Gradient-driven parking navigation using a continuous information potential field based on wireless sensor network
Introduction
Wireless sensor networks (WSNs) can assist large building and transportation system automation in numerous ways [4]. An appealing application of WSNs is to guide drivers to promptly locate vacant parking spaces in large parking structures. This cannot be accomplished with the aid of traditional global positioning systems (GPS) because most large parking facilities are located inside buildings where GPS signals are not applicable, such as airport parking lots. Even for outdoor parking structures, WSNs-based solutions are better because they are more accurate and efficient, such as parking lots surrounding large shopping malls. In addition, it does not require communication with satellites or consume users’ valuable smart phone data, jeopardizing monthly data plan limits. Studies [17], [30] perform localization based on the offline analysis of data collected from sensor networks.
An existing study [33] can accurately guide drivers to vacant parking spaces by constructing the virtual information field depended on harmonic functions. However, this method is restrictively constrained by two computationally expensive mathematical boundary conditions. Due to the limited computing power of embedded systems, users experience a long waiting time while driving. In addition, the approach frequently guides multiple drivers to the same vacant parking space. Unacceptable long delays renders the approach unrealistic due to high computational complexity and competition for the same parking spaces. In the following parts, we will propose a lower cost and convenient method that can overcomes the current difficulties with the novel mind from the brand new perspective. Simultaneously, we also discuss the fulfilling details of this new plan. In the Fig. 1, it vividly expresses the real scenario of navigation process.
We propose a novel approach to address the issues. To reduce the computational complexity, we relax the constraints by removing the Dirichlet [22] and Neumann boundary [28] conditions. These relaxations may reduce the accuracy of the detection for guidance. However, drivers may not need additional guidance after vacant visible parking spaces are found nearby. These guidance may alleviate competition by guiding drivers to an area with more vacant parking spaces. Our idea is inspired by the theory of magnetic field [3], [19], where the object in the field is always attracted by the location with the highest value. Our article construct a gradient field in the parking space structures; our approach will guide vehicles toward the highest value location along the gradient ascent path. Note that the well-studied robotic navigation algorithms [2] cannot be directly applied here since the latter case does not consider human guidance and has static destinations that are known in advance. As a basic physical concept, the information field is introduced in this paper. Sensor nodes are responsible for monitoring the availability of parking spaces. In real scenarios, the information for empty or used parking spaces is dynamically and efficiently collected to enable us to construct an entire virtual information field that reflects parking space information based on this physical concept (information field). This information field is constructed by the heat diffusion equation.
To make our approach feasible, it is also depended on relevant supporting hardware. With any sentient organism [23], a WSNs relies on sensory data from the real world. Sensory data are obtained from multiple sensors of different modalities in distributed locations. The sensors in our proposed WSNs parking navigation system can be classified into two types, namely, static nodes and mobile nodes. Static nodes are sensors that persistently monitor parking lots to provide information about vacant parking spaces. They communicate with surrounding static nodes and human guidance mobile nodes within their communication ranges. Mobile nodes are sensors that are attached to vehicles to query nearby static nodes and utilize the returned information to guide vehicles to their desired destination. Since the situations of parking spaces change over time, real-time tracking may induce heavy communication overheads within the sensor network. Therefore, an effective method that notifies the changes of parking spaces among the static nodes and enables mobile nodes to collect the latest information with minimum communication costs.
The remainder of the paper is organized as follows: Related studies are discussed in Section 2. In Section 3, after an introduction of information diffusion and heat equation, we propose a surface fitting model and establish a global information field. Section 4 presents a local information field reconstructed by Poisson equation, followed by numerical studies and simulations in Section 5. Conclusions are presented in Section 6.
Section snippets
Related works
Navigation is a rudimentary problem in many research areas, especially in robotics. Borenstein et al. [31] reported that the general mobile robot navigation task can be decomposed as an answer to three fundamental questions, namely, positioning (where am I), targeting (where am I going) and routing (how should I get there). A landmark-based approach for mobile robot navigation was developed [32], in which landmarks are deployed to provide accurate obstacle information. However, this scheme is
Problem statement and solution
Problem Statement
Our navigation algorithm is proposed in this section. In the following parts, a global information potential field is established by a partial differential equation, and two-step refinements are then applied to improve the smoothness of the initial field. The main idea is to use this global information field to navigate cars to the selected regions with higher information potential to fully utilize every parking spot in a parking structure and balance the load of different
Local potential field reconstruction by Poisson equation
A primary information field is set up according to the first step. Due to the establishment of the global information potential field, a mobile node can be guided to the region ΩLoc with a high information level in the field. In this section, we focus on guiding a mobile node to a specific parking space. Since the global information potential field is obtained via the use of a partial differential equation and an interpolation method, each point in the field may not be an authentic
Simulation and numerical studies
In this section, a comparative evaluation of our algorithm and related previous studies are presented [23], which were discussed in Section 2. Two aspects of the information field construction speed and the avoidance of competition are considered as the performance metrics for the comparison. A navigation example is given to illustrate the realism of our algorithm.
Conclusion and future work
In this paper, we have proposed a two-step gradient-driven navigation algorithm for guiding vehicles to vacant parking spaces in large parking structures. In the first step, a partial differential equation is used to establish a global potential field, and the refinement process helps to improve the accuracy of the global potential field for the first-step navigation. In the second step, a Poisson equation is employed to construct the local potential field in the navigation process, multiple
Acknowledgment
We would like to thank the anonymous reviewers for their valuable comments. We also sincerely appreciate Prof.Yong Qi for his valuable advices and helping. This work is supported by West Virginia Higher Education Policy Commission under Grant FRT2W762W. And this project is also supported by China Postdoctoral Science Foundation (No.2013M542370), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136118120010), NSFC Grant (Program No.11301414 and
References (35)
- et al.
Structural minimax probability machine
IEEE Trans. Neural Netw. Learn. Syst.
(2016) - et al.
Sobolev spaces
(2003) - et al.
Design considerations for a wireless sensor network for locating parking spaces
SoutheastCon, 2007. Proceedings. IEEE
(2007) - et al.
Integrated approach in the design of car park occupancy information system (coins)
IAENG Int. J. Comput. Sci.
(2008) - et al.
Mobile robot positioning: sensors and techniques
J. Field Rob.
(1997) - et al.
Reconstruction and representation of 3d objects with radial basis functions
Conference on Computer Graphics and Interactive Techniques
(2001) - et al.
Domain decomposition algorithms
Acta Numerica
(1994) Partial differential equations, graduate studies in mathematics
Am. Math. Soc.
(2009)- et al.
Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing
IEICE Trans. Commun.
(2015) - et al.
Comparison of fist-order finite difference and finite element alogorithms for the analysis of magnetic fields. part i: theoretical analsyis
Power Apparatus Syst. IEEE Trans.
(1982)