematics and dynamics attributes. The single steering wheel robot model constructed by the research institute is shown in Figure 4.

## 3.2 build physical simulation environment

The establishment of gazebo physical simulation needs a software framework based on ROS ﹤ control. It is a robot control middleware, which makes the upper layer and the lower layer hardware well connected, and makes up for the missing control part between the algorithm and the lower layer hardware. Gazebo is independent of ROS. It has an interface with ROS to complete the connection. It can simulate sensors, controllers, robots and objects in three-dimensional environment, and can generate actual sensor feedback and physical response between objects. In this study, we create a simulation environment in gazebo as shown in Figure 5, and put the single wheel model into it.

## 3.3 gmapping slam navigation algorithm based on single steering wheel AGV

The input of the algorithm is AGV odometer information, laser observation data information, TF transformation between lidar coordinate system and AGV base coordinate system, TF transformation between odometer coordinate system and AGV base coordinate system. The former TF is published by robot state publisher, and the latter TF and odometer information are published by the compiled odometer node. The process of realizing gmapping for single steering wheel vehicle is shown in rviz as shown in Figure 6.

# 4 algorithm simulation and analysis

The experimental platform is the operating system of Ubuntu. The software configuration platform adopts the kinetic version of ROS, and the three-dimensional visual chemical tool rviz visual experimental results of ROS are used. During the operation of the mobile robot, fast turning should be minimized. At the same time, a closed loop should be completed during the moving process of the mobile robot. The map Saver command of the map server function package should be called to save the results of map building. The experimental results are shown in Figure 7. In the figure, the white area represents the scanned barrier free area, and the black area represents the scanned barrier in the map. The algorithm samples 50 particles Compared with the simulation environment map 5 created in gazebo, the accuracy of the map 7 meets the application requirements.

# 5 Conclusion

The traditional slam is a differential driven robot model, but its application environment is limited. It is mainly used in 3C, e-commerce, express delivery and other fields, while in other broader industrial fields, a large number of applications are single steering wheel AGV, so the differential driven robot is not suitable. In order to solve the SLAM problem of indoor mobile robot, based on ROS and gmapping algorithm, this paper studies the gmapping slam navigation algorithm based on single steering wheel AGV, and its accuracy meets the requirements of industrial environment.

reference:

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[D] Harbin University of technology, 2017

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