Study of Route Building Algorithms Using Multiple Moving Devices

Academic Paper, 2017

12 Pages





Communication Protocols Comparison and Selection
Wireless Signal Extenders

A. Dijkstra Algorithm
B. Bellman–Ford Algorithm
C. A* Search Algorithm
D. Floyd–Warshall Algorithm
E. Johnson's Algorithm
Comparison of Shortest Path Algorithms

Real-Time Rerouting
RFID Driven Routing Algorithm




These article research es different aspects of monorail transportation industrial system. After the carrying out of the scientific research with the aim to consider the most suitable and widespread algorithms, to compare different path finding approaches and to build autonomic algorithm for optimal navigation with low-powered system, in which devices coupled with help of wireless connection and to choose computational resources keeping system reliable and efficient. The described in the article research considers: solution to overcome signal decay in wireless connection, prevention of collision between moving carts, deadlock problem solution, computation efforts minimization, study of ways to build a system so that the operator is not required to have good technical skill, the robustness and continuance communication aspect and the efficient use of the energy aspect. Routing algorithm based on writable RFID transponders presented.


The technically equipped and up to dated industrial areas must satisfy the need in constant efficiency improvement and continual decreasing costs with the goal to stay competitive amount the other existing in the market space companies.

To ensure more efficient human resources use through saving time and attempts of the working staffs in the big industrial areas. The ultralight Electro Monorail System (uEMS) project under professor Noche from University Duisburg-Essen and professor Künne from Dortmund Technical University supervising was suggested. The ultralight Electro Monorail System intended to transfer objects weighing up to 20 kg in big industrial areas. As a part of the projects aims, the uEMS system straggles to solve robustness and continuance communication, the optimal route calculation and built, the obstacles overcome, the deadlock prevention, the efficient use of the energy, the quick cooperation between the two or more moving units in the logistic system, system self-diagnostic, the automatic recover and rollback, the automatic real time typical error detection and the correction of system critical errors problems


The three most popular in industrial field communication technologies of wireless communication was considered. All of them correspond to Institute of Electrical and Electronics Engineers (IEEE) 802.15.1 (Bluetooth), 802.15.4 (ZigBee) and 802.11a/b/g (Wi-Fi) standards. The IEEE standard defines only physical (PHY) and medium access control (MAC) layers.


Wi-Fi is IEEE 802.11a/b/g standard for wireless local area network (WLAN) [1]. IEEE standard includes wireless local area network (WLAN) device-to-device connections, but usually used to connect device to wireless access point. This access point (Hotspot) usually working with range about 20 meters in normal urban environment, in open areas or with special antennas it can be extended to hundreds of meters. To achieve a signal coverage in complex cases or large areas, can be used several overlapping hotspots. The important aspect of using multiple access points is the presence of the same service set identifier (SSID) and same security settings. Clients migrate in such networks from one access point to another using signal state as selection criteria.


Bluetooth is IEEE 802.15.1 standard developed by Bluetooth Special Interest Group. This communication technology was invented by telecom vendor Ericsson in 1994 and was originally conceived as a wireless alternative to RS-232 data cables. It uses short-wavelength UHF (Ultra High Frequency) to exchanging data. This technology used for short-range connectivity and usually with attention for low energy consumption. Bluetooth working in WPAN (Wireless Personal Area Network), which interconnecting devices and range from centimeters to 10 meters (ideal circumstances up to 100meter), there are no access point in compare with Wi-Fi. Bluetooth have piconet mode with up to eight active devices in a master-slave relationship. As mentioned in Bluetooth Special Interest Group official website the Bluetooth Basic Rate/Enhanced Data Rate (BR/EDR) enables continuous wireless connections and uses a point-to-point (P2P) network topology for one-to-one (1:1) device communications. Bluetooth LE P2P optimizes data transfers with low power consumption. Bluetooth LE broadcast topology supports localized information sharing and is well suited for beacon solutions, such point-of-interest (PoI) information and item and way-finding services. [2]


Standard IEEE802.15.4 has low data rate to support low power consumption, same as Bluetooth it has short-range application. Usually transmission distance varies between 10 and 100 meters, depending in environment characteristics. This format works like generic mesh network. Security in ZigBee provided by 128-bit symmetric encryption keys. Band with is up to 250 kbit/s, this speed is usually enough for sensors, but not enough for internet based application. Network layer checks constantly network, to ensure that connection exists, provide redundancy by resending lost data if transaction error occurred. Security architecture based on security keys, inserted on initialization.

ZigBee network supports: ZigBee Coordinator – working as a root or bridge to other networks. Each network may have only one Coordinator and this device-started network; ZigBee Router – transfer data from other devices and can run some application functions; ZigBee End Device – saves battery, when while the device not in action it switches to the sleep mode. Talks to Coordinator or Router, or transfers data from other devices. [3]

Communication Protocols Comparison and Selection

The comparison of the Wi-Fi, Bluetooth and ZigBee was summarized in the research of Jin-Shyan Lee, Yu-Wie Su and Chung-Chou Shen [4]. Based on theirs work the followed comparison presented.

Data transfer speed is significantly better by Wi-Fi standard. Using the technology data transfer speed starts from 54 Mbps and go up to 1000 Mbps. In the current year, most applications using Wi-Fi technology achieve 300 Mbps speed; while by Bluetooth data transfer speed rate achieves only 1 Mb/s, while ZigBee 0.25Mb/s only. The highest rate of maximal signal rate comparison has Wi-Fi. The communication technology has the rate +5, which is more than double time more compared with Bluetooth technology. By ZigBee the rate is 0.

All three wireless technologies used for few decades, and have new advanced versions, upgrades and specific solutions to extend signal range. Bluetooth is short-range protocol, almost because it’s low-powered. Typically, we can talk about 1-10 meters’ range; last versions of Bluetooth (v 5) have theoretical maximum range up to 240 meters, the range varies due to environment conditions. It is important to specify some interference problem, which can influence. According to research [4] “If Bluetooth and Wi-Fi systems operate at the same time in close proximity they will interact (collide) with each other. The effect of Wi-Fi over Bluetooth shows a strong degradation of Bluetooth signal. Bluetooth transaction rate drops from 1.12 Mbps to 0.59 Mbps for TT-RR scenario and 0.95 Mbps to 0.3 Mbps for TR-RT scenario. “ . The highest rate of signal range and interference robustness has Wi-Fi. The Wireless Fidelity communication technology has the rate +5, which is 5 time more than the two other technologies.

Wireless connection of all discussed technologies uses radio waves. Each one of devices has either an internal or external antenna. By sending signal, devices produce transmitter, consume power and send signal with help of an antenna. For example, when we are talking about Wi-Fi signal, it has range 15-20 dBm, which means, the power of such a signal amount 32 to 100 milliwatt. By Bluetooth values variates normally between 0 and 10 dBm, which means it consumes between 1 and 10 mW power. ZigBee is even less powerful, than the Bluetooth, it’s transmitted power is between -25 to 0 dBm, this is equal to power between 5 µW to 1.0 mW. The highest rate of transmitter power control has Wi-Fi. This communication technology has the rate +5, which more than twice higher as by two other technologies.

Number of channels is important validation factor. Each one of technologies used overlapping devices. If neighbor devices are using exactly the same frequency, it may cause a serious interference of radio waves. To overcome this, each device with overlapping range should transmit their signal with different frequency. The number of different frequencies also called channels are important criteria for evaluation. Wi-Fi have 14 channels, important notify, that each country have specific regulations for allowable channels. We can use less than 50% of channels, depends on country. Bluetooth have 79 channels and ZibBee 16 channels. The highest rate by number of radio frequency channels factor have Bluetooth and Wi-Fi. The both technologies have the rate +5.

Number of channel bandwidth is also important component for evaluation. E.g. the bandwidth of Wi-Fi channel is 22 MHz. Each one the wireless technologies use some optimal relation between channel bandwidth and number of available channels. The channel bandwidth has maximal rate by Bluetooth and ZigBee communication technologies. The rate of the Wi-Fi little bit less.

Each one of the technologies use own modulation technic: the Wi-Fi 802.11b uses complementary coded keying (CCK), the Wi-Fi 802.11 a/g uses 64-channel orthogonal frequency division multiplexing (OFDM), the Bluetooth uses Gaussian frequency shift keying (GFSK) and the ZigBee uses binary quadrature phase shift keying (BPSK). Modulation type has maximal rate by all the considered technologies.

Coexistence mechanism is very important part of reliability. Each one of technologies has dynamic mechanism to allocate stable signal frequency. According to [4] “Since Bluetooth, ZigBee and Wi-Fi use the 2.4 GHz band, the coexistence issue must be dealt with. Bluetooth provide adaptive frequency hopping to avoid channel collision, while ZigBee and Wi-Fi use dynamic frequency selection and transmission power control.”. Coexistence mechanism has maximal rate by all the three studied technologies.

Wi-Fi use a Basic Service Set (BSS) when all stations can communicate with each other at physical layer. Bluetooth use Piconet to build ad hoc network, which connect wireless user group of devices. This structure use one master device and up to seven active slave devices and additional 255 slave devices can be inactive “parked”. Master device bring “parked” devices to live and back. ZigBee use Star, which consists of coordinator and several end devices. Tree topology also supported, here we have some intermediate router devices as good as mesh topology, which is poor peer-to-peer network, consists of one coordinator, several routers and end devices. All wireless technologies use efficient topology models, according to target applications and has maximal rate.

Bluetooth master device can work with 8 active slaves (and 255 not active). ZigBee star network work with over 65000 devices. Structured Wi-Fi support up to 2007 devices. Maximum number of cell nodes has ZigBee.

All the protocols have encryption and authentication. Although some entire security methods can be overcome, they are providing enough protection by the communication through Wi-Fi, Bluetooth and ZigBee. The security rate by all the considered technologies is 5.

The highest summary rate has the Wi-Fi communication technology and the other two has the same summary evaluation points, thus for the uEHB project the Wi-Fi protocol chosen.

Wireless Signal Extenders

Improved connectivity allows higher data transfer levels efficiency, data processing, evaluation and logging. The mobility of automotive system demand wireless signal transfer, control and monitoring. Thus, the mobility relies on a robust wireless network to collect, communicate and receive electronic data. Wireless signal range extender, in some literature named also wireless repeater, uses existing signal from broadcasting antenna and rebroadcast it to uncover by source antenna areas. Some signal extenders create their own separate network. The more extended variant of this technic called wireless access point. ..extenders are required to be embedded within the proximity of any scaffolding to compensate for the inevitable signal decay. [5]


The shortest path finding algorithms researched by many scientists of different institutions and organizations. Most the researches providing algorithms considering randomly generated networks, that has different from real road networks features. In this article, the evaluation of some most popular routing algorithms, regard to the special needs of the ultralight Electro Monorail System (uEMS) project, provided.

A. Dijkstra Algorithm

The most known algorithm for the single source shortest path problem is Dijkstra Algorithm. The algorithm first presented in Dijkstra’s paper in 1959. [6]. The problem, described in the Dijkstra’s work, was appropriate to construct the tree of minimum total length between the N nodes. Where tree is graph with only one path between every two nodes. The 2nd problem, described in same source, was finding a path of minimum total length between two given nodes P and Q. The algorithm has the preparation level including: Assign to each one of the nodes an infinitive value. The value “0” assigned to the start node; Set the initial node to Current Node. All other nodes marked as unvisited. It has also interaction level in which it is a need to: Consider the Current Node. Calculate their distances. Compare new calculated distance with the Current Node and assign the smaller value to the Current Node; Consider all neighbors node. The Current Node marks as visited; If destination node was marked, then stop, else return to the step “c”.

This algorithm makes “exploration” of nodes toward the destination. Each time algorithm propagates Current Node close to the destination, exploration executes outward from start point. This algorithm relative slow in some cases, then other searching shortest path algorithms.

The biggest disadvantage of the Dijkstra algorithm is a need to have a global information of the network.

B. Bellman–Ford Algorithm

Bellman–Ford algorithm computes the shortest paths from a single source to all the other vertices in bottom-up manner. For some topologies, it is considerably slower than Dijkstra’s algorithm. However, the Bellman–Ford algorithm is much more flexible, because the algorithm can also work with negative weights on edges, which brings important for our purpose advantages. The algorithm is suited for distributed systems and it is a typical example of the DPP (Dynamic Programming Problem). The importance of considering negative weights detailed and very exhaustively described in Sedgewick’s work in 2002 [7]

Bellman-Ford algorithm based on finite iterations, each iteration replaces edge index with actual value. All nodes should be calculated and between two indexes algorithm always use the smallest (the shortest way) index. It has complexity O (|V| |E|) where V – number of vertices (nodes) and E – number of edges. This algorithm has two main withdraws. The first drawback all nodes and edges should be known and second one is the fact, negative cycles, can prevent from finding a correct answer.

According to Sanan, Shivani et. al. work [8] this algorithm is Dynamic programming based algorithm and uses local knowledge of neighboring nodes only.

C. A* Search Algorithm

A* Search Algorithm developed by Peter Hart, Nils Nilsson and Bertram Raphael based on Dijkstra’s algorithm, but using heuristics for search guiding. This algorithm use best-first search, by sorting solutions and using only those, which have smallest edge values (usually this means the shortest path). Once again, between all short paths this algorithm use path, which can lead most quickly to the destination. It is one of the best and popular algorithms thanks it’s real-life adjusted path finding. The main drawback is a lack of possibility to work with negative edges.

The considered algorithm will always find a solution, if such one exists. Benefit of the A* search algorithm, that it considers weights of the already traveled distances. Algorithm visits the nodes to perform heuristic estimation. According to Delling, Daniel et. al. [9] the A* algorithm fit to practical travel-routing systems, it is generally outperformed by algorithms which can pre-process the graph to attain better performance.

D. Floyd–Warshall Algorithm

The Floyd–Warshall algorithm works, with the both the positive and the negative weight values. The limitation of this algorithm is appearance of negative cycles. According to Cormen [10] Floyd-Warshall algorithm is a graph analysis algorithm for finding shortest paths in a weighted graph with positive or negative edge weights. The presence of negative cycles, would make the algorithm returns false results. The algorithm useful also for finding transitive closure of a relation R.

The algorithm compares all the alternative paths between each two Nodes. This is the main distinction from the above described algorithms, for shortest path calculate between only two nodes. The Floyd–Warshall algorithm tests every single combination of edges, to discover the shortest path. A user should construct function with three parameters: first node, last node and intermediate node set. As a next step, the algorithm will work recursive. Such a recursion frequently called dynamic programming nature. The result of the running Floyd–Warshall algorithm, will be the distance between node i and node j in the graph matrix. It is takes O (V ^3) time to run the Floyd-Warshall algorithm. This algorithm is the best-suited one for dense graphs, because it does not depend on the number of edges.

E. Johnson's Algorithm

The Johnson’s algorithm allows positive and negative weights on the graph, but has some limitation by using negative weight cycles. The algorithm uses Bellman-Ford algorithm to calculate a transformation of the graph and remove all negative weights, then with help of Dijkstra’s algorithm calculates shortest path over prepared graph. The idea of Johnson’s algorithm to re-weight all edges and then to assign new weights, which are positive only. After the edges re-weighting, Dijkstra’s algorithm for every one of the nodes applied. Johnson’s algorithm use following four steps: Add new node S to the graph and connected this node by edge with zero weight to each one from other nodes; Appling Bellman-Ford algorithm, use node S from previous step as start node; Find heuristic weight to each node h(v), if this step detects a negative cycle, then – terminate execution; Reweighting of values on edges, by using values calculated in previous step by Bellman-Ford algorithm. New weight w (u,v) + h (u) – h (v) where u and v are edges. Remove node S from 1 step. Apply Dijkstra algorithm to find a shortest path from each node k to every other node in new reweighted graph. Because Johnson’s algorithm uses two other algorithms, it’s complexity is the sum of two algorithms: O (VE) + O (V2 log V) = O (V2 log V+VE)

Comparison of Shortest Path Algorithms

For the uEMS system routing algorithm based Bellman-Ford is more suitable. Bellman-Ford looks for alternative routing to avoid blocked part of the route. A * Search and Dijkstra algorithms in such a case are not useful, because they cannot work with negative weights.

Bellman Ford algorithm uses a local knowledge of neighboring nodes. This feature is very useful for complex system routing computation with multiple carts. If algorithm will use all the time all system information related to all nodes this approach can be unnecessarily complicated. For example, we have 30 carts in the system with 200 nodes. If all carts on the move, and sending request to the server, to calculate optimal route. For limited with computation resources server will be very important to use least information. If server calculate the optimal route for specific cart, using only 20 neighbor nodes in calculation. This may significant reduce computation power comparing to same case with 200 nodes. If we assume, that all carts calling few time routing algorithms in few minutes, this can cause server overloading. Using Bellman-Ford algorithm, which consider only neighbor nodes save computation resources.

Of case same computation power, issue relevant to route computation on cart side while moving in offline mode. In offline mode, cart cannot use a central server computation services.


The rapid growth of technological achievements increased demand on wireless connected, low-cost and low-powered coupled devices, building entire system. Wireless networks composed of the nodes can support a lot of functionality, which was inaccessible for such networks in in the recent past. The requirement can vary from system to system.

According to He, Yu et. al. [11] designing efficient routing services for sensor networks often needs to consider the properties of specific applications and/or networks…Each sensor node can operate autonomously with no central point of control and can make decisions based on the information it currently has. Networks composed of these sensor nodes can support many new applications such as physiological monitoring, environmental monitoring, precision agriculture, transportation, factory instrumentation and inventory tracking, condition based maintenance, smart spaces, and military surveillance

Real-Time Rerouting

Robots and automatic systems utilization in production and logistic, improves product and service quality, reduces costs and allows prediction of the future system behavior scenarios more precisely. Monorail based transportation system, equipped with autonomic carts can reduce costs and improve logistic process. Evaluation of such systems from full and half-manual to autonomous was possible by improving routing algorithm, computation power, sensors and power efficiency.

In real-life applications, temporary loss of wireless connection between modules is a quite possible scenario. Dynamic industrial environment has many factors, which may cause a wireless signal interference. Some modern wireless solutions may overcome these limitations, but unfortunately quite expensive. By giving some level of routing logic to the system, autonomous routing mode may help overcome connection lost problem.

This approach limited to loosing signal between stations only. If transportation cart will lose signal on charging station or on load station, this is a critical exception, because in this case cart cannot receive “call” signal from the user to start the route. Signal lost on monorail junctions is possible.

If signal lost happens while cart moves from departure to the target station, cart switches to autonomous routing. Simultaneously second part of the system, called Central Server, which is responsible for routing while cart has wireless connection, switches to the simulation mode. Central Server simulation ability need to predict probabilistic movement of the cart in offline mode, and prevent possible routing collisions with other online carts.

Simulation algorithm based on historical data from the system database, system logs and takes into account implemented autonomic routing logics in cart can predict with high probability actual position of the moving carts in autonomous mode. Central Server use State Machine approach to track the cart. Simulation model include following parameters:

- Last known cart positions based on RFID transponder.
- Current target destination and departure station.
- Cart speed level.
- Cart payload value (Kg).
- Cart self-diagnostic exceptions
- Battery level

Each cart in the monorail system equipped with RFID reader. This reader can read unique ID’s of RFID transponders distributed along the monorail track. Each important parts of the route marked by such RFID tags. Location of the tags known to the system and precisely determinates cart location.

Central Server maps the problem route section without wireless coverage. These sections have statistically high probability to lose wireless connection between cart and central server. Central server dynamically propagates this map, so that recent changes have a greater impact than long-standing.

Real-time rerouting reflects in the best way, user needs, but leads to over complexity and routing problems, such as deadlocks and unexpected delays. Of cause rerouting ability meet system requirements, because user should be able to cancel or change target station at any point of time. Proposed system, solve this problem by predictable simulation ability of Central Server.

RFID Driven Routing Algorithm

Rewritable stationary RFID transponders may hold all needed routing information to moving monorail carts. This assumption corrects only if monorail structure can be presented with Tree-structure. In a tree-structure, there is one and only one route between each two nodes. To simplify presented example, based on uEMS project in University Duisburg-Essen and complexity of real system was reduced to 3 level in tree depth. RFID identifier simplified to 12-digit decimal number with following encoding functionality:

Abbildung in dieser Leseprobe nicht enthalten

First element presented in Figure 1 encodes the types of system elements such like junctions, load or charge stations.

Proposed algorithm automates system setup. By starting initialization, operator need provide only one decision – manually select main loop, which represent root in tree structure. In initialization mode, cart bypasses recursive through the tree structure. After reaching any new RFID tag, system recognize type of the element and write new value to RFID tag with unique address using encoding presented in Figure 1. This identifier determinate location of the element in the tree, describe structure from the current node to the root node (main loop).

Abbildung in dieser Leseprobe nicht enthalten

This approach has many benefits:

1. Simplifies the system.
- Automatic setup process will configure the system and reduce human errors.
- Tree structure limited with one route between any two nodes simplifying debugging and testing processes.
- Tree structure hierarchy is easy to understand.

2. Low cost equipment.
- Computation power needed to execute setup and route algorithms are almost the same in computation with a power of a modern elevator. This routing logic may be implemented even with programmable logic controllers (PLC). Which belongs to simple industrial equipment.

3. Routing without system knowledge.
- Tree routing algorithm use only current node and nearest parent/children nodes. There is no need and sense to keep in memory information about all other nodes.

4. Automatic setup algorithm, work for setup and maintenance.
- Recursive setup algorithm identical for setup and reconfiguration, sense it is includes initialization of all RIFD transponders. It is running on initialized system

5. No programming skills needed to run setup in autonomic mode.
- Operator need only RFID writer/reader skill to initialize RFID tags and basic knowledge in tree hierarchy to choose the correct root node.

After initialization, moving cart can be routed to any station, guided only by information of current location and destination address. Routing algorithm do not need powerful computation ability and may execute without central server, full autonomous, with very simple equipment such as Programmable Logic Controllers (PLC). Such system has very high redundancy, can initialized, and operated by personal with low technical skills.


The research investigated different aspects to composite autonomic monorail transportation industrial low-powered system and supplements ultralight Electro Monorail System (uEMS) project. The result of this research are hints, recommendation and pseudo code implementation to facilitate development of innovative RFID driven routing algorithm for autonomic monorail network. This algorithm not only satisfying all the project requirements it also suggest solutions to most project limitations. The innovative part of the approach achieved through rewritable RFID tags serving as digital signposts. The carts front end software will be implemented based on the algorithm, that does not build routing plan, it is simply moving on and performs turns according to information stored in RFID tags. The immediate result was the ultralow computation power of autonomic cart. Thanks simplicity and low computation efforts needed to perform the solution code relative low cost and unsophisticated hardware can execute the logic of the chosen algorithm.

The research included possible routing problem solution study of ultralight monorail system. Dead lock problem was considered together with wireless connection loss overcome solutions, ways to catch system exceptions and record them in log for self-diagnostic and self-recovery module, predictable routing simulation suggestion for improve efficiency of the system were described.

The further research should focus on development of rules and regulations to deal with RFID driven routing algorithms. Those rules and regulations should declare correct behavior of carts on occupied segment of route, station, junction. RFID transponders research should compare different RFID formats, to allow algorithm to encode more information on RFID tags memory.


1 IEEE, Operations Center, Piscataway, NJ

2 Bluetooth Special Interest Group, Kirkland, Washington

3 ZigBee Alliance, Davis, CA

4 Jin-Shyan Lee, Yu-Wie Su and Chung-Chou Shen (2007): A Comparative Study of Wireless Protocols: Bluetooth, UWB, ZigBee, and Wi-Fi. In: The 33rd Annual Conference of the IEEE Industrial Electronics Society.

5 Zekavat, Payam et. al. (2014): Securing a Wireless Site Network to Create a BIM-allied Work-front. In: International Journal of Advanced Robotic Systems

6 Dijkstra, Edsger W. (1959): A note on two problems in connexion with graphs. In: Numerische Mathematik, vol. 1: 269-271

7 Sedgewick, Robert (2002): "Section 21.7: Negative Edge Weights". Algorithms in Java, 3.ed.

8 Sanan, Shivani (2013): Shortest Path Algorithm, International Journal of Application or Innovation in Engineering & Management (IJAIEM), vol. 3: 316 – 320

9 Daniel et. al. (2009): Algorithmics of Large and Complex Networks: Design, Analysis, and Simulation, 1. Springer: Berlin Heidelberg

10 Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L. (1990). Introduction to Algorithms (1st ed.). MIT Press and McGraw-Hill.

11 He, Yu et. al. (2006): An autonomic routing framework for sensor networks. In: Cluster Computing, vol. 9: 191–200

Excerpt out of 12 pages


Study of Route Building Algorithms Using Multiple Moving Devices
University of Duisburg-Essen
Catalog Number
ISBN (eBook)
ISBN (Book)
File size
985 KB
logistic, monorail, RFID
Quote paper
Dennis Belsky (Author)Alexander Goudz (Author)Bernd Noche (Author), 2017, Study of Route Building Algorithms Using Multiple Moving Devices, Munich, GRIN Verlag,


  • No comments yet.
Look inside the ebook
Title: Study of Route Building Algorithms Using Multiple Moving Devices

Upload papers

Your term paper / thesis:

- Publication as eBook and book
- High royalties for the sales
- Completely free - with ISBN
- It only takes five minutes
- Every paper finds readers

Publish now - it's free