Mobile Robots book 2011 Part 10 potx

Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions216 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 Fig. 5. D-Optimum trajectories of mobile actuators for one stationary sensor 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 Fig. 6. D-Optimum trajectories of mobile actuators for three stationary sensors 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 Fig. 7. D-Optimum trajectories of mobile actuators for one moving sensor 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 Fig. 8. D-Optimum trajectories of mobile actuators for two moving sensors Optimal Real-Time Estimation Strategies for a Class of Cyber-Physical Systems Using Networked Mobile Sensors and Actuators 217 As expected, for all cases, the performance criterion value decreases as the number of actuator increases. We can also notice that both the mobility, population and location of the sensors have a direct impact on the performance of the strategy. Therefore, we can suppose the existence of an optimal combination of sensor and actuator trajectories. 6.3 Optimal Sensor Trajectories (Online Results) In this section, we focus our attention on the performance of the online methodology described in Section 5. The experiment is run for different noise statistics and for each case results are given in the form of sensor trajectories and parameter estimates. For case 1, 0.0001 V , for case 2, 0.001 V , and for case 3, 0.01 V . In all cases, we consider 3 mobile sensors. The control of the mobile sensors u is limited between 0.7 and 0.7 . All three sensors have fixed initial positions (    1 00.1,0.1 s x ,    2 00.1,0.5 s x and    3 0 0.1,0.9 s x ). The results for the previously defined case are respectively given in Figure 9. for Case 1, in Figure 10 for Case 2 and in Figure 11 for Case 3. For each figure, subfigure (a) gives the sensor trajectories, the evolution of the estimates is shown in (b) and the measurements are given in (c). 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 iteration θ θ 1 θ 2 θ 3 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 time measurement sensor 1 sensor 2 sensor 3 (a) (b) (c) Fig. 9. Closed-loop D-Optimum experiment for 0.0001 V . From left to right (sensor trajectories, parameter estimates and sensor measurements) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 iteration θ θ 1 θ 2 θ 3 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 time measurement sensor 1 sensor 2 sensor 3 (a) (b) (c) Fig. 10. Closed-loop D-Optimum experiment for 0.001 V . From left to right (sensor trajectories, parameter estimates and sensor measurements) Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions218 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 1 x 2 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 iteration θ θ 1 θ 2 θ 3 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 time measurement sensor 1 sensor 2 sensor 3 (a) (b) (c) Fig. 11. Closed-loop D-Optimum experiment for 0.01 V . From left to right (sensor trajectories, parameter estimates and sensor measurements) From these figures, we have the following observations: • In all the cases, the sensors have similar trajectories as they try to follow the excitation wave along the 1 x axis   2 1 20exp 50 xt . • For low noise amplitude (cases 1 and 2), the experiment is long enough to obtain good estimates of the parameters. In case 3, the experiment is not long enough to obtain convergence. • In all cases, we can clearly observe that the trajectories of the mobile sensors change as the estimated values of the parameters are getting closer to the real values. 7. Conclusions In this chapter, we described a numerical procedure for optimal sensor-motion scheduling of diffusion systems for parameter estimation. The state of the art problem formulation was presented so as to understand our contribution to the field. The problem was formulated as an optimization problem using the concept of the Fisher information matrix. We then introduced the optimal actuation framework for parameter identification in distributed parameter systems. The problem was reformulated into an optimal control one. Later, using our developed “online” scheme, mobile sensors find an initial trajectory to follow and refine the trajectory as their measurements allow finding a better estimate of the system’s parameters. Using the Matlab PDE toolbox for the PDE system simulations, RIOTS_95 Matlab toolbox for solving the optimal path-planning problem and Matlab Optimization toolbox for the estimation of the system’s parameters, we were able to solve this parameter identification problem in an interlaced manner successfully. With the help of the Matlab PDE toolbox for the system simulations and RIOTS_95 Matlab toolbox for solving the optimal control problem, we successfully obtained the optimal solutions of all the introduced methods for illustrative examples. We believe, this chapter has for the first time laid the rigorous foundation for real-time estimation for a class of cyber-physical systems (CPS). Optimal Real-Time Estimation Strategies for a Class of Cyber-Physical Systems Using Networked Mobile Sensors and Actuators 219 8. Future Work Our future efforts will go towards combining all of the techniques described here into a single framework. Obtaining optimal trajectories for both moving actuators and moving sensors is a challenging but very exciting research topic. It should be emphasized that the “online” estimation methodology sets the basis for exciting future research. Indeed, we can now investigate problems related to communication between mobile nodes such as time-varying information sharing topology, communication range, information loss and other well-known problems in the scope of task-oriented mobile multi-agent systems. 9. Acknowledgements This work is supported in part by the NSF International Research and Education in Engineering (IREE) grant #0540179. Christophe Tricaud was supported by Utah State University Presidential Fellowship (2006-2007). The authors are grateful to Professors D. Ucięski and M. Patan of the Institute of Control and Computation Engineering University of Zielona Góra for constructive research collaborations over the years. Christophe Tricaud would like to thank Professors D. Ucięski and M. Patan for hosting his summer research visit in the Institute of Control and Computation Engineering University of Zielona Góra, in 2007 sponsored by an NSF IREE grant. YangQuan Chen appreciates the visit of Professor D. Ucięski to CSOIS in 2006 and his invited lecture at the International Mini-Workshop on DDDAS (http://mechatronics.ece.usu.edu/mas-net/dddas/ Dynamic Data Driven Application Systems sponsored by an NSF DDDAS/SEP grant. 10. References Atkinson, A. C. & Donev, A. N. (1992). Optimum Experimental Designs, Clarendon Press, Oxford Banks, H. T. & Kunisch, K. (1989). Estimation Techniques for Distributed Parameter Systems, Systems & Control: Foundations & Applications, Boston: Birkhäuser CPS (2008). C. S. Group, “Cyber-physical systems executive summary,” in Cyber-Physical Systems Summit, 2008. [Online]. Available: http://varma.ece.cmu.edu/summit/ CPS-Executive-Summary.pdf Chen Y. Q., “Mobile actuator/sensor networks (MAS-net) for cyber-physical systems,” USU ECE 6800 Graduate Colloquium, September 2008. [Online]. Available: http://www.neng.usu.edu/classes/ece/6800/ Chen, Y. Q. ; Moore, K. L. & Song, Z. (2004). Diffusion boundary determination and zone control via mobile actuator-sensor networks (MAS-net) – challenges and opportunities. Proceedings of SPIE Conference on Intelligent Computing: Theory and Applications II, part of SPIE’s Defense and Security. SPIE, April 2004, Orlando, FL., USA Fedorov, V. V. & Hackl, P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Springer-Verlag, New York Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions220 Gill H., Zhao W., and Znati T. (2008) “Call for papers for a special issue of on distributed cyber physical systems,” IEEE Transactions on Parallel and Distributed Systems (TPDS), vol. 19, no. 8, pp. 1150 – 1151, August 2008. Jennings, L. S. ; Fisher, M. E. ; Teo, K. L. & Goh, C. J. (2002). MISER 3: Optimal Control Software, Version 2.0. Theory and User Manual, Department of Mathematics, University of Western Australia, Nedlands Lee E. A. (2008) “Computing foundations and practice for cyber-physical systems: A preliminary report,” University of California, Berkeley, Tech. Rep. UCB/EECS- 2007-72, May 2007. [Online]. Available: http://chess.eecs.berkeley.edu/ pubs/306.html Ljung L. (2008) System Identification Toolbox TM7 User’s guide, The MathWorksTM, 2008. [Online]. Available: http://www.mathworks.com/products/sysid/ Kubrusly, C. S. & Malebranche, H. (1985). Sensors and controllers location in distributed systems — a survey. Automatica, 21, 2, (117–128) Quereshi, Z. H. ; Ng, T. S. & Goodwin, G. C. (1980). Optimum experimental design for identification of distributed parameter systems. International Journal of Control, 31, 1 (21–29) NSF (2006). “NSF workshop on cyber-physical systems,” October 2006. [Online]. Available: http://warma.ece.cmu.edu/cps/ Omatu, S. & Seinfeld, J. H. (1989). Distributed Parameter Systems: Theory and Applications. Oxford Mathematical Monographs, New York: Oxford University Press Patan, M. (2004). Optimal Observation Strategies for Parameter Estimation of Ditributed Systems. Ph.D. Dissertation, University of Zielona Góra Press Patan, M. ; Tricaud C. & Chen Y. Q. (2008). Resource-constrained sensor routing for parameter estimation of distributed systems. In Proceedings of the 17th IFAC World Congress, July 2008, Seoul, Korea Polak, E. (1997). Optimization, Algorithms and Consistent Approximations. Applied Mathematical Sciences, Springer-Verlag, New York Rafajówicz, E. (1986). Optimum choice of moving sensor trajectories for distributed parameter system identification. International Journal of Control, 43, 5, (1441–1451) Schwartz, A. L. (1996). Theory and Implementation of Numerical Methods Based on Runge-Kutta Integration for Solving Optimal Control Problems. PhD thesis, University of California, Berkeley Schwartz, A. ; Polak, E. & Chen, Y. Q. (1997). RIOTS - A Matlab Toolbox for Solving Optimal Control Problems, May 1997. http://www.accesscom.com/~adam/RIOTS/ Song, Z. ; Chen, Y. Q. ; Liang, J. & Ucięski, D. (2005). Optimal mobile sensor motion planning under nonholonomic constraints for parameter estimation of distributed parameter systems. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Alberta, Canada Stryk, O. von (1999). User’s Guide for DIRCOL, a Direct Collocation Method for the Numerical Solution of Optimal Control Problems. Version 2.1. Fachgebiet Simulation und Systemoptimierung, Technische Universität Darmstadt, November 1999 Sun, N. Z. (1994). Inverse Problems in Groundwater Modeling. Theory and Applications of Transport in Porous Media. Dordrecht, The Netherlands: Kluwer Academic Publishers Optimal Real-Time Estimation Strategies for a Class of Cyber-Physical Systems Using Networked Mobile Sensors and Actuators 221 Tricaud, C. ; Patan M. ; Ucięski, D. & Chen Y. Q. (2008). D-optimal trajectory design of heterogeneous mobile sensors for parameter estimation of distributed systems. Proceedings of 2008 American Control Conference, June 2008, Seattle, Washington, USA Tricaud, C. & Chen Y. Q. (2008a). Optimal Mobile Actuation Policy for Parameter Estimation of Distributed Parameter Systems, Proceedings of Eighteenth International symposium on Mathematical Theory of Networks and Systems (MTNS2008), July 2008, Virginia Tech, Blacksburg, Virginia, USA Tricaud, C. & Chen Y. Q. (2008b). Optimal Mobile Sensing Policy for Parameter Estimation of Distributed Parameter Systems: Finite Horizon Closed-loop Solution, Proceedings of Eighteenth International symposium on Mathematical Theory of Networks and Systems (MTNS2008), July 2008, Virginia Tech, Blacksburg, Virginia, USA Ucięski, D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification. CRC Press, Boca Raton, FL, Ucięski, D. (2000). Optimal sensor location for parameter estimation of distributed processes. International Journal of Control, 73, 13, (1235–1248) Ucięski, D. & Chen Y. Q. (2005). Time-optimal path planning of moving sensors for parameter estimation of distributed systems. Proceedings of 44th IEEE Conference on Decision and Control, and the European Control Conference, 2005, Seville, Spain Ucięski, D. & Chen, Y. Q. (2006). Sensor motion planning in distributed parameter systems using Turing’s measure of conditioning. Proceedings of 45th IEEE Conference on Decision and Control, 2006, San Diego, CA Walter, É. & Pronzato, L. (1997). Identification of Parametric Models from Experimental Data. Communications and Control Engineering. Springer-Verlag, Berlin WCPS (2008). The first international workshop on cyber-physical systems,” June 2008. [Online]. Available: http://www.qhdctc.com/wcps2008/ Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions222 11 Effective Heuristics for Route Construction of Mobile Data Collectors Samer Hanoun & Saeid Nahavandi Centre for Intelligent Systems Research Deakin University Australia 1. Introduction Wireless sensor networks (WSN) are composed of large numbers of small sensing self- powered nodes which are densely deployed either inside the phenomenon or very close to it (Akyildiz et al., 2002; Culler et al., 2004). The capabilities of these inexpensive, low-power communication devices ensure serving in a wide range of application domains (Chong and Kumar, 2003; Haenggi, 2004). While their potential benefits are clear, a number of open problems must be solved in order for wireless sensor networks to become viable in practice. These problems include issues related to deployment, security, calibration, failure detection and power management. Recently, significant advances have been accomplished in the field of mobile robotics (Engelberger, 1999), and robots have become increasingly more feasible in practical system design. Therefore, a number of problems with wireless sensor networks can be solved by including a mobile robot as an integral part of the system. Specifically, the robot can be used to deploy and calibrate sensors, detect and react to sensor failure, deliver power to sensors, and otherwise maintain the overall health of the wireless sensor network. Energy consumption is one of the most important requirements for many WSN applications. Since energy resources are scarce and battery replacement is not an option for networks with thousands of physically embedded sensor nodes, energy optimization for individual nodes is required as well as the entire network. In static wireless sensor networks, it is observed that, as data traffic must be concentrated towards the sink (base station), the nodes around that sink have to forward data for other nodes whose number can be very large; this problem always exists, regardless of what energy conserving protocol is used for data transmission. As a result, those bottleneck nodes around the sink deplete their batteries much faster than other nodes and, therefore, their lifetime upper bounds the lifetime of the whole network. Mobile collectors (mobile robots) are utilized to act as mechanical data carriers taking advantage of mobility capacity (Grossglauser and Tse, 2002) and physically approaching the sensors for collecting their data using single hop communication. This approach trades data delivery latency for the reduction of energy consumption of sensors; however, it shows remarkable enhancement in the network lifetime. Still, the data delivery latency depends mainly on the mobility regime applied by the collector. Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions224 In random mobility regimes (Burrell et al., 2004; Jain et al., 2006; Shah et al., 2003), random moving humans and animals act as "data mules", collect data opportunistically from sensor nodes when entering their communication ranges. A grid type topology is assumed for the network deployment with sensors located at the grid intersection points, where the mobile entities (data mules) can move in any of the four directions with equal probability (Shah et al., 2003) or move up and down the rows (Burrell et al., 2004). The random mobility regime shows improved data capacity (Grossglauser and Tse, 2002), however, in all cases, the worst-case latency of data delivery cannot be bounded. This unbounded latency may lead to excessive data caching at mobile entities, resulting in buffer overflows and data in transit may have to be dropped before being delivered to the destination, making it harder to provide transport layer reliability. In predictable mobility regimes (Baruah et al., 2004; Chakrabarti et al., 2003), vehicles moving on a predesigned path collect sensors data when they move near them. The sensor nodes learn the times at which they have connectivity with the vehicle, and wake up accordingly to transfer their data. The trajectory of the mobile vehicle is known to the sensor nodes, which helps the sensors to save energy by sleeping until the predicted time of data transfer comes. A queuing model (Chakrabarti et al., 2003) is introduced to accurately model the data collection process. Using this queuing system model, the success rate of data collection and power consumption are analysed. Also, applying reinforcement learning to locate the vehicle efficiently at any point of time along its path is studied in (Baruah et al., 2004). The predictable mobility regime provides efficient solutions for saving the sensors energy consumption; however, it lacks flexibility and scalability as the sensors have to relearn the new data transfer times if the vehicle's path change and the need for redesigning the vehicle's path when transplanted to other networks. In contrast, the controlled mobility regime adapts the motion strategy of the mobile collector according to the network runtime conditions to balance the sensors energy consumption and the data delivery latency. The message ferrying approach introduced in (Kansal et al., 2004; Zhao and Ammar, 2003; Zhao et al., 2004, 2005) controls the motion of a mobile relay to route messages between nodes in sparse networks. The idea is studied on networks with stationary sensor nodes (Kansal et al., 2004; Zhao and Ammar, 2003) and networks with mobile nodes (Zhao et al., 2004, 2005). The message ferry moves proactively to meet nodes wishing to send or receive packets and most communication involves short range radios for avoiding excessive energy consumption. The approach proves its strength in improving data delivery and energy efficiency; however, the collector acts only as a mobile relay between sparse sensor nodes. Controlling the mobile collector motion for efficient data collection is presented in (Gu et al., 2005; Ngai et al., 2007; Somasundara et al., 2004; Tirta et al., 2006). The motion strategy of the mobile collector (element) is formulated as a scheduling problem based on knowing in advance the sensors sampling intervals and the rate by which the events in the environment occur. Offline solutions are provided in (Gu et al., 2005; Ngai et al., 2007; Tirta et al., 2006) based on having advance knowledge regarding the deployment locations of the sensors, their data generation rates, and buffer sizes. The solutions presented minimize the data latency by optimizing the collector inter-arrival times while using single hop communication for data transfer to minimize the sensor's energy consumption, remains that all operate offline and maladaptive to the network operational conditions. An online solution is presented in (Somasundara et al., 2004) that overcomes some of the former Effective Heuristics for Route Construction of Mobile Data Collectors 225 problems. A mobile data collector is scheduled in real time to visit sensors such that no sensor buffer overflow occurs. The algorithm considers buffer overflow deadlines as well as distances between nodes in determining the visiting schedule. The new deadline for the node's future visit is updated, once it is visited and depends mainly on knowing the node's buffer size and sensing rate to compute its next overflow deadline. The solution works online; still, there is a requirement on having full knowledge about the operational parameters of the sensor node. This work is concerned with the controlled mobility regime. The former presents the solutions lying in this domain of research; however, more research remains and requires deep attention and addressing. The following are among these research points: x Offline solutions (Gu et al., 2005; Ngai et al., 2007; Tirta et al., 2006) produce optimized results but depend mainly on having in advance full knowledge about the network operational parameters, which may not be always feasible. Solutions working online and in real-time are needed to accommodate changes in the network operation. x The time required for the sensor's buffer to become full (overflow time) is assumed to be fixed and constant with time (Somasundara et al., 2004, 2007). Intelligent algorithms running locally on the sensor, performing local fusion and compression, impact the sensor's overflow time as this depends mainly on the data sensed and the quality threshold measures applied by the fusion and compression algorithms. Additionally, the overflow time can change with time according to the dynamics in the phenomenon which the sensors are sensing. Therefore, the change in the buffer overflow time with time has to be encountered in the solution. x In scenarios where sensor nodes form clusters (Younis and Fahmy, 2004), the mobile data collector can visit the centroids of these clusters (cluster heads). An early arrival would force the mobile collector to wait until enough data is aggregated at the cluster head, and a late arrival may cause missing some of the aggregated data. Adaptive schedule considering the runtime conditions of the sensors is required to handle such cases. x In event-driven sensor network applications, the dynamics in the phenomenon which the sensor nodes are sensing changes with time and the rate and times the events occur are not known ahead and even unpredictable. Moreover, in query-driven applications, the network operator may query the network to perform certain tasks, in irregular patterns. This requires that the motion strategy of the mobile collector to act based on these unpredictable situations. x Deploying thousands of sensors manually and setting their locations is not a feasible process and in most situations the sensors are deployed randomly in the environment. Moreover, some sensors may be carried by low mobile platforms and their locations change from time to time. These factors impact the mobile collector schedule and should be adopted properly. The network performance is considered to be dependent only on the sensor nodes in the network. However, the embedded capabilities of the mobile collector (i.e speed) can be utilized to enhance the network performance. Also, using multiple mobiles with appropriate cooperation strategies can add more benefit to the data collection operation. Adaptive decentralized solutions are required to take advantage of these capabilities. [...]... k  R, i  N, v: is the moving speed of the mobile collector in m/sec, 232 Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions Mobile Collector Route Design (MCRD): min T ¦A k (7) k where T is the overall route period, and each Ak is computed based on the distance cost between requests k and (k+1) and the speed selected by the mobile collector for servicing this request The... area of dimension 100 x 100 m2 is considered for the sensors deployment A number of sensor nodes varying from 50 to 100 sensors are distributed uniformly at random preserving homogenous node density among all areas in the sensing field x Sensor Parameters: Each sensor has a radio communication radius of 25m and a buffer of size 1 Kbyte x Mobile Collector Parameters: Initially the mobile collector is... power management Recently, significant advances have been accomplished in the field of mobile robotics (Engelberger, 1999), and robots have become increasingly more feasible in practical system design Therefore, a number of problems with wireless sensor networks can be solved by including a mobile robot as an integral part of the system Specifically, the robot can be used to deploy and calibrate sensors,... presents the steps followed by the mobile collector for constructing its route The minimum spanning tree is computed based, as presented by Algorithm 2, on partitioning the graph of the collection requests into two independent subsets, S and T, such that, S * T = N and S  T = ‡ and the set (S, T) is given by all arcs (i,j), where i  S, j  T, or i  T, j  S 234 Mobile Robots - State of the Art in Land,... network However, the embedded capabilities of the mobile collector (i.e speed) can be utilized to enhance the network performance Also, using multiple mobiles with appropriate cooperation strategies can add more benefit to the data collection operation Adaptive decentralized solutions are required to take advantage of these capabilities 226 Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative... of the sensing field The mobile collector moves with a fixed speed of 1m/s, and has a communication radius of 50m The mobile collector achieves communication with the sensor node when it is in the sensor's radio communication range x Simulation Time: The simulation run last for 50000 time units, and all results are averaged over 20 different independent networks 238 Mobile Robots - State of the Art... distance traveled by the mobile collector to the number of requests collected 5.2 Performance of the MST-R Figure 6(a) and 6(b) show the performance results of running the MST-R algorithm on the set of experiments described in Table 2 The number of requests m which the mobile collector uses for constructing its collection route ranged form 1 to 10 The case m = 1, is the case where the mobile collector service... where the mobile collector service the arriving requests one by one in a timely oriented manner As the mobile collector waits for more requests to arrive this increases the data 240 Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions collection time however in such a case the mobile collector service more requests on the same collection route which decrease its distance ratio... opportunities Proceedings of SPIE Conference on Intelligent Computing: Theory and Applications II, part of SPIE’s Defense and Security SPIE, April 2004, Orlando, FL., USA Fedorov, V V & Hackl, P (1997) Model-Oriented Design of Experiments, Lecture Notes in Statistics, Springer-Verlag, New York 220 Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions Gill H., Zhao W., and Znati... service becomes possible, but it is not permitted to arrive after the latest time window Node 0 represents the depot Each node i, apart from the depot, imposes a service requirement qi that can be a delivery from, or a pickup for the depot The main objective is 228 Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions to find the minimum number of tours, K*, for a set of identical . R, i  N, v: is the moving speed of the mobile collector in m/sec, Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions232 Mobile Collector Route Design (MCRD): min k k TA  . http://www.qhdctc.com/wcps2008/ Mobile Robots - State of the Art in Land, Sea, Air, and Collaborative Missions222 11 Effective Heuristics for Route Construction of Mobile Data Collectors Samer. nodes and, therefore, their lifetime upper bounds the lifetime of the whole network. Mobile collectors (mobile robots) are utilized to act as mechanical data carriers taking advantage of mobility