A Simulation Analysis of Formations for Flying Multirobot Systems


 Avice Emma Bruce
 3 years ago
 Views:
Transcription
1 A Simulation Analysis of Formations for Flying Multirobot Systems Francesco AMIGONI, Mauro Stefano GIANI, Sergio NAPOLITANO Dipartimento di Elettronica e Informazione, Politecnico di Milano Piazza Leonardo da Vinci 32, Milano, Italy Abstract. The ability of flying robots to navigate in a stable formation is the basis for a large number of applications, ranging from exploration to surveillance and rescue. However, the performances of 3D robot formations have not been extensively studied in literature. In this paper we present the results of a simulation study evaluating the adaptability of different flying robot formations to different kinds of environments. 1 Introduction Flying multirobot systems can effectively address several applications, including exploration, data acquisition, surveillance, rescue, inspection, and military operations [8]. In all these applications, the basic skill required to multirobot systems is the ability to flying while maintaining a stable formation, intended as the spatial arrangement of the robots in a given form [1, 9]. In this paper we present a simulation study evaluating the adaptability of different flying robot formations to different typologies of environments. This adaptability analysis, that constitutes the main original contribution of this paper, measures how well a formation behaves in an environment by referring to the average position error of the robots in the formation. Although several research projects are being pursued in this field, a systematic comparative study of the adaptability of 3D formations to environments is lacking in the current literature: this paper constitutes a first preliminary step in this direction. We run different sessions with a software tool we developed that simulates the flying robots, the environments, and their interaction and that allows for a detailed analysis of recorded data. Note that simulation is a valuable instrument in this case, since experiments with real flying robots are usually difficult and expensive to set up. This paper is organized as follows. The next section theoretically introduces the formations we considered. Section 3 presents the simulation setting used to produce the experimental evidence largely discussed in Section 4. Finally, Section 5 concludes the paper. 2 Formations for Flying Multirobot Systems The mathematical descriptions of the formations refer to the spatial relative position of a robot with respect to another robot given in spherical coordinates, namely horizontal (α i ) and vertical (β i ) angles and distance (ρ i ), as shown in Fig. 1. Each robot is uniquely identified by a number i, N is the total number of robots in the formation; ρ is the desired distance between two neighboring robots. All the formations we consider are
2 composed of a leader and of a number of followers. The relationships between the positions of the robots (the socalled control graph [2, 4, 5] or chain of friendship [6]) depend from the adopted control technique. According to [1], three main control techniques can be identified: neighborreferenced, leaderreferenced, and unitcenterreferenced. In this paper we mainly consider the widely used neighborreferenced technique, where each robot (except the leader) maintains its position with respect to the robot next to it. The formations of interest in this paper follow. Figure 1: The α i and β i angles and the distance ρ i between two robots Line (Fig. 2(a)). This is a 3D extension of a classical 2D formation (usually employed for mobile robots navigating on a surface) where β i = 0 i N/2 + 1 and, with neighborreferenced control technique, 0 if i N/2 α i = π if i > N/ The robot i follows the robot i+1 if i N/2 or follows the robot i 1 if i > N/2 +1. The leader is the robot i = N/ Column (Fig. 2(b)). This is a 3D extension of a typical 2D formation where β i = 0 i 1 and (with the neighborreferenced control technique) α i = π i 1. The robot 2 i follows the robot i 1. The leader is the robot i = 1. Wedge (or Arrowhead) (Fig. 2(c)). This is a 3D extension of another typical 2D formation, thus β i = 0 i N/2 + 1 and, with the neighborreferenced control technique, α i = π if i N/2 4 3π 4 if i > N/2 + 1 As in the Line, the robot i follows the robot i + 1 if i N/2 or follows the robot i 1 if i > N/ The 2D versions of the above formations (Line, Column, and Wedge) are used in [6] (and in [3, 10] for the Line) with neighborreferenced control technique. Snake (Fig. 2(d)). This is a formation possible only in 3D that generalizes the Column. α i and β i are not defined i 1. In the neighborreferenced control technique, the robot i follows the robot i 1. The leader is the robot i = 1. The neighborreferenced version of this formation extends the 2D convoy and chain (see, for example, [3]).
3 Star (Fig. 2(e)). It is a 3D extension of a 2D formation and does not exist in neighborreferenced version. Thus, we employ the leaderreferenced version in which each robot maintains its position with respect to that of the leader. β i = 0 and α i is not defined. All robots follow the leader, which is the robot 1. Sphere (Fig. 2(f)). It is an exclusively 3D formation that generalizes the Star formation and that, therefore, we consider in the leaderreferenced version. β i and α i are not defined. All robots follow the leader, which is the robot 1. These last two formations are firstly introduced in this paper as an original contribution. We stress that they require the leaderreferenced control technique. Figure 2: Flying robots formations (with N = 5) 3 Simulation Setting Simulator Overview. The simulator we developed (see Fig. 3) manages 3D world models with a set of obstacles (see The Environments below) and a number of flying robots. The simulator engine detects collisions between objects (robots and obstacles) and performs the moving and sensing activities of the robots. For each robot, the simulator provides a control interface via a tcp/ip socket that an external application (see Robot Controllers below) uses to determine the movements of the robot in the environment on the basis of the data acquired from the simulated sensors of the robot. We consider very simple proximity sensors placed in a starlike configuration to detect obstacles around the robot; the simulator allows also to define other types of sensors. The robots (actually, they controllers) communicate, for example to exchange their positions, by means of a radiolink channel managed by a socketbased component of the simulator. The simulator shows the evolution of the situation as a vrml model and generates some log files that record robot positions and other parameters (see Controllable and Measurable Parameters below) for subsequent analysis. All the software has been coded in c++. The Environments. The simulator allows to define structured environments composed of a plane (the ground) and of some regular solids (the obstacles). The size and the position of the obstacles are chosen during the initial definition of the environment. These environments are intended to be rough models of open areas with buildings. We study the adaptability of robot formations to the following four types of environments:
4 ENIVRONMENTS VRML SIMULATION DATA ANALYSIS ROBOTS, SENSORS SIMULATOR ENGINE SIMULATOR ROBOT CONTROLLERS Figure 3: The architecture of the simulator (a) the empty environment, (b) an environment with a large low obstacle, (c) an environment with a large high obstacle, and (d) an environment with many scattered obstacles (see Fig. 4). These environments represent particularly meaningful applicative scenarios for flying robots. In (a), we evaluate the effectiveness of robots control techniques and to provide a term of comparison with the other scenarios. In (b) and (c), we evaluate the basic obstacle avoidance properties of the formations. Finally, in (d), we evaluate the robustness of formations in presence of several irregular obstacles. Figure 4: An environment with many scattered obstacles (left) and a detail of a formation navigating in it (right) Controllable and Measurable Parameters. The controllable parameters regulate the behavior of the single robot in the formation (and, indirectly, of the team). The observable parameters evaluate the behavior of the robots in the formation. The only controllable parameter in our simulator is the robot position with respect to a given reference point. This reference point can be the position of the neighbor or of the leader (as discussed in the previous section). Each robot can control separately α i, β i, and ρ i, thus enabling a very simple holonomic control of robots. The robots move with constant velocity; a possible improvement could be the control of velocity and acceleration too. The main observable parameter we used is the average position error of a robot: the average (over the simulation steps) distance between the real position and the nominal position of the robot in the formation. The average position error expressed in spherical coordinates can be divided in the three components α, β, and ρ. The same observable parameter (calculated at every single time instant and not averaged) is also used in [2, 5] (in spherical coordinates, as in our case) and in [4, 7, 9] (in cartesian coordinates x, y, and, when applicable, z). The analysis, moreover, can be conducted with respect to a single robot or to the collective behavior of the formation (considering a second average over the robots); in the latter case, the parameter is still called average position error [1]. Robot Controllers. The robot controllers (Fig. 5 left) refer to an abstract model of holonomic flying robots (see above). This is a strong assumption since it does not
5 take into account the technological limitation of the real flying robots (e.g., aerostat, helicopter, flappingwings, or their combinations); however, it allows to preliminary explore the performance of the formations. A robot controller operates according to the following cycle: acquire the current position of the robot (from the simulator), communicate this position to the other robots, update the known positions of the other robots, acquire the sensor readings (from the simulator), determine the new position, communicate the new position to the simulator engine that performs collision checking. In the case of the leader of the formation, the new position accounts for navigation toward the goal and for obstacle avoidance. In the case of the followers, it accounts for obstacle avoidance and for flight in formation (respecting the positions to be maintained, calculated according to the formulas of Section 2). The overall formation behavior emerges from the behaviors of the single robots. Figure 5: The robot controller interfaces (left) and the results of a simulation (right) 4 Experimental Results In this section, we present some preliminary experimental results that shed some light on the relation between formations and environments. The experimental scenarios we considered consist in a formation composed of 5 flying robots that moves along the Y axis from a start point to a target point. The robots start in formation. The size of the environment is 400 (X), 600 (Y), 100 (Z), with respect to a generic measure unit. The formations we evaluated are those illustrated in Section 2. For each experimental scenario we report the average position errors (introduced in Section 3) calculated averaging the position error over the simulation steps (Fig. 5 right shows this error relative to β angle for Line). The computation time of a simulation of a formation flight in an environment is of the order of some seconds. The Empty Environment. Table 1 summarizes some of the obtained results. The distances are signed values; a negative distance means that two robots are closer than prescribed by the formation. The average position errors are calculated over all the simulation steps needed to reach the target point (ranging from 267 in the case of Column to 783 in the case of Snake). The (always positive) values reported in the last row are calculated by averaging the absolute values of the followers. In the
6 Robot Line (L) Column (C) Wedge (W) Snake (Sn) Star (St) Avg Table 1: The average position errors relative to the distance in the empty environment Line, the robots substantially respects they nominal positions. The control of the α angle (the results are not reported here) is a little bit problematic, since it induces some latency for the followers. This is particularly emphasized in the Wedge, where the latency in adjusting the α angle generates a waterfall of corrections that are not parallel to the main flying direction. As expected, Column and Snake do not suffer from the above problem but, instead, they show the whipping effect. Since the leader has no feedback from following robots and all the robots navigate at the same velocity, sometimes it keeps moving without considering the difficulties of the followers that can loose contacts. The whipping effect is more evident in the robot that immediately follows the leader, while it is attenuated in tail of the formation. Star has an acceptable behavior since the control parameters are less constrained. However, in the Star a robot that went out from the formation has problems in reentering it, because other robots obstacle the maneuver by their mere presence. An Environment with a Large Low Obstacle. In this experimental scenario, we put a single large low obstacle with dimension (100, 100, 30) in the empty environment to evaluate the obstacle avoidance behavior of the formations when the obstacle can be jumped (see Table 2; simulation steps range from 674 for the Line to 775 for the Snake). The Line behaves good but it still shows some latency in the followers. At the beginning and at the end of the jump some irregularities in the Line alignment appear (see In the Wedge the effort to control the α angle negatively influences the distance keeping. An interesting entangling effect shows up in this case: when the leader dives after jumping the obstacle and the followers are still over the obstacle, there are difficulties in maintaining the correct β angle, especially for the robot that immediately follows the leader. This entangling effect significatively influences also the Column (a long formation along the navigation direction), but not the Snake, since it relaxes the β angle control. However, the Snake suffers from a sort of intersection effect. This problem emerges when the (imaginary) segment that joins the position of a robot with that of its preceding reference intersects the obstacle; the robot, therefore, cannot follow directly the reference since it has to avoid the obstacle, with obvious loss of control efficiency. Finally, the Star and Sphere behave quite well: their great flexibility constitutes an advantage in this case. An Environment with a Large High Obstacle. In this experimental scenario, we put a single large high obstacle with dimension (100, 100, 90) in the empty environment to evaluate the obstacle avoidance behavior of the formations when the obstacle can be encircled (see Table 3; simulation steps range from 649 for the Snake to 1019 for the Line and the Wedge). The Line shows a sort of wall effect: since the formation distribution is perpendicular to the flight direction, the leader passes very close to the left side of the obstacle causing control problems to the right part of formation (robots 4 and 5). Robot 4 has serious problems in keeping the distance and the α angle
7 Robot L C W Sn St Sphere (Sp) Avg L C W L C W St Table 2: The average position errors relative to the distance (left), α angle (center), and β angle (right) in an environment with a large low obstacle Robot L C W Sn St Sp Avg L C W Table 3: The average position errors relative to the distance (left) and α angle (right) in an environment with a large high obstacle but avoids the obstacle to the left side; robot 5 avoids the obstacle to the right side breaking the formation. The Wedge improves the control of the α angle but it is worse in distance control: both robot 4 and robot 5 avoid the obstacle from the right side breaking the formation (see For the Column, an horizontal entangling effect disturbs the control of α angle (see In Snake, the intersection and whipping effects are present. However, when we exclude robot 2 from the analysis, the Snake outperforms the Column. We note that the intersection effect is often emphasized by the whipping effect, but this point (and, more generally, the relationships among the effects we identified) deserves more attention. Finally, note that some of the effects could be reduced by changing the formation of the team during navigation. An Environment with Many Scattered Obstacles. In this experimental scenario, formations basically behave as in the previous ones by jumping and encircling the obstacles, but other interesting situations emerged (see Table 4; simulation steps range from 699 for the Snake to 1024 for the Line). For the Column, there is an interesting blade effect by which an obstacle cuts the formation after the leader. It happens when the leader surpasses the obstacle and continues toward the target and the followers (trying to control the β angle) stay in a stall position (see The blade effect can be both horizontal and vertical. In the Snake, the whipping effect is attenuated since the horizontal translation of the leader is often reduced while encircling or jumping obstacles and the followers can easily maintain the formation. Moreover, the blade effect does not affect the Snake (see /formations/mosnake.avi). In conclusion, the Snake, according to the adopted observable parameter, appears to be the most suitable formation for environments with several scattered obstacles. This also shows that, in general, the 2D formations could not be directly employed for effective 3D flying robots without relaxing some constraints, such as those on α and β angles.
8 Robot L C W Sn St Sp Avg L C W L C W St Table 4: The average position errors relative to the distance (left), α angle (center), and β angle (right) in an environment with many scattered obstacles 5 Conclusions The (preliminary) results of the simulation study presented in this paper show several effects that can influence the adoption of a formation in a given environment. However, the task often imposes the formation to be adopted; for example, the Sphere is used when there is a strong need to protect the leader in the center. Future work will be devoted to extend the experimental analysis by including other formations proposed in literature (such as diamond, rectangle, triangle, circle, and arc), other control techniques (leaderreferenced and unitcenterreferenced), and more controllable and measurable parameters. References [1] T. Balch and R.C. Arkin. Behaviorbased formation control for multirobot teams. IEEE Transactions on Robotics and Automation, 14(6): , [2] A. Das, R. Fierro, V. Kumar, J. Ostrowski, J. Spletzer, and C. Taylor. A visionbased formation control framework. IEEE Transactions on Robotics and Automation, 18(5): , [3] G. Dudek, M. Jenkin, E. Milios, and D. Wilkes. Experiments in sensing and communication for robot convoy navigation. In Proc. IEEE/RSJ Conf. on Intelligent Robots and Systems, volume 2, pages , [4] R. Fierro, C. Belta, J. Desai, and V. Kumar. On controlling aircraft formations. In Proc. IEEE Conf. on Decision and Control, volume 2, pages , [5] R. Fierro, A. Das, V. Kumar, and J. Ostrowski. Hybrid control of formation of robots. In Proc. IEEE Conf. on Robotics and Automation, pages , [6] J. Fredslund and M. Mataric. A general algorithm for robot formations using local sensing and minimal communication. IEEE Transactions on Robotics and Automation, 18(5): , [7] J.K. Hall and M. Pachter. Formation manuevers in three dimensions. In Proc. IEEE Conf. on Decision and Control, volume 1, pages , [8] M. Tambe. Towards flexible teamwork. Journal of Artificial Intelligence Research, 7:83 124, [9] P.K.C. Wang. Navigation strategies for multiple autonomous robots moving in formation. Journal of Robotics Systems, 8(2): , [10] E. Yoshida, T. Arai, J. Ota, and T. Miki. Effect of grouping in local communication system of multiple mobile robots. In Proc. IEEE/RSJ Conf. on Intelligent Robots and Systems, volume 2, pages , 1994.
On evaluating performance of exploration strategies for an autonomous mobile robot
On evaluating performance of exploration strategies for an autonomous mobile robot Nicola Basilico and Francesco Amigoni Abstract The performance of an autonomous mobile robot in mapping an unknown environment
More informationRobotic Sensor Networks: An Application to Monitoring ElectroMagnetic Fields 1
Robotic Sensor Networks: An Application to Monitoring ElectroMagnetic Fields 1 Francesco AMIGONI a,2, Giulio FONTANA a and Stefano MAZZUCA a a Dipartimento di Elettronica e Informazione, Politecnico di
More informationCHAPTER 1 INTRODUCTION
CHAPTER 1 INTRODUCTION 1.1 Background of the Research Agile and precise maneuverability of helicopters makes them useful for many critical tasks ranging from rescue and law enforcement task to inspection
More informationDistributed Sensing for Cooperative Robotics
Distributed Sensing for Cooperative Robotics Guilherme Augusto Silva Pereira Advisor: Prof. Mário Fernando Montenegro Campos VERLab Vision and Robotics Laboratory/UFMG CoAdvisor: Prof. Vijay Kumar GRASP
More informationOnboard electronics of UAVs
AARMS Vol. 5, No. 2 (2006) 237 243 TECHNOLOGY Onboard electronics of UAVs ANTAL TURÓCZI, IMRE MAKKAY Department of Electronic Warfare, Miklós Zrínyi National Defence University, Budapest, Hungary Recent
More informationDecentralized motion planning for multiple robots subject to sensing and communication constraints
University of Pennsylvania ScholarlyCommons Departmental Papers (MEAM) Department of Mechanical Engineering & Applied Mechanics March Decentralized motion planning for multiple robots subject to sensing
More informationIN this work we have studied the problem of achieving
1 A General Algorithm for Robot Formations Using Local Sensing and Minimal Communication Jakob Fredslund, Maja J Matarić Abstract We study the problem of achieving global behavior in a group of distributed
More informationMultiRobot Tracking of a Moving Object Using Directional Sensors
MultiRobot Tracking of a Moving Object Using Directional Sensors Manuel Mazo Jr., Alberto Speranzon, Karl H. Johansson Dept. of Signals, Sensors & Systems Royal Institute of Technology SE 44 Stockholm,
More informationInteractive Motion Simulators
motionsimulator motionsimulator About the Company Since its founding in 2003, the company Buck Engineering & Consulting GmbH (BEC), with registered offices in Reutlingen (Germany) has undergone a continuous
More informationLab # 3  Angular Kinematics
Purpose: Lab # 3  Angular Kinematics The objective of this lab is to understand the relationship between segment angles and joint angles. Upon completion of this lab you will: Understand and know how
More informationPath Tracking for a Miniature Robot
Path Tracking for a Miniature Robot By Martin Lundgren Excerpt from Master s thesis 003 Supervisor: Thomas Hellström Department of Computing Science Umeå University Sweden 1 Path Tracking Path tracking
More informationForce/position control of a robotic system for transcranial magnetic stimulation
Force/position control of a robotic system for transcranial magnetic stimulation W.N. Wan Zakaria School of Mechanical and System Engineering Newcastle University Abstract To develop a force control scheme
More informationMathematics on the Soccer Field
Mathematics on the Soccer Field Katie Purdy Abstract: This paper takes the everyday activity of soccer and uncovers the mathematics that can be used to help optimize goal scoring. The four situations that
More informationOntological Communication for Improved Command and Cooperation Of Heterogeneous Mobile Robots Systems
Faculty of Automation and Computer Science Eng. LUCIA VĂCARIU PhD THESIS Ontological Communication for Improved Command and Cooperation Of Heterogeneous Mobile Robots Systems ABSTRACT Thesis advisor: Prof.
More informationProcedure In each case, draw and extend the given series to the fifth generation, then complete the following tasks:
Math IV Nonlinear Algebra 1.2 Growth & Decay Investigation 1.2 B: Nonlinear Growth Introduction The previous investigation introduced you to a pattern of nonlinear growth, as found in the areas of a series
More informationAdaptation of the ACO heuristic for sequencing learning activities
Adaptation of the ACO heuristic for sequencing learning activities Sergio Gutiérrez 1, Grégory Valigiani 2, Pierre Collet 2 and Carlos Delgado Kloos 1 1 University Carlos III of Madrid (Spain) 2 Université
More informationDEVELOPMENT OF HELICOPTER SAFETY DEVICES
25 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES DEVELOPMENT OF HELICOPTER SAFETY DEVICES Wayne Lam, Cees Bil *RMIT University Keywords: helicopter, crash, simulation, MADYMO Abstract Recent investigations
More informationJava simulator for an autonomous mobile robot operating in the presence of sensor faults
Adam Srebro 1 Java simulator for an autonomous mobile robot operating in the presence of sensor faults Abstract This paper presents a twodimensional mobile robot simulator written in Java. This robot
More informationBENEFIT OF DYNAMIC USE CASES TO EARLY DESIGN A DRIVING ASSISTANCE SYSTEM FOR PEDESTRIAN/TRUCK COLLISION AVOIDANCE
BENEFIT OF DYNAMIC USE CASES TO EARLY DESIGN A DRIVING ASSISTANCE SYSTEM FOR PEDESTRIAN/TRUCK COLLISION AVOIDANCE Hélène Tattegrain, Arnaud Bonnard, Benoit Mathern, LESCOT, INRETS France Paper Number 090489
More informationRobot Manipulators. Position, Orientation and Coordinate Transformations. Fig. 1: Programmable Universal Manipulator Arm (PUMA)
Robot Manipulators Position, Orientation and Coordinate Transformations Fig. 1: Programmable Universal Manipulator Arm (PUMA) A robot manipulator is an electronically controlled mechanism, consisting of
More informationSection 1.1. Introduction to R n
The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to
More informationIntelligent Submersible ManipulatorRobot, Design, Modeling, Simulation and Motion Optimization for Maritime Robotic Research
20th International Congress on Modelling and Simulation, Adelaide, Australia, 1 6 December 2013 www.mssanz.org.au/modsim2013 Intelligent Submersible ManipulatorRobot, Design, Modeling, Simulation and
More informationINJECTION MOLDING COOLING TIME REDUCTION AND THERMAL STRESS ANALYSIS
INJECTION MOLDING COOLING TIME REDUCTION AND THERMAL STRESS ANALYSIS Tom Kimerling University of Massachusetts, Amherst MIE 605 Finite Element Analysis Spring 2002 ABSTRACT A FEA transient thermal structural
More informationCurriculum Vitae et Studiorum
Curriculum Vitae et Studiorum Alberto Quattrini Li March 21, 2015 Contents Personal Data 1 Position and Education 1 Education................................................ 1 Academic Positions and Affiliations..................................
More informationREAL TIME TRAFFIC LIGHT CONTROL USING IMAGE PROCESSING
REAL TIME TRAFFIC LIGHT CONTROL USING IMAGE PROCESSING Ms.PALLAVI CHOUDEKAR Ajay Kumar Garg Engineering College, Department of electrical and electronics Ms.SAYANTI BANERJEE Ajay Kumar Garg Engineering
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationwith functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationDevelopment of a Flexible and Agile Multirobot Manufacturing System
Development of a Flexible and Agile Multirobot Manufacturing System Satoshi Hoshino Hiroya Seki Yuji Naka Tokyo Institute of Technology, Yokohama, Kanagawa 226853, JAPAN (Email: hosino@pse.res.titech.ac.jp)
More informationVRSPATIAL: DESIGNING SPATIAL MECHANISMS USING VIRTUAL REALITY
Proceedings of DETC 02 ASME 2002 Design Technical Conferences and Computers and Information in Conference Montreal, Canada, September 29October 2, 2002 DETC2002/ MECH34377 VRSPATIAL: DESIGNING SPATIAL
More informationPrentice Hall Mathematics Courses 13 Common Core Edition 2013
A Correlation of Prentice Hall Mathematics Courses 13 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates
More informationLecture L6  Intrinsic Coordinates
S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0 Lecture L6  Intrinsic Coordinates In lecture L4, we introduced the position, velocity and acceleration vectors and referred them to a fixed
More informationArtificial Intelligence and Robotics @ Politecnico di Milano. Presented by Matteo Matteucci
1 Artificial Intelligence and Robotics @ Politecnico di Milano Presented by Matteo Matteucci What is Artificial Intelligence «The field of theory & development of computer systems able to perform tasks
More informationSynthesizing Adaptive Navigational Robot Behaviours Using a Hybrid Fuzzy A* Approach
Synthesizing Adaptive Navigational Robot Behaviours Using a Hybrid Fuzzy A* Approach Antony P. Gerdelan 1 and Napoleon H. Reyes, Ph.D. 2 1 Computer Science, Institute of Information and Mathematical Sciences,
More informationFRANCESCO BELLOCCHIO S CURRICULUM VITAE ET STUDIORUM
FRANCESCO BELLOCCHIO S CURRICULUM VITAE ET STUDIORUM April 2011 Index Personal details and education 1 Research activities 2 Teaching and tutorial activities 3 Conference organization and review activities
More informationM2M for Telecommunications Companies. Strategy Dimensions for Entering the M2M Market
M2M for Telecommunications Companies Strategy Dimensions for Entering the M2M Market 62 Detecon Management Report blue 1 / 2015 Telecommunications companies find themselves facing the threat of stagnating
More informationNavigation of Mobile Robots Using Potential Fields and Computational Intelligence Means
Acta Polytechnica Hungarica Vol. 4, No. 1, 007 Navigation of Mobile Robots Using Potential Fields and Computational Intelligence Means Ján Vaščák Centre for Intelligent Technologies, Department of Cybernetics
More informationMathematics Common Core Cluster. Mathematics Common Core Standard. Domain
Mathematics Common Core Domain Mathematics Common Core Cluster Mathematics Common Core Standard Number System Know that there are numbers that are not rational, and approximate them by rational numbers.
More informationMathematics 1. Lecture 5. Pattarawit Polpinit
Mathematics 1 Lecture 5 Pattarawit Polpinit Lecture Objective At the end of the lesson, the student is expected to be able to: familiarize with the use of Cartesian Coordinate System. determine the distance
More informationExmoR A Testing Tool for Control Algorithms on Mobile Robots
ExmoR A Testing Tool for Control Algorithms on Mobile Robots F. Lehmann, M. Ritzschke and B. Meffert Institute of Informatics, Humboldt University, Unter den Linden 6, 10099 Berlin, Germany Email: falk.lehmann@gmx.de,
More informationBiggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
More informationAN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2000
M31 AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2000 APPLIED MATHEMATICS  ORDINARY LEVEL FRIDAY, 23 JUNE  AFTERNOON, 2.00 to 4.30 Six questions to be answered. All questions
More informationSales and Operations Planning in Company Supply Chain Based on Heuristics and Data Warehousing Technology
Sales and Operations Planning in Company Supply Chain Based on Heuristics and Data Warehousing Technology JunZhong Wang 1 and PingYu Hsu 2 1 Department of Business Administration, National Central University,
More informationContributions to Gang Scheduling
CHAPTER 7 Contributions to Gang Scheduling In this Chapter, we present two techniques to improve Gang Scheduling policies by adopting the ideas of this Thesis. The first one, Performance Driven Gang Scheduling,
More informationcommunication between two digital agents in geometry friends.
UDC 004.8 Yamada A., Mozgovoy M. communication between two digital agents in geometry friends. 1. Introduction. Digital games take a role of a story teller. Efficient, realistic storytelling requires realistic
More informationUndergraduate Student * This work was partially supported by NASA, Grant Number NNX09AH69G and Michigan Space Grant Consortium.
Modeling and Gait Design of a 8Tetrahedron Walker Robot* Miguel Abrahantes, James Dratz, Cornelius Smits, Leif Nelson Department of Engineering, Hope College, Holland, MI Abstract This work describes
More informationInterVehicle Communication Protocol for Cooperatively Capturing and Sharing Intersection Video
InterVehicle Communication Protocol for Cooperatively Capturing and Sharing Intersection Video Kazuya Kotani, Weihua Sun, Tomoya Kitani, Naoki Shibata, Keiichi Yasumoto, and Minoru Ito Graduate School
More informationAutodesk Inventor Tutorial 3
Autodesk Inventor Tutorial 3 Assembly Modeling Ron K C Cheng Assembly Modeling Concepts With the exception of very simple objects, such as a ruler, most objects have more than one part put together to
More informationVibrations can have an adverse effect on the accuracy of the end effector of a
EGR 315 Design Project  1  Executive Summary Vibrations can have an adverse effect on the accuracy of the end effector of a multiplelink robot. The ability of the machine to move to precise points scattered
More informationStudents will understand 1. use numerical bases and the laws of exponents
Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?
More informationInteractive Virtual Simulator (IVS) of SixLegged Robot Katharina
Interactive Virtual Simulator (IVS) of SixLegged Robot Katharina U. SCHMUCKER, A. SCHNEIDER, V. RUSIN Fraunhofer Institute for Factory Operation and Automation, Magdeburg, Germany ABSTRACT The sixlegged
More informationA vector is a directed line segment used to represent a vector quantity.
Chapters and 6 Introduction to Vectors A vector quantity has direction and magnitude. There are many examples of vector quantities in the natural world, such as force, velocity, and acceleration. A vector
More informationTEAM formation is one of the salient features of multiple
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 16, NO. 1, JANUARY 2008 85 A Differential Game Approach to Formation Control Dongbing Gu, Member, IEEE Abstract This paper presents a differential
More informationOn Fleet Size Optimization for MultiRobot FrontierBased Exploration
On Fleet Size Optimization for MultiRobot FrontierBased Exploration N. Bouraqadi L. Fabresse A. Doniec http://car.minesdouai.fr Université de Lille Nord de France, Ecole des Mines de Douai Abstract
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationTechnology to Control Hybrid Computer Systems
INFORMATION TECHNOLOGY Hynomics (formerly HyBrithms Corporation, formerly Sagent Corporation) Technology to Control Hybrid Computer Systems Businesses and industries, both large and small, increasingly
More informationDynamic Temporal Planning for Multirobot Systems
Dynamic Temporal Planning for Multirobot Systems C. Ugur Usug and Sanem SarıelTalay {usugc,sariel}@itu.edu.tr Istanbul Technical University Artificial Intelligence and Robotics Laboratory (AIR http://air.cs.itu.edu.tr
More informationand Technology, Takayama, Ikoma, Nara , Japan of Engineering, The University of Tokyo, Hongo, Bunkyoku, Tokyo , Japan
A Cognitive Robot Architecture based on Tactile and Visual Information Kazunori Terada 1,, Takayuki Nakamura 1, Hideaki Takeda 1, and Toyoaki Nishida 2 1 Graduate School of Information Science, Nara Institute
More informationDINAMIC AND STATIC CENTRE OF PRESSURE MEASUREMENT ON THE FORCEPLATE. F. R. Soha, I. A. Szabó, M. Budai. Abstract
ACTA PHYSICA DEBRECINA XLVI, 143 (2012) DINAMIC AND STATIC CENTRE OF PRESSURE MEASUREMENT ON THE FORCEPLATE F. R. Soha, I. A. Szabó, M. Budai University of Debrecen, Department of Solid State Physics Abstract
More informationSensors in robotic arc welding to support small series production
Sensors in robotic arc welding to support small series production Gunnar Bolmsjö Magnus Olsson Abstract Sensors to guide robots during arc welding have been around for more than twenty years. However,
More informationPlanning to Fail  Reliability Needs to Be Considered a Priori in Multirobot Task Allocation
Planning to Fail  Reliability Needs to Be Considered a Priori in Multirobot Task Allocation Stephen B. Stancliff, John Dolan The Robotics Institute Carnegie Mellon University Pittsburgh, PA, USA {sbs,jmd}@cmu.edu
More informationFactoring Patterns in the Gaussian Plane
Factoring Patterns in the Gaussian Plane Steve Phelps Introduction This paper describes discoveries made at the Park City Mathematics Institute, 00, as well as some proofs. Before the summer I understood
More informationContent. Chapter 4 Functions 61 4.1 Basic concepts on real functions 62. Credits 11
Content Credits 11 Chapter 1 Arithmetic Refresher 13 1.1 Algebra 14 Real Numbers 14 Real Polynomials 19 1.2 Equations in one variable 21 Linear Equations 21 Quadratic Equations 22 1.3 Exercises 28 Chapter
More informationA HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION
A HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION Zeshen Wang ESRI 380 NewYork Street Redlands CA 92373 Zwang@esri.com ABSTRACT Automated area aggregation, which is widely needed for mapping both natural
More informationA Generic Model for the Design of MultiRobot Applications
A Generic Model for the Design of MultiRobot Applications S. Rocher and D. Duhaut Laboratoire de Robotique de Paris Université Pierre et Marie Curie 1012 avenue de l Europe 78140 VELIZY FRANCE Abstract:
More informationMiddle Grades Mathematics 5 9
Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from realworld situations. 2. Apply problemsolving strategies
More informationSeparation of Concerns in Componentbased Robotics
Separation of Concerns in Componentbased Robotics Davide Brugali Università degli Studi di Bergamo, Italy Robot Control Architectures Typical functions implemented in software Acquiring and interpreting
More informationA Robust Method for Solving Transcendental Equations
www.ijcsi.org 413 A Robust Method for Solving Transcendental Equations Md. Golam Moazzam, Amita Chakraborty and Md. AlAmin Bhuiyan Department of Computer Science and Engineering, Jahangirnagar University,
More informationTeraPlot Graph Plotting and Data Analysis for Science and Engineering
TeraPlot Graph Plotting and Data Analysis for Science and Engineering TeraPlot graphing software gives you everything you need for publication quality graph plotting in science and engineering. At its
More informationTHEORETICAL MECHANICS
PROF. DR. ING. VASILE SZOLGA THEORETICAL MECHANICS LECTURE NOTES AND SAMPLE PROBLEMS PART ONE STATICS OF THE PARTICLE, OF THE RIGID BODY AND OF THE SYSTEMS OF BODIES KINEMATICS OF THE PARTICLE 2010 0 Contents
More informationObjectives After completing this section, you should be able to:
Chapter 5 Section 1 Lesson Angle Measure Objectives After completing this section, you should be able to: Use the most common conventions to position and measure angles on the plane. Demonstrate an understanding
More informationNEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers
More informationSafety Verification of the Small Aircraft Transportation System Concept of Operations
Safety Verification of the Small Aircraft Transportation System Concept of Operations Victor Carreño 1 NASA Langley Research Center, Hampton, Virginia, 23681 César Muñoz 2 National Institute of Aerospace,
More informationHumanlike Arm Motion Generation for Humanoid Robots Using Motion Capture Database
Humanlike Arm Motion Generation for Humanoid Robots Using Motion Capture Database Seungsu Kim, ChangHwan Kim and Jong Hyeon Park School of Mechanical Engineering Hanyang University, Seoul, 133791, Korea.
More informationObject Following Fuzzy Controller for a Mobile Robot
Copyright 2012 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational Intelligence and Electronic Systems Vol. 1, 1 5, 2012 Irfan Ullah 1, Furqan
More informationNew York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
More informationCurriculum Mapping  Key Stage 3 Subject : Mathematics Topics addressed Skills acquired Crosscurricular links Progression links to future years
Year 7 (CORE) Sequences and rules Order, add and subtract decimals Order, add and subtract negative s Rounding and estimates Paper and pencil methods to add, subtract, divide and multiply Perimeter and
More informationAutomatic Train Control based on the MultiAgent Control of Cooperative Systems
The Journal of Mathematics and Computer Science Available online at http://www.tjmcs.com The Journal of Mathematics and Computer Science Vol.1 No.4 (2010) 247257 Automatic Train Control based on the MultiAgent
More informationSimulation Platform for Performance Test for Robots and Human Operations
RobotHuman Teamwork in Dynamic Adverse Environment: Papers from the 2011 AAAI Fall Symposium (FS1105) Simulation Platform for Performance Test for Robots and Human Operations Masaru Shimizu and Tomoichi
More informationPerformance Prediction, Sizing and Capacity Planning for Distributed ECommerce Applications
Performance Prediction, Sizing and Capacity Planning for Distributed ECommerce Applications by Samuel D. Kounev (skounev@ito.tudarmstadt.de) Information Technology Transfer Office Abstract Modern ecommerce
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationMultiresource Shop Scheduling With Resource Flexibility and Blocking Yazid Mati and Xiaolan Xie
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 1 Multiresource Shop Scheduling With Resource Flexibility and Blocking Yazid Mati and Xiaolan Xie Abstract This paper proposes a general scheduling
More information0017 Understanding and Using Vector and Transformational Geometries
Tom Coleman INTD 301 Final Project Dr. Johannes Vector geometry: 0017 Understanding and Using Vector and Transformational Geometries 3D Cartesian coordinate representation:  A vector v is written as
More informationProjectile motion with "measure Dynamics" TEP. Related topics Parabolic trajectory, uniformly accelerated motion, and ballistics
Projectile motion with "measure Dynamics" TEP Related topics Parabolic trajectory, uniformly accelerated motion, and ballistics Principle A steel sphere is launched by a ballistic unit and the resulting
More informationPARAMETRIC MODELING. David Rosen. December 1997. By carefully layingout datums and geometry, then constraining them with dimensions and constraints,
1 of 5 11/18/2004 6:24 PM PARAMETRIC MODELING David Rosen December 1997 The term parametric modeling denotes the use of parameters to control the dimensions and shape of CAD models. Think of a rubber CAD
More informationA PHOTOGRAMMETRIC APPRAOCH FOR AUTOMATIC TRAFFIC ASSESSMENT USING CONVENTIONAL CCTV CAMERA
A PHOTOGRAMMETRIC APPRAOCH FOR AUTOMATIC TRAFFIC ASSESSMENT USING CONVENTIONAL CCTV CAMERA N. Zarrinpanjeh a, F. Dadrassjavan b, H. Fattahi c * a Islamic Azad University of Qazvin  nzarrin@qiau.ac.ir
More informationKindergarten Math I can statements
Kindergarten Math I can statements Student name:. Number sense Date Got it Nearly I can count by 1s starting anywhere from 1 to 10 and from 10 to 1, forwards and backwards. I can look at a group of 1 to
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationHow formal modeling addresses advanced issues in railway signalling
How formal modeling addresses advanced issues in railway signalling Alessandro Fantechi University of Florence Dipartimento di Ingegneria dell Informazione Florence, Italy January 28, 2015 Univ. of Surrey
More informationPrentice Hall Algebra 2 2011 Correlated to: Colorado P12 Academic Standards for High School Mathematics, Adopted 12/2009
Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level
More informationTessellations. A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps.
Tessellations Katherine Sheu A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps. 1. The picture below can be extended to a tessellation
More informationAn EnergyBased Vehicle Tracking System using Principal Component Analysis and Unsupervised ART Network
Proceedings of the 8th WSEAS Int. Conf. on ARTIFICIAL INTELLIGENCE, KNOWLEDGE ENGINEERING & DATA BASES (AIKED '9) ISSN: 179519 435 ISBN: 97896474512 An EnergyBased Vehicle Tracking System using Principal
More informationDesignSimulationOptimization Package for a Generic 6DOF Manipulator with a Spherical Wrist
DesignSimulationOptimization Package for a Generic 6DOF Manipulator with a Spherical Wrist MHER GRIGORIAN, TAREK SOBH Department of Computer Science and Engineering, U. of Bridgeport, USA ABSTRACT Robot
More informationCONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. XVI  Fault Accomodation Using Model Predictive Methods  Jovan D. Bošković and Raman K.
FAULT ACCOMMODATION USING MODEL PREDICTIVE METHODS Scientific Systems Company, Inc., Woburn, Massachusetts, USA. Keywords: Fault accommodation, Model Predictive Control (MPC), Failure Detection, Identification
More informationDeployment Strategies for Distributed Complex Event Processing
Noname manuscript No. (will be inserted by the editor) Deployment Strategies for Distributed Complex Event Processing Gianpaolo Cugola Alessandro Margara Received: July 19th, 212 / Accepted: date Abstract
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationMultiRobot Task Scheduling
MultiRobot Task Scheduling Yu ("Tony") Zhang Lynne E. Parker Distributed Intelligence Laboratory Electrical Engineering and Computer Science Department University of Tennessee, Knoxville TN, USA IEEE
More informationVisualization Techniques in Data Mining
Tecniche di Apprendimento Automatico per Applicazioni di Data Mining Visualization Techniques in Data Mining Prof. Pier Luca Lanzi Laurea in Ingegneria Informatica Politecnico di Milano Polo di Milano
More informationExam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.
Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the
More informationComal Independent School District PreAP PreCalculus Scope and Sequence
Comal Independent School District Pre PreCalculus Scope and Sequence Third Quarter Assurances. The student will plot points in the Cartesian plane, use the distance formula to find the distance between
More information