Path planning problems involve computing or finding a collision free path between two positions. A special kind of path planning is complete coverage path planning, where a robot sweeps all area of free space in an environment. There are different methods to cover the complete area; however, they are not designed to optimize the process. This paper proposes a novel method of complete coverage path planning based on genetic algorithms. In order to check the viability of this approach the optimal path is tested in a virtual environment. The simulation results confirm the feasibility of this method

Cortes, M. L.

Schaffner, H.

Kotula, J.

Sulek, Z.

Kojouharov, I.

Voss, B.

Ameil, F.

Koch, K.

Pietri, S.

Gerl, J.

Pietralla, N.

Bednarczyk, P.

Crossref

Optimal area covering using genetic algorithms

GSI Repository

Development and test of a segmented Time-of-Flight plastic detector∗M. L. Corte´s†1,2, H. Schaffner2, I. Kojouharov2, B. Voss2, F. Ameil2, K. Koch2, S. Pietri2, J. Gerl2,N. Pietralla1, P. Bednarczyk3, J. Kotuła3, Z. Sułek3, and the PreSPEC and AGATA collaborations1TU Darmstadt, Darmstadt, Germany; 2GSI, Darmstadt, Germany; 3IFJ PAN, Krako´w, PolandIntroductionImproved SIS primary beam intensities converts directlyinto higher yields of exotic nuclei. Improvements to theFRS [1] tracking detectors are necessary to allow for higherrates. This concerns in particular the rate at the intermedi-ate focal plane S2 where tracking detectors allowing forrates higher than 106s−1 are needed.In September 2010 a first Finger detector made of 15strips of plastic scintillator, 14 mm wide each, was suc-cessfully commissioned and used [2]. As an upgrade fromthat detector, a new Finger detector was developed consist-ing of 51 strips, 4.4 mm wide, of BC420 plastic scintillator.This detector is used as a test case for further developmentsfor HISPEC/DESPEC at FAIR.SetupEach pair of strips was glued to a bended UV-transparentPMMA light guide using a 2 component silicon glue. Thelight guides were then optically coupled to HamamatsuR9880U-01 photo-multiplier tubes (PMTs) using siliconpads. To power up the PMTs, 13 power supplies were used,each one powering up 4 tubes. Independent potentiometerswere added to the setup to allow independent adjustmentof the voltages. Figure 1 shows the new Finger detectormounted.Figure 1: The new Finger detectorThe PMTs are read-out using the LANDFEE discrimi-nator. This electronics determines the leading and trailingedges of the incoming PMT pulses as time signals. These∗Work partially supported by HIC4FAIR† m.l.cortes@gsi.detwo times are then recorded using two CAEN V1290 Mul-tihit TDCs. Using the two times given by the electronics itis possible to obtain, apart from the time of occurrence, thetime-over-threshold (ToT) of the signal, which provides ameasure of the signal amplitude. TRIPLEX cards [3] areused for the remote control of the thresholds and to obtainan OR signal and an analogue sum of the signals for mon-itoring. One of the TRIPLEX cards is connected with anetwork module which makes the system remote control-lable via Ethernet by a lab-view program.In-beam testThe New Finger detector was tested from Februaryto April 2014 as part of the PreSPEC-AGATA setup atGSI [4]. Time and ToT spectra were obtained for Fe andNi beams with different intensities. The efficiency of thenew Finger detector was in average 2% lower than the oneof the standard scintillator at S2, mainly because of gapsbetween the strips. Figure 2 shows a typical ToT spectrumrecorded in one of the PMTs. Using these spectra it is pos-ToT (arb. units)6 8 10 12 14Counts110210310Finger_FingerToF_ToT026Entries  38885Mean     7.32RMS     0.866Underflow       0Overflow        0Integral  3.888e+04Skewness   3.689ToT026  17:58:27  2014-04-12  Analysis/Histograms/Finger/FingerToF/ToT/Finger_FingerToF_ToT026Figure 2: Time-over-threshold spectrumsible to decide which strip had the higher charge collectionand therefore which was the strip that was hit. Position andtiming information from that strip were used for each eventand a preliminary analysis was performed. Figure 3 showsthe correlation between the strip selected as being hit andthe position determined in TPCs. In spite of the clear cor-relation, background is also present, coming from two dif-ferent sources: The high rate present as S2, which reducesthe performance of the TPCs and the possibility of havingGSI SCIENTIFIC REPORT 2013 NUSTAR-GS-03doi:10.15120/GR-2014-1-NUSTAR-GS-03 117TPC position (mm)-100 -80 -60 -40 -20 0 20 40 60 80 100Finger strip01020304050Finger_XXcorrelationTPC_first_vs_secondEntries  49747Mean x   11.39Mean y   26.51RMS x   46.54RMS y   9.847Integral   4.801e+04Skewness x  -0.1367Skewness y  -0.1014       0       0       0      41   48011     178       0    1517       0first_vs_second  20:53:14  2014-04-11  Analysis/Histograms/Finger/XXcorrelationTPC/Finger_XXcorrelationTPC_first_vs_secondFigure 3: Strip number vs. position projected from TPCstwo particles hitting the Finger detector during the sametrigger, which gives the possibility of a wrong strip selec-tion. To study this effect, the number of PMTs fired perevent was calculated. When all fired PMTs are consecutivethey are considered as coming from a single particle inter-action. When they are not consecutive, a second particlecould have produced the signals. The number of this setsof consecutive PMTs is called cluster multiplicity. Figure 4shows the number of clusters recorded versus the numberof PMTs fired. We can see that for the case of one particleNumber of clusters0 1 2 3 4 5 6 7Number of PMTs fired0246810121416Finger_FingerToF_cluster_multiplicity_vs_MultiplicityEntries  251586Mean x   1.919Mean y   3.781RMS x  0.6496RMS y   1.771Integral   2.516e+05Skewness x  0.9962Skewness y  0.9361       0       0       0       0  251586       0       0       0       0110210310410cluster_multiplicity_vs_Multiplicity  21:03:17  2014-04-11  Analysis/Histograms/Finger/FingerToF/Finger_FingerToF_cluster_multiplicity_vs_MultiplicityFigure 4: Cluster multiplicity vs. PMT multiplicitythe most likely is to have two PMTs fired, correspondingto one strip. The rest of the events can be properly recon-structed with more detailed analysis.Using the timing information given by the strip selected,the Time-of-Flight (ToF) between the new Finger detectorand the scintillator placed in the last focal point of FRS(S4) was calculated. Figure 5 shows the ToF versus theatomic number of the particles obtained from the MUSICionization chambers.ToF (arb. units)154 156 158 160 162 164 166 168Z21.021.522.022.523.023.524.024.5Finger_FingerTofVsZ_first_vs_secondEntries  94158Mean x   163.2Mean y   22.77RMS x   2.167RMS y  0.4292Integral   2.952e+04Skewness x   -1.48Skewness y  -0.7013    7415    6037   16832   13725   29516   18655     444     735     799first_vs_second  17:57:47  2014-04-12  Analysis/Histograms/Finger/FingerTofVsZ/Finger_FingerTofVsZ_first_vs_secondFigure 5: Time of flight vs. atomic numberThis plot presents a preliminary identification plot andcan be further improved by a more detailed analysis whichincludes strip selection, considering multiple particles andproper calibrations.OutlookA new Finger detector with higher count rate capabilitieswas developed and tested. ToT technique to select the stripwas proved to be feasible. The preliminary analysis of thedata obtained during the PreSPEC-AGATA campaign 2014show a reasonable efficiency and the possibility to charac-terize multiple particles hitting the detector. The outcomeof this study will be used to optimize further developmentsfor a Time-of-Flight detector at the Super FRS.References[1] H. Geissel et al. Nucl. Instr. Meth. B70 (1992) 286[2] F. Ameil et al. “Time of flight with a segmented plastic fin-ger detector at high particle rate”, GSI Scientific Report 2011(2012) 171[3] K. Koch et al., “TRIPLEX, an Upgrade for the TACQUILASystem”, GSI Scientific Report 2010 (2011) 235[4] H.J.Wollersheim, “Relativistic Coulomb Excitation: FromRISING to PreSPEC”, Acta Phys. Pol. B42 (2011), 705NUSTAR-GS-03 GSI SCIENTIFIC REPORT 2013118 doi:10.15120/GR-2014-1-NUSTAR-GS-03

Development and test of a segmented Time-of-Flight plastic detector

Jimenez, Paulo A.

Shirinzadeh, Bijan

Nicholson, Ann

Alici, Gursel

Research Online

University of Wollongong Research Online Faculty of Engineering - Papers (Archive) Faculty of Engineering and Information Sciences 1-1-2007 Optimal area covering using genetic algorithms Paulo A. Jimenez Monash University Bijan Shirinzadeh Monash University Ann Nicholson Monash University Gursel Alici University of Wollongong, gursel@uow.edu.au Follow this and additional works at: https://ro.uow.edu.au/engpapers  Part of the Engineering Commons https://ro.uow.edu.au/engpapers/1783 Recommended Citation Jimenez, Paulo A.; Shirinzadeh, Bijan; Nicholson, Ann; and Alici, Gursel: Optimal area covering using genetic algorithms 2007, 1-6. https://ro.uow.edu.au/engpapers/1783 Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: research-pubs@uow.edu.au     Abstract— Path planning problems involve computing or finding a collision free path between two positions. A special kind of path planning is complete coverage path planning, where a robot sweeps all area of free space in an environment. There are different methods to cover the complete area; however, they are not designed to optimize the process. This paper proposes a novel method of complete coverage path planning based on genetic algorithms. In order to check the viability of this approach the optimal path is tested in a virtual environment. The simulation results confirm the feasibility of this method. I. INTRODUCTION  ONVENTIONAL goal-oriented and map-based path planning methods do not address the problem of complete coverage path planning, in which a path is found to ensure that every point in a given workspace is covered at least once. Complete coverage is needed for a variety of commercial and governmental applications such as vacuum cleaners robots, painter robots, landmine detection, mapping, harvesters, and lawn mowers.   In general, there are two ways of covering an area: exhaustive and random coverage. Exhaustive coverage is best used when the robot’s niche is limited (indoors); because of time and power restrictions, it is not suitable for covering large environments completely. Random coverage, on the other hand, does not guarantee complete coverage, but it does not necessarily require costly localization sensors or computational power.  II. RELATED WORK  Various approaches to complete coverage path planning have been developed, e.g. Artificial Potential Field (APF), cellular decomposition, template based, sensor-based, neural networks and fuzzy logic. APF, for instance,  Manuscript received January 15, 2007. This work was supported by an Australian Research Council (ARC) Linkage grant.  Paulo A. Jimenez is with Robotics And Mechatronics Research Laboratory, Department of Mechanical Engineering, Monash University, Clayton, VIC 3800, Australia  Bijan Shirinzadeh is with Robotics And Mechatronics Research Laboratory, Department of Mechanical Engineering, Monash University, Clayton, VIC 3800, Australia. Ann Nicholson is with Information Technology, Monash University, Clayton, VIC 3800, Australia  Gursel Alici is with School of Mechanical, Materials, and Mechatronic Engineering, University of Wollongong determines the positions to which the robot should move by controlling the forces that move the robot. Ratering and Gini [1] navigate in a known environment using a hybrid APF that combines two different types of APF. Hussein and Elnagar [2] propose the use of Maxwell’s equation to eliminate local minima problem in APF. The concept behind cellular decomposition is to decompose the environment into a number of non-overlapping cells. Wong and MacDonald approach [3] uses natural landmarks in the environment to construct subregions. Choset [4] uses Boustrophedon, back and forth ox-like motions, to cover cells. Using a template based method, the complete trajectory is planned as a sequence of pre-defined trajectories or templates. The template based method introduced by Caravalho et al. [5] is able to deal with newly appearing obstacles. Slack’s planner [6], which combines APF and Template Based approaches, responds to changes in the environment. Sensory based approaches use incoming sensory data to search a path that passes through all parts. Acar and Choset’s method [7] finds and cover all critical points in an unknown map, thus covering the whole area. Lui et al. [8] provide sensor information to motion templates; then the robot uses random search to cover the area. Neural Network approach uses biologically inspired networks to produce path for total coverage; Luo et al. [9] were able to build a local map dynamically and avoid obstacles. Probabilistic methods utilises a probability density map to sweep an area passing over most of the critical points (e.g. landmines). Acar’s robot [10] recovered landmines in an unstructured indoor environment, where the robot has a probability map of the landmines. Although, these methods cover the complete area, they are not designed to optimize the process.  In this paper, a genetic optimization is proposed for an area covering problem for a relatively structured environment (office building or factories). The  environment is divided in sub-regions as in cellular decomposition method [11]. Then a path for each region is created. Since finding a solution for several sub-regions is time consuming and computationally costly, a genetic optimization algorithm is used to provide the most efficient coverage path planning.   Optimal Area Covering using Genetic Algorithms Paulo A. Jimenez, Bijan Shirinzadeh, Ann Nicholson and Gursel Alici C 1-4244-1264-1/07/$25.00 ©2007 IEEE  III. PROPOSED ALGORITHM  Consider a planar region R, which describes an indoor environment, populated with polygonal obstacles. In general, R may be divided into a series of polygonal sub-regions hole-free as shown in Figure 1. The idea behind this decomposition is to discriminate between geometric areas, or cells that are free and areas that are occupied by objects.   Figure 1: Horizontal decomposition  Using Horizontal decomposition it is possible to obtain a global undirected graph (Figure 2) }{ LSG ,=  where S and L represent the sub-regions, and connections respectively.   Figure 2: Graph of the Global region.  The Decomposition Algorithm performs two main operations: it divides R into simple, connected sub-regions S; and it determines which clear cells are adjacent and constructs a Global Graph.  Each sub-region can be represented as a completed weighted graph { }WLVS ,,=    where: { }( )3,...,, 21 ≥= nvvvV n  is the vertex set { }VvveE jiij ∈= ,|  is the edge set { })(,,00| nNjiwwwW iiijij ∈∀=∧>=  is the cost set iv  is the ith vertex ije  is the edge connecting the vertices vi and vj ijw  is the cost corresponding to edge eij )(nN  is the subset { }n,...,2,1 of the natural number set  Testing every possibility for N nodes in a solution would be N! which is time and resource consuming. Hence, a genetic algorithm will be employed to optimize the process.  A. Genetic Path Planner Genetic Algorithms (GA) utilize an interactive approach, inspired by evolution via natural selection, to solve optimization problems. In a GA, the solutions (genome or chromosome) are initialized randomly. These populations are evaluated based on fitness functions; higher fitness values will have more chance of passing to following generations [12]. In order to maintain a constant number of chromosomes, new populations of candidate solutions replace existing chromosomes; they are generated by applying operators inspired by biologic genetic variation. The most popular operators are selection, crossover (also called recombination), and mutation. The strength of GA lies in their ability to implicitly identify the favorable proprieties associated with potential solutions. The genetic process is shown in Figure 3. To illustrate this more concretely, the processes applied to the area covering problem is described as follows.  1-4244-1264-1/07/$25.00 ©2007 IEEE   Figure 3: Genetic Process  1) Encoding: One of the first decisions to be made before building a GA is the selection of the encoding scheme. Encoding the chromosome cannot be simply the list of nodes in the order visited; therefore, more complex encoding methods are required.   In this study, the genome is made of two parts: head and body. The head contains the order of the sub-regions as well as starting and finishing points. The body holds the solution for each sub-region; each solution is represented by the link between two nodes. The genome or Chromosome is shown in Figure 4.   Figure 4: Chromosome Encoding  2) Generation of initial solutions: Firstly a random order is given to each sub-region; the only rule here is to choose a neighboring area if possible. As a result, random chromosomes are generated for each region based on two common templates, zigzag and windowing. Variations in directions provide a diversity of templates (Figure 5). In this case, solutions have to pass over all of the nodes of the graph.   Figure 5: Motion Templates  3) Fitness Function: The evaluation function serves as the major link between the problem and the algorithm. The fitness function rates individuals in the population: the fitter the individuals, the better their chances of survival and reproduction. Two parameters are reasonable to evaluate the fitness of individual chromosomes: total distance traveled and time. The time varies according to number of turns as shown in [13, 14]. An appropriate fitness function is constructed as:  ∑∑ += timewdistwF timedisti ,   where wdist and wtime represent (%) weighs for distance and time respectively, in this study time was converted to distance in order to add these physical values.  4) Genetic operators: Two different genetic operators were developed to improve the fitness. Crossover and Mutation are related to the corresponding strategies of evolution and adapted for similar operations.  Crossover is the processes of exchanging information between chromosomes by mixing attributes. For simplicity, a random crossover point is adopted here. Any crossover offspring must meet the following requisites. The first node is always at starting location. Each node must be covered at least once. To reduce time and distance each node should be cover only once, however it is possible to find some solutions where it is necessary to pass through nodes already covered. 1-4244-1264-1/07/$25.00 ©2007 IEEE   Mutation is any change in the chromosome; its principal objective is to introduce variation into the population. For the purposes of this algorithm, mutation is based on a random operation. Two nodes are randomly selected from the population, then swapped; in this way the solution will be valid. IV. SIMULATION RESULTS  The goal was to generate a feasible moving path, which is required to start from the origin and cover the area. Firstly, the algorithm divided the area into sub-regions. Next, a large number of possible solutions were provided using directional variations in two moment templates, zigzag and windowing. The optimization criteria were length and time, where time is depends on the number of turns. These criteria were evaluated and an optimal solution obtained. The path provided by the genetic planner is shown in Figure 6.   Figure 6: Optimal Area Covering Path  This method has two programs: the first one is a genetic path planner which produces a series of nodes (path) for the robot to cover an area. The other is a virtual environment where the robot follows the path generated by the path planner. The simulation allows to verify the robots trajectory according to the genetic path planner. Thus, the robot performance can be seen whenever it encounters a known obstacle. However if an unexpected obstacle comes across, the robot finds its way back and process to the next node. The virtual environment is composed of boxes and robots. The virtual robot possessed IR sensors to avoid collision.  Figure 7 show the robot moving around the room. In addition to IR sensors, the virtual robot has contact sensors for narrow paths. Whenever the robot could not reach a node, it found its way back and proceeded to the next node.   Figure 7: Robot Simulation  V. CONCLUSION  A novel solution for the optimal covering problem, based on a genetic algorithm has been successfully developed here. By means of cellular decomposition the whole region was divided into sub-areas, which subsequently were split into nodes. Subsequently, a genetic algorithm found the best path for the robot to follow combining two templates. The best solution is based on the minimum value of the fitness function. Simulation results showed the feasibility of the proposed planner. In addition, the genetic operations such as crossover and mutation could be applied to similar optimization problems. ACKNOWLEDGMENT  The authors wish to thank Murray Mc Donald and FloorBotics International for their input and support. REFERENCES  [1] S. Ratering and M. Gini, "Robot Navigation in a Known Environment with Unknown Moving Obstacles," Autonomous Robots 1(2), 149-165 (1995) [2] A. M. Hussein and A. Elnagar, "Motion planning using Maxwell's equations," in IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2347- 2352, Lausanne, Switzerland (2002). [3] S. C. Wong and B. A. MacDonald, "A topological coverage algorithm for mobile robots," in IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1685-1690, Las Vegas. Nevada (2003). [4] H. Choset, "Coverage of Known Spaces: The Boustrophedon Cellular Decomposition," Autonomous Robots 9(3), 247-253 (2000) [5] R. N. De Carvalho, H. A. Vidal, P. Vieira and M. I. Ribeiro, "Complete coverage path planning and guidance for cleaning 1-4244-1264-1/07/$25.00 ©2007 IEEE  robots," in IEEE International Symposium on Industrial Electronics, pp. 677-682, Guimaraes, Portugal (1997). [6] M. G. Slack, "Navigation templates: mediating qualitative guidance andquantitative control in mobile robots," IEEE Transactions on Systems, Man and Cybernetics 23(2), 452-466 (1993) [7] E. U. Acar and H. Choset, "Critical point sensing in unknown environments," in IEEE International Conference on Robotics and Automation, , pp. 3803-3810, San Francisco, CA, USA (2000). [8] Y. Liu, S. Zhu, B. Jin, S. Feng and H. Gong, "Sensory navigation of autonomous cleaning robots," in World Congress on Intelligent Control and Automation, pp. 4793-4796, Hangzhou, P.R. China (2004). [9] C. Luo, S. X. Yang and M. Q.-H. Meng, "Real-time Map Building and Area Coverage in Unknown Environments," in IEEE International Conference on Robotics and Automation, pp. 1736-1741, Barcelona, Spain (2005). [10] E. U. Acar, H. Choset, Y. Zhang and M. Schervish, "Path Planning for Robotic Demining: Robust Sensor-based Coverage of Unstructured Environments and Probabilistic Methods," The International Journal of Robotics Research 22(7), 441-466 (2003) [11] S. Thrun, "Learning metric-topological maps for indoor mobile robot navigation," Artificial Intelligence 99(1), 21-71 (1998) [12] R. C. Eberhart and Y. Shi, "Comparison between Genetic Algorithms and Particle Swarm Optimization," in International Conference on Evolutionary Programming VII, pp. 611-616 (1998). [13] E. M. Arkin, M. A. Bender, E. D. Demaine, S. P. Fekete, J. S. B. Mitchell and S. Sethia, "Optimal Covering Tours with Turn Costs," Society for Industrial and Applied Mathematics 35(3), 531–566 (2005) [14] W. Sheng, H. Chen, N. Xi and Y. Chen, "Tool path planning for compound surfaces in spray forming processes," IEEE Transactions on Automation Science and Engineering 2(3), 240-249 (2005) 1-4244-1264-1/07/$25.00 ©2007 IEEE

English

http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2828&context=engpapers

Development and test of a segmented Time-of-Flight plastic detector

Abstract

Similar works

Full text

Available Versions

Crossref

GSI Repository

Research Online