Multi robot system assisted by information networks - Research Article
Cooperative simultaneous localization and mapping algorithm based on distributed particle filter
International Journal of Advanced Robotic Systems January-February 2019: 1–8 ª The Author(s) 2019 DOI: 10.1177/1729881418819950 journals.sagepub.com/home/arx
Shuhuan Wen1,2 , Jian Chen1,2, Xiaohan Lv1,2 and Yongzheng Tong1,2
Abstract In this article, cooperative simultaneous localization and mapping algorithm based on distributed particle filter is proposed for multi-robot cooperative simultaneous localization and mapping system. First, a multi-robot cooperative simultaneous localization and mapping system model is established based on Rao-Blackwellised particle filter and simultaneous localization and mapping (FastSLAM 2.0) algorithm, and an median of the local posterior probability (MP)-cooperative simultaneous localization and mapping algorithm combined with the M-posterior distributed estimation algorithm is proposed. Then, according to the accuracy advantage of the early landmarks comparing to the later landmarks in the simultaneous localization and mapping task, an improved time-median of the local posterior probability (MP)-cooperative simultaneous localization and mapping algorithm based on time difference optimization is proposed, which optimizes the weights of the local estimation and improves the accuracy of the global estimation. The simulation results show that the algorithm is practical and effective. Keywords Particle filter, simultaneous localization and mapping, distributed system, multiple robots Date received: 28 August 2018; accepted: 26 November 2018 Topic: Mobile Robots and Multi-Robot Systems Topic Editor: Lino Marques Associate Editor: Jonghoek Kim
Introduction Multi-robot system outperforms single-robot systems in the efficiency of performing tasks, fault tolerance, robustness, reconfigurability, and hardware cost.1 For example, multiple robots can complete subtasks in parallel to improve work efficiency through task decomposition. The multirobot system can increase redundancy, eliminate the failure point, and increase the robustness of the system through the cooperation among the members. The multi-robot system can increase optional solutions and reduce system cost as well as complexity.2 Therefore, multi-robot coordination and cooperation have great research significance in the field of robotics as a new form of robot application.3 In the complex environment without autonomous navigation tools such as BeiDou Navigation Satellite System and GPS, multi-robot
system needs to complete autonomous detection of unknown environments and create maps through cooperation. Since the end of the 1990s, the multi-robot cooperative simultaneous localization and mapping (CSLAM) problem has become a research hot spot in the field of robot cognition
1
Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China 2 School of Electrical Engineering, Yanshan University, Qinhuangdao, China Corresponding author: Shuhuan Wen, Key Lab of Industrial Computer Control Engineering of Hebei Province, School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 based on the single-robot simultaneous localization and mapping (SLAM) problem.4,5 Because the main directions of the current studies are in the data association and the map fusion, nowadays the majority of CSLAM cannot be separated from simple combinations of single robot SLAM. Tan and Wang6 regarded the multi-robot CSLAM system as a special multi-sensor network which is the wireless sensor network (WSN) using the distributed state estimation method. The application of some particle filter algorithms in the multirobot CSLAM system is described in the work of Carlone et al.,7,8 Pei et al.,9 and Gao et al.10 In the work of Va´zquez and Mı´guez,11 Yan et al.,12 and Wu et al.,13 distributed particle filter algorithm has been successfully used in multi-sensor networks, but there are few relevant studies in multi-robot CSLAM. Because the multi-robot CSLAM system is different from the multi-sensor network, the relevant algorithms suitable for WSN cannot be directly used in the multi-robot CSLAM system. The distributed multi-robot CSLAM algorithm proposed in this article regards the multi-robot CSLAM system as a special WSN system. Using the improved relevant algorithms, the feasibility problems of related algorithms are solved in different fields, and the multi-robot cooperation is performed in the filter part. Then, the level of multi-robot coordination is more in-depth and significant improvements have been achieved. Compared with the single-robot SLAM, the multi-robot CSLAM needs to use an appropriate structure to bring all the robots together into a complete system, and then design related algorithms to perform the cooperation between the robots. Multi-robot CSLAM system is divided into centralized structure and distributed structure.14 In the centralized multi-robot CSLAM, a data fusion center needs to be set up to process the local information from each robot, and then, the local estimation is integrated into a global estimation. The generation of control information of the robot and the final global map are completed through the central processing module. 14 However, centralized structure CSLAM system relies excessively on the central module. Once the central module is damaged, the entire system will lose its effectiveness. Moreover, in the SLAM task, the data have an incremental form. As the data increase, the control of the centralized system becomes more difficult and the reliability will be deteriorated. The distributed multi-robot CSLAM system doesn’t have central control module comparing to the centralized structure, and the robot has independent decision-making capabilities. Each robot in the system is called a node. Each node executes an independent SLAM algorithm and transmits its own data to the neighbor nodes in the form of broadcasting. A symmetrical distributed algorithm is used to obtain and update the respective global maps between the robots.14 At present, the distributed filtering technology has been widely used in other fields. Cunningham et al.
International Journal of Advanced Robotic Systems extended the algorithm to the CSLAM algorithm under large scale according to the early smoothing and mapping algorithm and proposed decentralized data fusion (DDF)SLAM.15 The multi-robot CSLAM system is similar to the WSN system. Although there are many differences between them, multi-robot CSLAM is a WSN system that can move and change autonomously. In addition to observing the targets (landmarks), it also needs to estimate the state of their respective nodes. Therefore, although the distributed filtering algorithm can’t be transplanted from the WSN system to the multi-robot CSLAM system directly, the idea of the distributed filtering algorithm has a very broad space for development in the multi-robot CSLAM. Prior to this, relevant researchers have studied SLAM problems based on distributed fusion filtering methods. The specific approach is to decentralize the filtering-based single-robot SLAM process into multiple isomorphic subfilters. Then, the system outputs the local estimation of these sub-filters. Finally, the global estimation can be obtained by fusion filter. This method is very similar to the scenario of the multi-robot CSLAM task, but the multirobot CSLAM system is more complex. Moreover, there is more redundant information in the multi-robot system that can be used by improving the algorithm. Distributed particle filter has been widely used in the field of WSNs and single-robot SLAM. The filtering process of each node is regarded as a sub-filter.16 The output information of the sub-filter is the input of the fusion filter, and the fusion filter completes the estimation from local information to global information. Whether it is a WSN or a single-robot SLAM system, they are quite different from the multi-robot CSLAM system.13,17–21 The difference is the complexity of the system and the data types of the local estimation, so the related distributed particle filter algorithm cannot be directly transplanted to the multi-robot CSLAM system. Therefore, the first problem in this article is to solve the feasibility of the algorithm, improve the traditional fusion filtering process, and propose a distributed particle filtering method suitable for multi-robot CSLAM system. In this article, a distributed particle filter algorithm for CSLAM task is introduced in this article. Based on the M-posterior estimation method, a multi-robot median of the local posterior probability (MP)-CSLAM algorithm is proposed. Compared with the original FastSLAM2.0 algorithm, the multi-robot MP-CSLAM algorithm has an advantage in estimation accuracy. Finally, by analyzing the accuracy of landmarks in each period during the task, the time-MP-CSLAM (TMP-CSLAM) algorithm which optimizes the weighted value of fusion filter by taking the advantages of the accuracy of early landmarks is proposed. Compared with the original MP-CSLAM algorithm, the estimation error becomes smaller, the accuracy becomes higher, and the performance of the algorithm is further improved.
Wen et al.
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Multi-robot CSLAM system model During the walking of the robot, the navigation is mainly based on the waypoints. The robot uses its own position and the target waypoint to calculate control uik ¼ ðG; V Þ, which travels to the target point at the current time. After adding process noise, uik ¼ uik þ wik ¼ ðGn; V nÞ. So the state transition process is 3 2 xik 1 ð1Þ þ V n dt cos Gn þ xik1 ð3Þ 6 7 6 7 xik ¼ 6 xi ð2Þ þ V n dt sin Gn þ xi ð3Þ 7 ð1Þ k1 4 k1 5
n of robot j. The median of the two particle sets is O medianðzim ; zjn Þ, and the median center is obtained by the Weiszfeld algorithm. Define þj i j ziðm; nÞ ¼ ½zm ; zn þj where iiii 2 f1 : ðN i þ N j Þg, ziiii 2 ziðm; nÞ . forðjj ¼ 1 : R; jj þ þÞ iteration is NX i þ Nj
zjj þ 1 ¼
xik 1 ð3Þ þ V n dt sinðGnÞ= WB where WB is the wheelbase of the wheeled robot. The observation model of robot i is zik;m ¼ hðym ; xik ; vk;m Þ
iiii ¼ 1 NiX þ Nj iiii¼1
ð2Þ
where zik;m is the observation of robot i with regard to landmark m at time k and is the coordinate of landmark m in the coordinate system of robot i. ym is the output information of sensors, vk;m is the observation noise which is Gaussian white noise. If the noise variance is R, the observation noise is " pffiffiffi # Rrandnð1Þ i vk;m ¼ pffiffiffi ð3Þ Rrandnð1Þ
ð6Þ
~ iiii ziiii w jjziiii zjj jj
ð7Þ
1 jjziiii zjj jj
Equation (7) converges at a finite number of iteration steps. After equation (7) convergence, the final zjj is the median center O median ðzim ; zjn Þ of the particle set ~ iiii ¼ W cq wiiii w
ð8Þ
where c 2 fi; jg; q 2 fm; ng. After obtaining the median center of the particle set, we need to calculate the median center distance of the node particle set Di;m median ¼
Ni X
i j ~ iiii jjzi;ii w m O medianðzm ; zn Þjj
ð9Þ
ii ¼ 1
The information of landmark m returned by the laser sensor at time k is ym ð1Þ ym ¼ ð4Þ ym ð2Þ where ym ð1Þ is the distance from the landmark to the sensor and ym ð2Þ is the polar angle relative to the sensor. Adding noise to ym results in ynm ¼ ym þ vik;m . Then from ynm to zik;m , there is 2 3 xik ð1Þ þ ynm ð1Þ cos ynm ð2Þ þ xik ð3Þ 6 7 5 ð5Þ zik;m ¼ 4 i i xk ð2Þ þ ynm ð1Þ sin ynm ð2Þ þ xk ð3Þ
M-posterior algorithm Va´ zquez and Mı´guez proposed an M-posterior algorithm.11 The main idea is to use the median center of the particle set to weight the particle set. The median center of the set of particles refers to a point in space, and the weighted distance between the points and each point in the particle set is the minimum. The median center is approximated by the optimal solution in the aspect of minimum variance, and the local weighted information is adjusted based on this point. After an iteration process of finite steps, the global estimation is almost optimal. The landmark m of robot i is associated with the landmark
The particle set is weighted by the median center distance. The center distance of the particle set is weighted by W imedian ¼ 1=Di;m median .
MP-CSLAM algorithm The CSLAM algorithm introduced in this article is based on the M-posterior algorithm. It is defined as MP-CSLAM algorithm. The main process of the algorithm is as follows: 1. The robots i and j, respectively, run separate particle filter programs to obtain a set of particles N
i;ii Mapi ¼ fzi;ii 1:Mi ; wk gii ¼ 1 of the landmark. 2. The robot exchanges data with adjacent robots and performs data association to obtain the association result f Tableiii ði; jÞgiiiMtable ¼1 . 3. The weighted value of local particle is initialized. The situation introduced in this article has two robots, so the robot node dimension is NV ¼ 2, and
W im ¼ W jn ¼
1 1 ¼ NV 2
ð10Þ
4. According to the association result, two robot landmarks sets are combined, and for the set of landmarks particles of the knot group, the median center O median ðzim ; zjn Þ is obtained using equations (6) to (8), and the median distance Di;m median is computed.
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International Journal of Advanced Robotic Systems Then, it is weighted W imedian ¼ 1=Di;m median according to the median distance. 5. Integration and normalization of weighted value. Informal form ~ i ¼ Wi W m median
ð11Þ
~ i ¼ Wj W n median
ð12Þ
Normalized W im
¼
W jn ¼
~i W m ~i þW ~jÞ ðW m n ~j W n ~i þW ~jÞ ðW m n
ð13Þ Figure 1. The comparison of accuracy between early landmark and later landmark.
ð14Þ Table 1. The accuracy of landmarks’ observation at different times.
6. Within a limited iteration step R, turn to step 4. 7. Perform distributed estimation: Local estimation zim ¼
N X
ii zi;ii m wk
ð15Þ
ii ¼ 1
Global estimation ði;jÞ
zðm;nÞ ¼ W im zim þ W jn zjn
ð16Þ
CSLAM task characteristics and improved algorithm Superiority features of early landmark accuracy In the SLAM problem, although the SLAM algorithm using the filtering method can suppress the error to some extent, this method cannot completely eliminate the error. Then, the error of the system becomes greater and greater. The robot’s estimation of its own pose will drift toward a certain direction, and the landmark estimation at this time will also drift toward this direction as a whole. Figure 1 shows the fitting situation of the local map generated by the robot at different times with the real landmarks in the simulation experiment. The green star sign represents the true location of the landmark in the environment, and the red dot cluster is the distribution of the particles. The early landmarks in Figure 1 are the landmarks that the robot found around in early 50 steps, and the later landmarks are found after 1000 steps. The particle clusters of the early landmarks are basically fitted to the true location of the landmarks, while the later landmarks are all drifting to the left of the true location of the landmarks. And then it also can be seen that the early landmarks have an absolute advantage of accuracy over the later landmarks.
Time/step
4
700
1264
1846
2660
Error/m Time/step Error/m
0.33 2996 3.70
0.64 3344 4.93
0.81 3800 5.12
1.32 4344 7.28
2.19
Table 1 selects the landmarks observed by the robot at different times and records the time when the landmark is observed and the error of the estimated position of the landmark in the last constructed map relative to the real position (data correct to the second decimal places). Table 1 reveals that the error of the landmark observed by the robot at the earliest stage is only 0.33 m, and the error of the landmark observed in the medium term is about 2.19– 3.70 m. At the end of the robot walking process, the error reaches about 7.28 m. It can be seen from these data that if the local map of a single-robot is globally estimated as a whole, the local weighted value cannot be measured. Because the accuracy of the landmarks observed by the robots at different times varies greatly, a more detailed weighting scheme must be used to weight the corresponding local estimation for each landmark. And with the absolute advantage of the accuracy of the early landmarks, some robots’ early landmarks can be used to correct the later landmarks of other robots. In other words, when the initial position of the robot has been calibrated and multiple robots share the same coordinate system, the robot can communicate with each other through the intersection of the robots to form a closed loop of the SLAM ahead of time, which can improve the efficiency of the task. Figure 2 shows the trend of the error of the landmarks observed by the robot in different periods. The error has positive correlation with time. In other words, during performing the SLAM task, its overall estimation accuracy will be attenuated with the time. In distributed estimation, this accuracy attenuation can be regarded as the local weighted value decreasing in the global estimation.
Wen et al.
5 N
i;ii Mapi ¼ fzi;ii 1:Mi ; wk gii ¼ 1 for the landmarks. 2. The robot exchanges data with neighboring robots and performs data association to obtain the correlation result f Tableiii ði; jÞgiiiMtable ¼1 . i j ðm; nÞ 3. The time weight value W time ¼ að timem timen Þ is calculated according to the period when the set of landmark particle forms. 4. The local weighted value of the particle set is weighted using time difference
8
error/m
6
4
2
0
4
700
1264
1846
2660 2996 3344 3800
ðm;nÞ
4344
t/0.025s
Figure 2. Histogram of landmark accuracy at different times.
TMP-CSLAM algorithm When two local estimations with different precisions participate in the global estimation, it is difficult to measure their local characteristics and use them as a basis for weighting. The previous algorithm is to consider all particle sets and weight each local estimation based on their median center distance. 1/Nv is used to initialize the local weighted value. Because the particle set with high precision is clearly dominant in the global estimation, the optimal estimation should tend to the local estimation represented by this particle set. In the calculation process of weighted median center, the weighted value of this part should increase appropriately to optimize the estimation. TMP-CSLAM based on time difference optimization for initial local weighted value is proposed in this article. In a multi-robot distributed SLAM system, each robot runs a distributed CSLAM algorithm that is symmetric with each other. Taking the robot i as an example, if the robot i observes the landmark lim at the h time, a time stamp timeim ¼ h is set for the landmark. The time of the landmark ljn associated with the robot j is timejn . Certainly, when the robot encounters an early-observed landmark or an already observed landmark, the time process needs to be calibrated. The simplest case is considered here. In order to describe the accuracy attenuation of the SLAM system with time step, a parameter a is used to represent the divergence of the system in each time step. Then, the change of the weighted value of the landmark information observed by the robot resulting from the different time steps can be expressed as follows i;ðm;nÞ
W time
i
j
¼ að timem timen Þ
ð17Þ
In this way, the overall process of the algorithm is as follows: 1. The robots i, j, respectively, run separate FastSLAM 2.0 programs to obtain their respective particle sets
W im ¼ W time
ð18Þ
W jn ¼ 1 W im
ð19Þ
5. The two robot landmark sets are combined according to the association result, and the weighted median center O median ðzim ; zjn Þ of the landmark particle set of the group is obtained. Then the median m distance Di;median is obtained and landmark particle sets are weighted according to the median distance m using W imedian ¼ 1=Di;median . 6. Integration and normalization of weighted value. Informal form ~ i ¼ Wi W m median
ð20Þ
~ i ¼ Wj W n median
ð21Þ
Normalized W im
~i W m
¼
W jn ¼
~i þ W ~jÞ ðW m n ~j W n ~i þ W ~jÞ ðW m n
ð22Þ
ð23Þ
7. Within a limited iteration step R, turn to step 5. 8. Perform distributed estimation: Local estimation zim ¼
N X
ii zi;ii m wk
ð24Þ
ii ¼ 1
Global estimation ði;jÞ
zðm;nÞ ¼ W im zim þ W jn zjn
ð25Þ
Simulation research The experiment uses MATLAB (MATLAB 2014a [version 8.3.0.532]) as a simulation platform, and traditional test maps in similar research are used. In order to show the advantages of multi-robot efficiency and precision, the route is square and has been shown in Figure 3. The robot
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International Journal of Advanced Robotic Systems Table 2. Weighted value corresponding to the landmarks in local maps constructed by robot nodes. Landmark number
1
2
3
4
5
W1 W2 Landmark number W1 W2 Landmark number W1 W2
0.8447 0.1553 6 0.1430 0.8570 11 0.3582 0.6418
0.7569 0.2431 7 0.1928 0.8072 12 0.6391 0.3609
0.7934 0.2066 8 0.2966 0.7034 13 0.2034 0.7966
0.6014 0.3986 9 0.4432 0.5568 14 0.7090 0.2910
0.4075 0.5925 10 0.7777 0.2223 15 0.5469 0.4531
0.5
Figure 3. The trajectory of robots and the map built by multiple robots. x-error/m
0.3 0.2 0.1 0
0
500
1000 1500 2000 2500 3000 3500 4000 4500 t/0.025s
Figure 4. The comparison of the X-axis direction error among FastSLAM2.0 algorithm, median of the local posterior probability (MP)-CSLAM algorithm, and TMP-CSLAM. MP-CSLAM: MPcooperative simultaneous localization and mapping; TMP-CSLAM: time-MP-cooperative simultaneous localization and mapping.
0.8
Fastslam2.0 MP-CSLAM TMP-CSLAM
0.6 y-error/m
starts from different coordinate points, and the initial position has been calibrated in the simulation process. Each robot node shares one coordinate system. The single robot executes the FastSLAM 2.0 program with a time step of 0.025 s. The observation interval is 0.1 s, and the number of sampled particles is N ¼ 100. The general speed of the robot is set to 3 m s1, the maximum turning angle is 30 , and the general turning angular speed is 20 s1. The control noise is Gaussian white noise with standard deviation 0.3 m s1, and the observed noise is Gaussian white noise with standard deviation 0.1 m. In addition, the simulation platform built in this article has designed a complete function to calculate error. In order to display the algorithm designed in this article and to improve the performance of the algorithm, each robot node runs the independent FastSLAM 2.0 algorithm and obtains their local estimation in the same simulation experiment. In addition, the system runs the MPCSLAM distributed estimation algorithm and the improved TMP-CSLAM distributed estimation algorithm. The two algorithms obtain a global estimation by sharing the same one set of local estimation. The estimation and the map data are used to calculate and record the average error of each landmark at each moment. The curve of error changing with time is drawn for comparisons of the two algorithms, and the algorithm performance was analyzed according to simulation error. Table 2 presents the weighted value of the local estimation obtained by robot 1 in the process of running a symmetric distributed particle filter algorithm. It can be seen that the weighted value of the local estimation is not a single value, but a set of weighted value for all landmarks in the local map. Each weighted value has a one-to-one correspondence with each landmark in the map, which can solve the problem that each landmark affects each other because of different precision, and provides a framework base for the feasibility of the algorithm.
Fastslam2.0 MP-CSLAM TMP-CSLAM
0.4
0.4 0.2 0
0
500
1000 1500 2000 2500 3000 3500 4000 4500 t/0.025s
Figure 5. The comparison of the Y-axis direction error among FastSLAM2.0 algorithm, median of the local posterior probability (MP)-CSLAM algorithm, and TMP-CSLAM. MP-CSLAM: MPcooperative simultaneous localization and mapping; TMP-CSLAM: time-MP-cooperative simultaneous localization and mapping.
The red and blue curves in Figure 3 are the trajectories of robot 1 and robot 2, respectively, and the red and blue point sets are local estimations of the landmarks constructed by robot 1 and robot 2, respectively. These local estimations will form a global estimation during the fusion filtering process. In order to analyze the
Wen et al. performance of the algorithm, the errors generated during the operation of the robot are recorded in Figures 4 and 5, and the errors in the X-axis direction and the Y-axis direction are analyzed. The error recorded in this simulation experiment is the average error of each landmark observed during the robot walking. Figures 4 and 5 show the error comparison in the X-axis direction and the Y-axis direction among the FastSLAM2.0 algorithm, the MP-CSLAM algorithm, and TMP-CSLAM. It can be seen that the robots began to meet at around 2400 steps and began to observe the common landmarks. The average error of the robot running the FastSLAM 2.0 algorithm is marked in red line with circle sign, the average error of the multi-robot MP-CSLAM algorithm is marked in green line with square sign, and the average error of the multi-robot TMP-CSLAM algorithm is marked in blue line with star sign. Before the robots’ encounter, there is no difference among them, and they belong to the same curve. When the robots meet, the TMP-CSLAM algorithm begins to take advantage of accuracy, the average error of the system is reduced, and the algorithm is valid.
Conclusion This article proposes a multi-robot MP-CSLAM algorithm based on the M-posterior estimation method. Then, by analyzing the period and accuracy of the landmarks in the map, it is concluded that the local estimation of the early landmarks by the robot is more accurate than that of the later landmarks. And using the accuracy advantage of early landmarks, the improved TMP-CSLAM algorithm is proposed based on the MP-CSLAM algorithm. The simulation shows that the accuracy of MP-CSLAM is superior to the traditional FastSLAM 2.0 algorithm. The improved TMPCSLAM algorithm has lower estimation error and higher accuracy than MP-CSLAM algorithm. However, there still exist two disadvantages. As time increases, the accuracy of recursive landmark points has an important relationship with the data association algorithm of landmarks. However, we didn’t do enough research on data association. And the CSLAM system in this article can’t perform perfectly in the face of large scenes and large loops because of the lack of loop closing. Thus, data association and loop closing are the future work we will do. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (project no. 61773333).
7 ORCID iD Shuhuan Wen
https://orcid.org/0000-0002-7646-4958
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