An online path planning approach of mobile robot based on particle filter

Industrial Robot: An International Journal An online path planning approach of mobile robot based on particle filter Yang Gao Shu-dong Sun Da-wei Hu Lai-jun Wang

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To cite this document: Yang Gao Shu-dong Sun Da-wei Hu Lai-jun Wang, (2013),"An online path planning approach of mobile robot based on particle filter", Industrial Robot: An International Journal, Vol. 40 Iss 4 pp. 305 - 319 Permanent link to this document: http://dx.doi.org/10.1108/01439911311320813 Downloaded on: 04 July 2016, At: 14:02 (PT) References: this document contains references to 40 other documents. To copy this document: [email protected] The fulltext of this document has been downloaded 263 times since 2013*

Users who downloaded this article also downloaded: (2012),"Comparing the efficiency of five algorithms applied to path planning for industrial robots", Industrial Robot: An International Journal, Vol. 39 Iss 6 pp. 580-591 http://dx.doi.org/10.1108/01439911211268787 (2013),"Optimal trajectory planning for industrial robots using harmony search algorithm", Industrial Robot: An International Journal, Vol. 40 Iss 5 pp. 502-512 http://dx.doi.org/10.1108/IR-12-2012-444 (2012),"Complete coverage path planning of mobile robots for humanitarian demining", Industrial Robot: An International Journal, Vol. 39 Iss 5 pp. 484-493 http://dx.doi.org/10.1108/01439911211249779

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Research article

An online path planning approach of mobile robot based on particle filter Yang Gao School of Automobile, Chang’an University, Xi’an, China

Shu-dong Sun School of Mechatronics, Northwestern Polytechnical University, Xi’an, China, and

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Da-wei Hu and Lai-jun Wang School of Automobile, Chang’an University, Xi’an, China Abstract Purpose – Path planning in unknown or partly unknown environment is a quite complex task, partly because it is an evolving globally optimal path affected by the motion of the robot and the changing of environmental information. The purpose of this paper is to propose an online path planning approach for a mobile robot, which aims to provide a better adaptability to the motion of the robot and the changing of environmental information. Design/methodology/approach – This approach treats the globally optimal path as a changing state and estimates it online with two steps: prediction step, which predicts the globally optimal path based on the motion of the robot; and updating step, which uses the up-to-date environmental information to refine the prediction. Findings – Simulations and experiments show that this approach needs less time to reach the destination than some classical algorithms, provides speedy convergence and can adapt to unexpected obstacles or very limited prior environmental information. The better performances of this approach have been proved in both field and indoor environments. Originality/value – Compared with previous works, the paper’s approach has three main contributions. First, it can reduce the time consumed in reaching the destination by adopting an online path planning strategy. Second, it can be applied in such environments as those with unexpected obstacles or with only limited prior environmental information. Third, both motion error of the robot and the changing of environmental information are considered, so that the global adaptability to them is improved. Keywords Robots, Programming and algorithm theory, Mobile robot, Path planning, Particle filter, Online Paper type Research paper

I. Introduction

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finished based on a changed and incomplete map which is drawn according to the inaccurate sensing information. In addition, the motion error of the robot may also increase the difficulty by deviating the robot from the path planed before. This paper is thus trying to present a near-optimal solution to the path-planning problem of mobile robot in such case by considering the influence of both the inaccurate motion of the robot and the changing and incomplete map. Many techniques have been proposed for the path planning of mobile robot. Some excellent summaries on path planning are available (LaValle, 2006; Sariff and Buniyamin, 2006). Most of these techniques rely on the exploration of the configuration space (C-space). The C-space is defined as an N-dimensional space for which each of the N axes represents a degree of freedom (DOF) of the robot. Then the exiting techniques can be divided into three types: global path planning, local path planning and hybrid path planning.

Industrial Robot: An International Journal 40/4 (2013) 305– 319 q Emerald Group Publishing Limited [ISSN 0143-991X] [DOI 10.1108/01439911311320813]

This project was supported by the Special Funds for Basic Scientific Research of Central Colleges, Chang’an University (CHD2011JC176, CHD2011JC105) and the National Natural Science Foundation of China (51108040).

In the past few decades, mobile robot has attracted much focus in a wide range of applications, and shown high potential for further growth. As one of the fundamental requirements confronting mobile robot, path planning can be regarded as a search problem on how to find a feasible and optimal trajectory from the starting position to the destination. Unfortunately, in many actual applications, we often expect to finish the planning task in partly unknown environment where limited sensing ability; limited prior environmental knowledge and dynamic change of operating environment are given. Therefore, path planning becomes much more difficult in such cases as the task must be

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An online path planning approach of mobile robot

Industrial Robot: An International Journal

Yang Gao, Shu-dong Sun, Da-wei Hu and Lai-jun Wang

Volume 40 · Number 4 · 2013 · 305 –319

Global path planning searches for a globally optimal collision free path in many types of “map” which are extracted from the C-space or other environmental information (Meyer and Filliat, 2003). An excellent summary is available (Wooden, 2006). Typically, the “map” includes the following types: Voronoi diagram (Bhattacharya and Gavrilova, 2008), regular grid, generalized cones, quad-tree, vertex graph, road map (Bhattacharya and Gavrilova, 2008) and Visibility Graph (Lozano-Pe´rez and Wesley, 1979). Based on the map, many kinds of path finding algorithm are employed to find the path. Typically, the finding algorithm also includes many types, such as graph searching algorithms, intelligent optimization algorithms and sampling-based algorithms. Graph searching algorithms, such as A *, D *, D *lite (Hart et al., 1968; Stentz, 1995; Sun et al., 2010), are improved from the well-known formal approach named Dijkstra’s algorithm. They are generally heuristic algorithms, providing faster searching ability and better adaptability to the changed map. Many intelligent optimization algorithms, such as genetic algorithm (Manikas et al., 2007), particle swarm optimization (PSO) (Saska et al., 2006), ant colony system (Garcia et al., 2009) are also employed with the motive that the path finding problem can be treated as a constrained optimization problem. Sampling-based algorithms sample the C-space and form a roadmap or a random tree. As a result, searching on the road map or random tree would obtain the desired path (Bhattacharya and Gavrilova, 2008; Bohlin and Kavraki, 2000; Jaillet et al., 2005; van den Berg and Overmars, 2005). As a complete survey of the whole “map” is applied, global path planning generally can guarantee the optimal path if it exists. However, most of them are time-consuming and full knowledge of the environment is needed. Consequently, they are generally executed off-line, which limits their adaptability to the changing of environmental information and the motion error of the robot. In contrast, local path planning considers only a subset of the C-space. It generally provides a mapping from the sensing information to the motion command. Several groups of approaches have been developed. One of the most general and simple approaches is the Potential Field approach developed by Khatib (1986) that helps the robot move along the gradient of a potential field. Borenstein et al. have developed the virtual force field (VFF) and vector field histogram (VFH) (Ulrich and Borenstein, 2000) approaches which basically combine the potential field method and certainty grid based world modeling. Fuzzy logical control methods (Huang et al., 2007; Wang and Liu, 2008) are another well known groups. They guide the robot according to human driving experience and are easier to be understood. Dynamic window approach (Fox et al., 1997) controls the motion with both obstacles and the driving ability of the robot considered. It is capable to guarantee a feasible and safe motion of the robot. In general, these approaches are efficient enough to be executed online and are capable to deal with both the motion error and the changing of environmental information. However, they cannot guarantee the destination to be reached for the lack of global consideration, and also suffer from the local minimal problem although great efforts has been made to overcome it (Huang, 2009). Hybrid path planning approaches (Chang and Yamamoto, 2008; Wang et al., 2002) combine both types of approaches mentioned above to avoid their drawbacks while retain the strong point. They can be further divided into two types based on the combination method: sub target based

approaches (Bruijnen et al., 2007; Chang and Yamamoto, 2008), where local path planning is guided by the sub target chosen from the global path; behavior based approaches (Hamner et al., 2008; Tarokh, 2008), where the global behavior incorporates the local behavior into a final behavior. Hybrid path planning obtains moderate adaptability from the local path planning part. However, their adaptabilities are restrained in local scale because of their offline planning model of the global path planning part. All the three types of path planning approach may be used in the partly unknown environment. Owing to the limited dependence on environmental information and its online planning model, local path planning provides good adaptability for such environment (Die´guez et al., 2003). Especially, in the case that either global environmental information or location information is not available, local path planning is an appropriate choice. Most global path planning approaches suffer from their limited adaptability in partly unknown environment. It is mainly because they need to be able to replan quickly as their knowledge of the environment changes, however, it is difficult to be achieved. So, many improved algorithms have been investigated. Incremental searching algorithms such as D *lite, D * search the path based on prior planning result instead of starting a new planning process, with the help of which faster replanning may be achieved. Some other algorithms do not plan a new optimal path while confronting unpredictable obstacles or other changes of the map. Instead, they only locally refine the prior optimal path so that the near optimal path could be quickly gained (Jolly et al., 2009). Hybrid path planning is an attractive manner to solve the planning problem in such environment (Zhang et al., 2009). However, it still may fail since the robot is unable to reach the original path for a variety of reasons, such as blocked paths. In this paper, an online global path planning approach is proposed. It treats the globally optimal path as a dynamically changing state affected by the motion of the robot and the changing of environmental information. Particle filter is then used to estimate the changing globally optimal path online. The eatimation will be affected by both the motion error and the up to date environmental information on time, so that the adaptability to both of them will be enhanced. The paper is organized as follows. Section II presents the problem statement. Section III describes our approach. In Section IV several simulations are carried out to demonstrate the advantages of the proposed approach. Section V presents a simulation in 3D environments. Section VI presents experiments. Section VII presents a conclusion.

II. Problem statement Let P0 denote the location of the mobile robot (call it Rob), R denote the path, and subscript t denote the corresponding value on time t. Let Ta denote the location of the destination, C denote the 2D workspace of Rob, and MC denote the map of C where Rob is treated as a point-like robot and the obstacles have been enlarged by the safe radius. Assume time t is the current time, and Rob always knows: . P0,t; . Ta which would never be changed; . MCt which has recorded all the environmental information; and . the boundary of C. 306

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An online path planning approach of mobile robot

Industrial Robot: An International Journal

Yang Gao, Shu-dong Sun, Da-wei Hu and Lai-jun Wang

Volume 40 · Number 4 · 2013 · 305 –319

Let us consider the path planning problem as Rob moving in 2D partly unknown environment (X-Y plane) as Figure 1 shows. In the partly unknown environment, some parts are prior known (shown as the grid black areas), while some unexpected obstacles exist (shown as the gray areas). At time t0, Rob is initially located at P00 and it draws a map MC0, which includes both the prior known parts and the recently discovered obstacles, as shown in Figure 1. The circle around Rob denotes its sensing range, where the recently discovered obstacles (black areas in the circle) are included. Suppose Rob has obtained the globally optimal path R0 in MC0. When following R0 to a new location P01 at time t1, P01 is deviated from R0 due to the motion error. More than that, a new map MC1 is obtained at P01, and new obstacles have been discovered as shown in Figure 1. For both reasons, the globally optimal path changes to R1, and it becomes a changing item before Rob reaches the destination. Due to the change of globally optimal path as Figure 1 shows, path planning offline cannot obtain an efficient solution on time. Exiting online path planning approaches such as local path planning may trap the robot into a local minimal. Hybrid path planning will get better performance if it combines an online global path planning algorithm. Hence, in this paper, we will discuss online path planning problem in a partially unknown environment, in order to obtain better adaptability.

Pi2 1 and Pi are the start point and the end point of ri, 0 0 respectively. P i21 and P i are the tangent vectors at Pi2 1 and Pi, respectively, (Saska et al., 2006). This implementation of the cubic functions enables us to connect the two splines by a simple rule as is shown in Definition 1. Similarly, we can further connect n splines to form a path as is shown in Definition 2: 8 F 1 ðT Þ ¼ 2T 3 2 3T 2 þ 1 > > > > > < F 2 ðT Þ ¼ 22T 3 þ 3T 2 ð2Þ F ðT Þ ¼ T 3 2 2T 2 þ T > > > 3 > > : F 4 ðT Þ ¼ T 3 2 T 2

Definition 1. For a Ferguson spline rk described by equation (3), if equation (4) is satisfied, then spline ri is smoothly connected to the spline rk: 0

ð3Þ P k21 ¼ P i

3.1 Path description using Ferguson splines Ferguson splines are used as a description of the path of the robot due to their advantages: they are smooth and thus easily to be followed; they can be easily implemented and could be smoothly connected together; they can easily define a path travelling through the given points with given velocity. A Ferguson spline ri is defined by equation (1) (Saska et al., 2006):

0

ð4Þ

0

r i ðT Þ ¼ P i21 F 1 ðT Þ þ P i F 2 ðT Þ þ P i21 F 3 ðT Þ þ P i F 4 ðT Þ ð1Þ

3.2 Particle filter Particle filter is a popular nonparametric filter used to solve complex problems such as nonlinear filter problem and filter problem with multimodal belief. So far, a posterior probability density over the state space conditioned on the collected data has been estimated, so that the dynamically changing state could be estimated. The data typically consist of an alternating sequence of time indexed observation ot, and the control measurement ut which describe the dynamics of the state st. Equation (5) shows how the posterior probability density is estimated by using its approximation on the basis of a dirac delta measure function dð · Þ, and M samples sit (i ¼ 1, . . . ,M) weighted by vit. There are two well known particle filters: sequential importance sampling (SIS) particle filter which has been developed since the past decades, forms the basis of most particle filters. It consists of recursive propagation of the weights and particles, and each measurement is received sequentially; sampling importance resampling (SIR) Filter is the most commonly used particle filter which has been developed on the basis of the SIS algorithm. As is shown in the following pseudo-code, SIR adds a resample procedure to SIS. Therefore, the degeneracy problem that all but one particle have negligible weight, is greatly improved. SIR is then employed by this paper. Further introductions could be found in the study

In the equation, Fj(T) j ¼ 1, . . . ,4 are four Ferguson multinomials described by equation (2), parameter T [ [0, 1], Figure 1 Rob moving in a partly unknown environment Y

Ta

R1

P01

0

P k21 ¼ P i

Definition 2. For n Ferguson splines ri (i ¼ 1, . . . ,n), if every spline ri is smoothly connected to the next one riþ 1, and P0 is the start point of r1, Ta is the end point of the last spline r n, then these n Ferguson splines compose a path R, and the points Pi (i ¼ 1, . . . ,n 2 1) which connect the two neighboring splines are called connecting points. Accordingly, path R can be further described as a set of 0 0 points and tangent vectors like R {P0, P 0 , . . . ,Pn, P n } (Podsedkowski et al., 2001). Considering P0 and Ta are always known, the total number of variables which define a path is 4n.

III. Methodology

0

0

r k ðT Þ ¼ P k21 F 1 ðT Þ þ P k F 2 ðT Þ þ P k21 F 3 ðT Þ þ P k F 4 ðT Þ

R0

P00

X

307

An online path planning approach of mobile robot

Industrial Robot: An International Journal

Yang Gao, Shu-dong Sun, Da-wei Hu and Lai-jun Wang

Volume 40 · Number 4 · 2013 · 305 –319

of Arulampalam and Sebastian (Arulampalam et al., 2002; Sebastian et al., 2005):

obstacle point. For a feasible R, the first fraction of equation (6) represents the shorter length requirement, and the second fraction represents the safety requirement that keeps further away from the obstacles. Weight a implies the relative importance between them. It is also implied by equation (6) that the evaluation E $ 1, and E should be as less as possible. For an unfeasible R, equation (6) grants the biggest evaluation Emax. Therefore, the globally optimal path and its evaluation Etmin can be defined as Definition 3. Definition 3. The feasible path that gets the minimal evaluated value Etmin, is then called the globally optimal path Rtmin. As described before, the motion error and the changing environmental information may cause the change of Rtmin. To estimate the changing Rtmin, we treat it as a dynamic changing state st. A state-space model which is shown in equations (9) and (10) can then be used to describe the relationship between Rtmin and the factors which cause its changing:

Pðst jo1:t Þ