CONTEMPORARY ROBOTICS - Challenges and Solutions Part 8 pot

Controloffuelcellsystemsinmobileapplications 201 inverter (DC/AC converter) 24 V DC/230 V AC, followed by a single phase electrometer or voltage and current measurement (for the DC output). Parts of the AC output (interconnection with the isolated electric network or electrical power network) are reactance coils (damping of electric surges) and circuit breaker(s). The circuit breaker terminals represent a handover point with the electrification system (isolated network). Negative pressuer valve (0,6 bar abs.) Solenoid valve H 2 output P Pressure sensor COOLING AIR CIRCLE Radial fan H 2 Input Filter of mechanical impurities CS 2CS 1 Reduction valve Pressure relief valve (1,6 bar abs.) Mass Flow-meter CS 3 T P Qm Mechanical ball valve Filter of mechanical impurities M Compressor CS 4 Negative pressure valve (0,7 bar absol.) Pressure relief valve (1,4 bar abs.) H2 input solenoid valve Mass Flow-meter CS 5 T P Qm Air / O 2 input solenoid valve BLDC motor TT Manometer Pressure relief valve 25 bar abs. HYDROGEN CIRCLE OXIDANT CIRCLE P Pressure sensor Air / O 2 Input P CS 8 H2 output solenoid valve Pressure sensor CS 6 Air / O 2 output solenoid valve H 2 O Output from humidifiers Pressure relief valve 25 bar abs. T T T Mass Flow-meter CS 7 T P Qm Cooling air input solenoid valve Product water reservoir PEM FUEL CELL (NEXA Power Module, Ballard) POWER OUTPUT DC/DC Converter Inverter (DC/AC Converter) A V PP Filter 5 m Pressure sensor Hydrogen reservoirs Air / O 2 Input 1 ph (3 ph) Electrometer Isolated Alternating Current El. Power Network 50 Hz, 230 V or work in Parallel mode with El. Power Network 50 Hz, 230 V A V SIGNAL BUS (U 1 – U 47 , U stack ) Fuel cell, reactants and products qualities/properties sensors Control unit (PLC TECOMAT TC600) Measuring station Measuring of chemical composition of air (oxygen, hydrogen, ), independent hydrogen leakage sensor, temperature, pressure and humidity sensor Direct Current El. Power Network 24 V DC Temperature sensor PC Station (Storing, back-up, visualization, LAN/WAN) T P φ C H 2 O 2 Pressure relief valve (1,4 bar abs.) H 2 input humidifier Compressed air reservoir Ait / O 2 input solenoid valve Negative pressure valve (0,7 bar abs.) Amperemeter Voltmeter Cooling air input Hot cooling air is flowing along hydrogen reservoirs and warm them up Cooling air input Solenoid valve Mechanical ball valve Air / O 2 input humidifier Air / O 2 output Fig. 5. A summary block diagram of a system with a fuel cell Nexa Power Module designating particular circuits and system elements. Fuel cell signal bus – for purposes of laboratory monitoring of a source with a fuel cell, it is suitable to install a system of sensors on a fuel cell and its immediate surrounding to monitor voltage of particular elementary fuel cells and the whole stack, internal, surface and cooling air output temperature sensors, concentration of hydrogen in the nearby surrounding of the fuel cell, etc., according to required tested parameters). A measuring station – represents a reference measurement point in the distance of approx. 5 to 10 m from a source, and its immediate vicinity, in order to find limit conditions in calculations of power balances, and in order to secure the safety of persons and equipment nearby the prototype. The measuring station is equipped by sensors of temperature, pressure and humidity of the ambient air, sensor of concentration of oxygen in the air, and sensor or detector of hydrogen escape into the surrounding environment. A mobile PC station represented by a portable computer provides acquisition (back-up) and processing of measured data, their visualization on the intranet/internet, and interconnection of a real system with a software model. 3.3 Hydrogen circuit control Hydrogen is supplied to the power source system from reservoirs with compressed gas or metal hydride, which is heated by the air leaving the cooling fuel cell circuit. Hydrogen reservoirs are followed by a mechanical ball and solenoid valve providing disconnection/separation of a hydrogen circuit from the gas reservoirs (tanks). This is followed by a reduction valve decreasing the hydrogen pressure from reservoirs (up to 25 bar abs.) to the operation pressure (from 1.1 to 1.5 bar abs.). Another element is most usually a mass flow-meter measuring the mass flow-rate (volume flow rate, temperature and pressure) of hydrogen passing the flow-meter (approx. 30 NL/min max.). Still before hydrogen entering the fuel cell, it passes through a humidification unit where it is saturated by water vapor as needed. A solenoid valve is situated at the exit from a fuel cell providing controlled hydrogen discharge from the fuel circuit. The fuel circle can be also equipped by a pressure sensor monitoring the hydrogen pressure in reservoirs and before the hydrogen entry into a reduction valve. Further, the surface temperature of reservoirs with a metal hydride is monitored. 3.4 Reaction air circuit control A compressor suctions the surrounding air via a filter of mechanical impurities and drives it into a compressed air reservoir. The compressed air reservoir of the volume of approx. 10 - 20 NL serves to stabilization (uniformity) of the air/oxygen flow into a fuel cell. The reservoir is equipped by a safety/relief valve (1.5 bar abs.) and underpressure valve (0.7 bar abs.) and its input and output are blocked by a solenoid valve in order to control the pressure and volume flow of the oxidizing agent into a fuel cell. In the reach of the oxidizing agent, mass flow-meter (approx. 120 NL/min max.) and humidifier follow in order to saturate the oxidizing agent by water vapors. Water leaving the humidifier is downtaken into a product water reservoir (tank). From there, water passes through humidifiers and is discharged into the sewerage, or it is further used. 3.5 Cooling air circuit control The cooling air is suctioned by a radial fan from the surrounding environment into a cooling circle. The cooling air passes through the filter of mechanical impurities and radial fan into a mass flow-meter equipped by a sensor of temperature and pressure (approx. 500 NL/min max.), from where it is further driven to cooling channels inside bipolar plates of a fuel cell. The exit from the fuel cell cooling air is equipped by temperature sensors. The heated cooling air is driven to hydrogen reservoirs. 4. Control of a vehicle powered by a fuel cell The vehicle powered by hydrogen fuel cell needs an electronic control system assuring operation of its different parts. The complex electronic control is necessary already for basic CONTEMPORARYROBOTICS-ChallengesandSolutions202 operation of the vehicle, because there are a lot of subsystems that have to be coordinated and controlled. The control system assures especially following tasks: Control of fuel cell operation – a hydrogen input valve control, a combustion products output valve control, a fuel cell fan control, coupling of produced electrical energy to an electric DC-drive system. Control of DC-drive system – motor current control, speed control. Processing security tasks – assuring safe operation of a fuel cell system and a drive system, processing of hydrogen detector information, temperature measuring. Managing the driver control panel – complete interface to pilot that allows controlling the car – start/stop, speed set point, time measuring, emergency buttons and indicators. Creating data archives with saved process variables – saving important process data to archives that can be then exported and analyzed. Sending actual data to display panel in car – display panel in the car is the “process” visualization of the system. All important data are online displayed on it. Communication with a PC monitoring station – control system send data and receive commands from the PC monitoring station using wireless communication system. 4.1 Basic fuel cell control A basic fuel cell control concerns in a proper fuel cell operation in its all activity phases. For this task, most usually an electronic control system is used. The control system provides particularly (see Fig 6): Safe start of the cell activity – fuel cell start is a sequence of activities which should be made for the cell to be transferred to a status when it supplies the electric power. This particularly means to supply the reaction air (Place 2, Fig. 6) and reaction hydrogen (Place 4, Fig. 6) into the whole volume of the fuel cell. After achieving some cell voltage level, the system enters a stage of the electric power production. Proper cell functioning in the stage when it supplies the power to the appliance – in this stage, the cell supplies electric power to the appliance (Place 6, Fig. 6). In a point of the cell control, practically no control actions are requited, a basic control system task is to monitor statues of important variables – fuel cell voltage and current, temperature, and potentially also other ones. Based on these variables, it can be assessed whether the cell is loaded regularly or whether it is overloaded and, therefore, there is a risk of its damage. Safe fuel cell switch-off – a process of a fuel cell switch-off contains again several actions which put the cell into a not active status. This particularly means shutting off the reaction hydrogen inlet and consumption of reaction gases which were left in the fuel cell volume (Place 8, Fig. 6). The consumption of these reaction gases will take place when the hydrogen inlet is closed however an appliance is still connected. Under such conditions, the residual hydrogen is consumed from the cell volume, and, simultaneously, cell voltage drops. In case of the voltage drop below some limit, the appliance can be disconnected, and the cell enters a state when it is switched off. In the Place 6, Fig. 6 , a situation can occur when the cell should be immediately shut off as well as the appliance should be immediately disconnected (status 9, Fig. 6). This can be done however the residual hydrogen inside the fuel cell can cause membrane damage. Therefore, the described switching off method is only suitable to apply in critical situations (e.g. when hydrogen escape is detected) and still, however, it is suitable to provide reaction gases use or removal from the cell volume. Reaction to non-standard situations (safety functions) – this particularly means states related to the fuel cell operation which could result into system safety decrease or to its damage. This particularly means cell overheating, hydrogen escape, reaction gas pressure increase, etc. 4.2 Electric drive control The electric drive of a car with a fuel cell is the main consumer of electric power supplied by the fuel cell. The drive control has a critical influence on the car power consumption. Two basic conceptions are applied for fuel cell driven vehicles: A conception when a fuel cell supplies the power into some power system of a vehicle as e.g. a battery or a super capacitor. Applying this conception, a fuel cell can run in the optimal regime and need not necessarily to respond immediately to load demands. A vehicle power system designed in this way can draw the power also from other sources, it can apply power recuperation, etc. A conception when a fuel cell supplies the power directly into the electric drive system of the vehicle. In this design, it should immediately respond to load demands. The drive unit should be controlled so that the power takeoff from the cell is sufficiently continuous and smooth and the cell is not overloaded. A way of the drive control depends on its type. It can be a DC motor, a motor with electronic commutation, a synchronous motor, etc. A motor type should be chosen according to required properties of a vehicle. The drive usually needs to use an electronic control system. This control system can be a part of the control system for a fuel cell, or it can be a separate system. Controloffuelcellsystemsinmobileapplications 203 operation of the vehicle, because there are a lot of subsystems that have to be coordinated and controlled. The control system assures especially following tasks: Control of fuel cell operation – a hydrogen input valve control, a combustion products output valve control, a fuel cell fan control, coupling of produced electrical energy to an electric DC-drive system. Control of DC-drive system – motor current control, speed control. Processing security tasks – assuring safe operation of a fuel cell system and a drive system, processing of hydrogen detector information, temperature measuring. Managing the driver control panel – complete interface to pilot that allows controlling the car – start/stop, speed set point, time measuring, emergency buttons and indicators. Creating data archives with saved process variables – saving important process data to archives that can be then exported and analyzed. Sending actual data to display panel in car – display panel in the car is the “process” visualization of the system. All important data are online displayed on it. Communication with a PC monitoring station – control system send data and receive commands from the PC monitoring station using wireless communication system. 4.1 Basic fuel cell control A basic fuel cell control concerns in a proper fuel cell operation in its all activity phases. For this task, most usually an electronic control system is used. The control system provides particularly (see Fig 6): Safe start of the cell activity – fuel cell start is a sequence of activities which should be made for the cell to be transferred to a status when it supplies the electric power. This particularly means to supply the reaction air (Place 2, Fig. 6) and reaction hydrogen (Place 4, Fig. 6) into the whole volume of the fuel cell. After achieving some cell voltage level, the system enters a stage of the electric power production. Proper cell functioning in the stage when it supplies the power to the appliance – in this stage, the cell supplies electric power to the appliance (Place 6, Fig. 6). In a point of the cell control, practically no control actions are requited, a basic control system task is to monitor statues of important variables – fuel cell voltage and current, temperature, and potentially also other ones. Based on these variables, it can be assessed whether the cell is loaded regularly or whether it is overloaded and, therefore, there is a risk of its damage. Safe fuel cell switch-off – a process of a fuel cell switch-off contains again several actions which put the cell into a not active status. This particularly means shutting off the reaction hydrogen inlet and consumption of reaction gases which were left in the fuel cell volume (Place 8, Fig. 6). The consumption of these reaction gases will take place when the hydrogen inlet is closed however an appliance is still connected. Under such conditions, the residual hydrogen is consumed from the cell volume, and, simultaneously, cell voltage drops. In case of the voltage drop below some limit, the appliance can be disconnected, and the cell enters a state when it is switched off. In the Place 6, Fig. 6 , a situation can occur when the cell should be immediately shut off as well as the appliance should be immediately disconnected (status 9, Fig. 6). This can be done however the residual hydrogen inside the fuel cell can cause membrane damage. Therefore, the described switching off method is only suitable to apply in critical situations (e.g. when hydrogen escape is detected) and still, however, it is suitable to provide reaction gases use or removal from the cell volume. Reaction to non-standard situations (safety functions) – this particularly means states related to the fuel cell operation which could result into system safety decrease or to its damage. This particularly means cell overheating, hydrogen escape, reaction gas pressure increase, etc. 4.2 Electric drive control The electric drive of a car with a fuel cell is the main consumer of electric power supplied by the fuel cell. The drive control has a critical influence on the car power consumption. Two basic conceptions are applied for fuel cell driven vehicles: A conception when a fuel cell supplies the power into some power system of a vehicle as e.g. a battery or a super capacitor. Applying this conception, a fuel cell can run in the optimal regime and need not necessarily to respond immediately to load demands. A vehicle power system designed in this way can draw the power also from other sources, it can apply power recuperation, etc. A conception when a fuel cell supplies the power directly into the electric drive system of the vehicle. In this design, it should immediately respond to load demands. The drive unit should be controlled so that the power takeoff from the cell is sufficiently continuous and smooth and the cell is not overloaded. A way of the drive control depends on its type. It can be a DC motor, a motor with electronic commutation, a synchronous motor, etc. A motor type should be chosen according to required properties of a vehicle. The drive usually needs to use an electronic control system. This control system can be a part of the control system for a fuel cell, or it can be a separate system. CONTEMPORARYROBOTICS-ChallengesandSolutions204 P la ce 1 F C o ff P la ce 2 C o m pre s so r 3 0 0% S ta rt A N D n en í C h y b a P la ce v 3 C o m pre s so r 1 0 0% H o u t o pe n 2 0 s P la ce 4 H in o p e n 2 s P la ce 5 H o u t c lo s e d 9 s P la ce 6 L o ad c o nn e c te d -F C s u pp lie s e lec tr ic a l e n e rg y U > 4 0V P la ce 8 H in c lo s e d (lo ad c o nn e c te d) S to p O R E rr o r P la ce 1 0 H o u t o pe n U < U m in P la ce 9 H in o p e n (lo ad d is co n n ec te d ) C ritic a l e rr or O R C ritic a l s to p O K 2 m in P la ce 1 1 H o u t c lo s e d P la ce 1 2 B lo w in g – O p e n nin g o f H o u t fo r 1 s . 8 m in O K S w itc h in g -o ff w a s n ’t c au s e d b y e r ro r Switching-on of fuel cell Switching-off of fuel cell Fig. 6. Basic fuel cell control. 4.3 User-pilot interface A fuel cell vehicle should be equipped by a user interface which enables a driver to control the vehicle. The complexity of this user interface depends on a vehicle character, however, it should contain at least primary control elements and indicators for the fuel cell system control: Controller for the fuel cell switching on and off. Controller for setting a required vehicle speed. Vehicle status indicators – of a character of display or set of indicators regarding the fuel cell condition, operation mode, defects and faults, speed, electrical variables, etc. 5. An example of a real application A team of several specialists and students of Department of Measurement and Control, VSB- Technical University of Ostrava has designed and realized a prototype of hydrogen powered car based on fuel cell technology and electrical DC drive. The car was realized according to rules of Shell Eco-Marathon competition which is focused on economization of energy in mobile vehicles. The project is called HydrogenIX (Fig. 7), development and testing activities were realized between 2005 and today. The project is closely related with the educational process and motivation of students for further research activity in the form of construction of a mobile system driven by electrical motor and fed from electrochemical generator with the fuel cell. By the HydrogenIX project and related technical and technological problems, the team tries to involve the students of bachelor, master and doctoral degree on Faculty of Mechanical Engineering and Faculty of Electrical Engineering and Computer Science to problems of non-traditional power sources and their applications. Fig. 7. The HydrogenIX car. Car parameters: Aerodynamic shape of the car body. Power of the fuel cell – 1.2 kW. 2 DC motor of 150W. 0 5 10 15 20 25 30 35 40 45 Distance (m) 238 434 656 836 946 1134 1291 1461 1736 1971 2180 2409 2640 2827 3041 3268 3468 Actual speed (km/h) Av. speed (km/h) U(V) I1(A) I2(A) Fig. 8. A record of data of a run at the race circuit in Nogaro, France. Controloffuelcellsystemsinmobileapplications 205 P la ce 1 F C o ff P la ce 2 C o m pre s so r 3 0 0% S ta rt A N D n en í C h y b a P la ce v 3 C o m pre s so r 1 0 0% H o u t o pe n 2 0 s P la ce 4 H in o p e n 2 s P la ce 5 H o u t c lo s e d 9 s P la ce 6 L o ad c o nn e c te d -F C s u pp lie s e lec tr ic a l e n e rg y U > 4 0V P la ce 8 H in c lo s e d (lo ad c o nn e c te d) S to p O R E rr o r P la ce 1 0 H o u t o pe n U < U m in P la ce 9 H in o p e n (lo ad d is co n n ec te d ) C ritic a l e rr or O R C ritic a l s to p O K 2 m in P la ce 1 1 H o u t c lo s e d P la ce 1 2 B lo w in g – O p e n nin g o f H o u t fo r 1 s . 8 m in O K S w itc h in g -o ff w a s n ’t c au s e d b y e r ro r Switching-on of fuel cell Switching-off of fuel cell Fig. 6. Basic fuel cell control. 4.3 User-pilot interface A fuel cell vehicle should be equipped by a user interface which enables a driver to control the vehicle. The complexity of this user interface depends on a vehicle character, however, it should contain at least primary control elements and indicators for the fuel cell system control: Controller for the fuel cell switching on and off. Controller for setting a required vehicle speed. Vehicle status indicators – of a character of display or set of indicators regarding the fuel cell condition, operation mode, defects and faults, speed, electrical variables, etc. 5. An example of a real application A team of several specialists and students of Department of Measurement and Control, VSB- Technical University of Ostrava has designed and realized a prototype of hydrogen powered car based on fuel cell technology and electrical DC drive. The car was realized according to rules of Shell Eco-Marathon competition which is focused on economization of energy in mobile vehicles. The project is called HydrogenIX (Fig. 7), development and testing activities were realized between 2005 and today. The project is closely related with the educational process and motivation of students for further research activity in the form of construction of a mobile system driven by electrical motor and fed from electrochemical generator with the fuel cell. By the HydrogenIX project and related technical and technological problems, the team tries to involve the students of bachelor, master and doctoral degree on Faculty of Mechanical Engineering and Faculty of Electrical Engineering and Computer Science to problems of non-traditional power sources and their applications. Fig. 7. The HydrogenIX car. Car parameters: Aerodynamic shape of the car body. Power of the fuel cell – 1.2 kW. 2 DC motor of 150W. 0 5 10 15 20 25 30 35 40 45 Distance (m) 238 434 656 836 946 1134 1291 1461 1736 1971 2180 2409 2640 2827 3041 3268 3468 Actual speed (km/h) Av. speed (km/h) U(V) I1(A) I2(A) Fig. 8. A record of data of a run at the race circuit in Nogaro, France. CONTEMPORARYROBOTICS-ChallengesandSolutions206 7. Conclusion The top perspective is provided by an electromotor drive with a current source from a fuel cell which transfers the power contained in the fuel (hydrogen or hydrocarbon) directly to electric power. Currently, long-term verification testing has been taking place. This comprises verification of prototypes for a purpose of introduction of series and mass production. A principal fuel cell problem is represented by development of an electrolyte meeting the criteria of mass production, performance efficiency, service life and price. 8. References Fromm E. (1998). Kinetics of Metal-Gas Interactions at Low Temperature Hydryiding, Oxidation, Poisoning, Springer-Verlag Berlin Heidelberg New York, ISBN 3-540-63975-6, Germany. Kameš J. (2008). Alternativní palivo – vodík. Published by Czech Technical University in Prague, ISBN 978-80-254-1686-0, Prague, Czech Republic. Kurzweil P. (2003). Brennstoffzellen-technik, Grundlagen, Komponenten, Systeme, Anwendungen. Vieweg, ISBN 3-528-03965-5, Wiesbaden, Germany. Larminie J. & Dicks A. (2003). Fuel Cell Systems Explained, Second Edition, John Wiley & Sons Ltd., ISBN 978-0-470-84857-9, Chichester, England. Pukrushpan, J. T.; Stefanopoulou, A. G., Peng, H. (2004). Control of fuel cell power systems: principles, modeling, analysis and feedback design, Springer, ISBN 1-85233-816-4, London, United Kingdom. ModelingandAssessingofOmni-directionalRobotswithThreeandFourWheels 207 ModelingandAssessingofOmni-directionalRobotswithThreeandFour Wheels HélderP.Oliveira,ArmandoJ.Sousa,A.PauloMoreiraandPauloJ.Costa X Modeling and Assessing of Omni-directional Robots with Three and Four Wheels Hélder P. Oliveira, Armando J. Sousa, A. Paulo Moreira and Paulo J. Costa Universidade do Porto, Faculdade de Engenharia INESC-Porto – Instituto de Engenharia de Sistemas e Computadores do Porto Portugal 1. Introduction Robots with omni-directional locomotion are increasingly popular due to their enhanced mobility when compared with traditional robots. Their usage is more prominent in many robotic competitions where performance is critical, but can be applied in many others applications such as service robotics. Robots with omni-directional locomotion offer advantages in manoeuvrability and effectiveness. These features are gained at the expense of increased mechanical complexity and increased complexity in control. Traditional mechanical configuration for omni-directional robots are based on three and four wheels. With four motors and wheels, it is expected that the robot will have better effective floor traction (Oliveira et al., 2008), that is, less wheel slippage at the expense of more complex mechanics, more complex control and additional current consumption. Common robotic applications require precise dynamical models in order to allow a precise locomotion in dynamical environments. Such models are also essential to study limitations of mechanical configurations and to allow future improvements of controllers and mechanical configurations. The presented study is based on a single prototype that can have both configurations, that is, the same mechanical platform can be used with three wheels and then it can be easily disassembled and reassembled with a four wheeled configuration. A mathematical model for the motion of the robot was found using various inertial and friction parameters. The motion analysis includes both kinematical and dynamical analysis. 1.1 Context Robots with omni-directional locomotion are holonomic and they are interesting because they allow greater manoeuvrability and efficiency at the expense of some extra complexity. One of the most frequent solutions is to use some kind of variation of the Mecanum wheels proposed by (Diegel et al., 2002) and (Salih et al., 2006). Omni-directional wheel design is quite delicate and different wheels exhibit very different performances. Wheel construction is often application specific and the presented work uses the wheels shown in Fig. 1. These wheels are built in-house for several demanding applications. The prototype used in the experiments uses four wheels of this kind to achieve 12 CONTEMPORARYROBOTICS-ChallengesandSolutions208 omni-directional locomotion. A robot with four wheels is expected to have more traction than its three wheeled counterpart. In both configurations the motor plus wheel assemblies are identical to the photograph seen in Fig. 2. Fig. 1. 5DPO omni-directional wheel Fig. 2. Motor and wheel A robot with three or more motorized wheels of this kind can have almost independent tangential, normal and angular velocities (holonomic property). Dynamical models for this kind of robots are not very common due to the difficulty in modeling the several internal frictions inside the wheels, making the model somewhat specific to the type of wheel being used (Oliveira et al., 2008) and (Williams et al., 2002). Frequent mechanical configurations for omni-directional robots are based on three and four wheels. Three wheeled systems are mechanically simpler but robots with four wheels have more acceleration with the same kind of motors. Four wheeled robots are expected to have better effective floor traction, that is, less wheel slippage - assuming that all wheels are pressed against the floor equally. Of course four wheeled robots also have a higher cost in equipment, increased energy consumption and may require some kind of suspension to distribute forces equally among the wheels. (a) Three wheeled configuration (b) Four wheeled configuration Fig. 3. Configurations for the prototype In order to study and compare the models of the three and four wheeled robots, a single prototype was built that can have both configurations, that is, the same mechanical platform can be used with three wheels and then it can be disassembled and reassembled with a four wheel configuration, see Fig. 3. Data from experimental runs is taken from overhead camera, see Fig. 4. The setup is taken from the heritage of the system described in (Costa et al., 2000) that currently features 25 frames/second, one centimeter accuracy in position (XX and YY axis) and about three degrees of accuracy in the heading of the robot. Fig. 4. Image from overhead camera In order to increase the performance of robots, there were some efforts on the studying their dynamical models (Campion et al., 1996), (Conceicao et al., 2006), (Khosla, 1989), (Tahmasebi et al., 2005), (Williams et al., 2002) and kinematic models (Campion et al., 1996), (Leow et al. 2002), (Loh et al. 2003), (Muir & Neuman, 1987), (Xu et al., 2005). Models are based on linear and non linear dynamical systems and the estimation of parameters has been the subject of continuing research (Conceicao et al., 2006), (Oliveira et al., 2008) and (Olsen and Petersen, 2001). Once the dynamical model is found, its parameters have to be estimated. The most common method for identification of robot parameters are based on the Least Squares Method and Instrumental Variables (Astrom & Wittenmark, 1984). However, the systems are naturally non-linear (Julier & Uhlmann, 1997), the estimation of parameters is more complex and the existing methods (Ghahramani & Roweis, 1999), (Gordon et al., 1993), (Tahmasebi et al., 2005) have to be adapted to the model's structure and noise. 2. Mechanical Configurations Fig. 5 and Fig. 6 present the configuration of the three and four wheeled robots respectively, as well as all axis and relevant forces and velocities of the robotic system. The three wheeled system features wheels separated by 120º degrees, and the four wheeled by 90º degrees. ModelingandAssessingofOmni-directionalRobotswithThreeandFourWheels 209 omni-directional locomotion. A robot with four wheels is expected to have more traction than its three wheeled counterpart. In both configurations the motor plus wheel assemblies are identical to the photograph seen in Fig. 2. Fig. 1. 5DPO omni-directional wheel Fig. 2. Motor and wheel A robot with three or more motorized wheels of this kind can have almost independent tangential, normal and angular velocities (holonomic property). Dynamical models for this kind of robots are not very common due to the difficulty in modeling the several internal frictions inside the wheels, making the model somewhat specific to the type of wheel being used (Oliveira et al., 2008) and (Williams et al., 2002). Frequent mechanical configurations for omni-directional robots are based on three and four wheels. Three wheeled systems are mechanically simpler but robots with four wheels have more acceleration with the same kind of motors. Four wheeled robots are expected to have better effective floor traction, that is, less wheel slippage - assuming that all wheels are pressed against the floor equally. Of course four wheeled robots also have a higher cost in equipment, increased energy consumption and may require some kind of suspension to distribute forces equally among the wheels. (a) Three wheeled configuration (b) Four wheeled configuration Fig. 3. Configurations for the prototype In order to study and compare the models of the three and four wheeled robots, a single prototype was built that can have both configurations, that is, the same mechanical platform can be used with three wheels and then it can be disassembled and reassembled with a four wheel configuration, see Fig. 3. Data from experimental runs is taken from overhead camera, see Fig. 4. The setup is taken from the heritage of the system described in (Costa et al., 2000) that currently features 25 frames/second, one centimeter accuracy in position (XX and YY axis) and about three degrees of accuracy in the heading of the robot. Fig. 4. Image from overhead camera In order to increase the performance of robots, there were some efforts on the studying their dynamical models (Campion et al., 1996), (Conceicao et al., 2006), (Khosla, 1989), (Tahmasebi et al., 2005), (Williams et al., 2002) and kinematic models (Campion et al., 1996), (Leow et al. 2002), (Loh et al. 2003), (Muir & Neuman, 1987), (Xu et al., 2005). Models are based on linear and non linear dynamical systems and the estimation of parameters has been the subject of continuing research (Conceicao et al., 2006), (Oliveira et al., 2008) and (Olsen and Petersen, 2001). Once the dynamical model is found, its parameters have to be estimated. The most common method for identification of robot parameters are based on the Least Squares Method and Instrumental Variables (Astrom & Wittenmark, 1984). However, the systems are naturally non-linear (Julier & Uhlmann, 1997), the estimation of parameters is more complex and the existing methods (Ghahramani & Roweis, 1999), (Gordon et al., 1993), (Tahmasebi et al., 2005) have to be adapted to the model's structure and noise. 2. Mechanical Configurations Fig. 5 and Fig. 6 present the configuration of the three and four wheeled robots respectively, as well as all axis and relevant forces and velocities of the robotic system. The three wheeled system features wheels separated by 120º degrees, and the four wheeled by 90º degrees. CONTEMPORARYROBOTICS-ChallengesandSolutions210 Fig. 5. Three wheeled robot Fig. 6. Four wheeled robot Fig. 5 and Fig. 6 show the notation used through-out this paper, detailed as follows:  x, y, θ - Robot's position (x,y) and θ angle to the defined front of robot;  d [m] - Distance between wheels and center robot;  v 0 , v 1 , v 2 , v 3 [m/s] - Wheels linear velocity;   0 ,  1 ,  2 ,  3 [rad/s] - Wheels angular velocity;  f 0 , f 1 , f 2 , f 3 [N] - Wheels traction force;  T 0 , T 1 , T 2 , T 3 [Nm] - Wheels traction torque;  v, vn [m/s] - Robot linear velocity;   [rad/s] - Robot angular velocity;  F v , F vn [N] - Robot traction force along v and vn;  T [Nm] - Robot torque (respects to ). The reader should be aware that in omni-directional robotics, the front of the robot is arbitrarily defined according to the intuitive notion of the robot mechanics. Of course, the v direction follows the front of the robot and the vn direction is orthogonal. 3. Motion Analysis and Model Determination 3.1 Kinematic model In order to find motion models for a surface vehicle, the pose of the vehicle must be identified as (x, y, θ) and associated velocities are     dt tdx tv x  ,     dt tdy tv y  ,     dt td t    . The following text uses the notation presented in Fig. 5 and Fig. 6, where the defined “front” also defines the v direction and its orthogonal vn direction. Equation (1) allows the transformation from linear velocities v x and v y on the static (world) axis to linear velocities v and vn on the robot's axis.                                                           t tv tv tt tt t tvn tv y x     100 0cossin 0sincos (1) 3.1.1 Three Wheeled Robot Wheel velocities v 0 , v 1 and v 2 are related with robot's velocities v, vn and  as described by equation (2).                                                       t tvn tv d d d tv tv tv   3cos3sin 10 3cos3sin 2 1 0 (2) Applying the inverse kinematics is possible to obtain the equations that determine the robot velocities related with the wheels velocities. Solving in order of v, vn and , the following can be found:        tvtvtv 02 3 3           (3)          tvtvtvtvn 102 3 2 3 1                (4)          tvtvtv d t 210 3 1           (5) 3.1.2 Four Wheeled Robot The relationship between the wheels velocities v 0 , v 1 , v 2 and v 3 , with the robot velocities v, vn and  is described by equation (6).                                                         t tvn tv d d d d tv tv tv tv  01 10 01 10 3 2 1 0 (6) It is possible to obtain the equations that determine the robot velocities related with wheels velocity but the matrix associated with equation (6) is not square. This is because the system is redundant. It can be found that:        tvtvtv 13 2 1         (7)        tvtvtvn 20 2 1         (8)            tvtvtvtv d t 3210 4 1           (9) 3.2 Dynamic The dynamical equations relative to the accelerations can be described in the following relations:         tFtFtF dt tdv M CvBvv   (10) [...]... T(Nm) u(V) (rad/s) 2 3.7062 0.1324 4 8. 681 0.2319 6 13.4305 0.2 789 8 18. 3492 0.2972 10 21 .82 34 0.3662 12 26.2269 0.3971 Table 1 Experience 1 - Results for the three wheeled configuration Fig 10 Experience 1 - Results for the three wheeled configuration The plots shown in Fig 11 present the results obtained with experience 2 2 18 CONTEMPORARY ROBOTICS - Challenges and Solutions (a) Direction v (b) Direction... 0 .83 1 345.7 12 0.425 402.1 12 0.456 397.0 12 0.715 360.5 12 0.641 371.5 12 1.164 301.0 12 0.272 423.7 12 0.515 389 .0 12 1.454 266.3 Table 3 Experimental tests with motor 0 Fig 14 Experimental tests for motor 0 m0 / i0 ((rad/s)/A) 2910.1 415.7 945.0 87 0.3 503.6 579.6 2 58. 4 1553 .8 755.2 183 .1 u 0 / i0 (Ω) 79.2 14.4 28. 2 26.3 16.7 18. 7 10.3 44.0 23.2 8. 2 220 CONTEMPORARY ROBOTICS - Challenges and Solutions. .. (V/(rad/s)) 3 wheels 4 wheels 0. 089 0.0325 5:1 0.0259 Modeling and Assessing of Omni-directional Robots with Three and Four Wheels R (Ω) M (kg) J (kgm2) Bv (N/(m/s)) Bvn (N/(m/s)) B (Nm/(rad/s)) Cv (N) Cvn (N) C (Nm) Table 6 Parameters of dynamical models 223 4.3111 1.944 2.34 0.0169 0.02 28 0.5 082 0.49 78 0. 487 0 0.6763 0.0130 0.0141 1.90 68 1 .87 38 2.0423 2.21 98 0.0971 0.1 385 5.6 Model Validation Experiences... configuration and (ii) four wheeled configuration The analysis of the errors of the experimental runs shown in Fig 16, in accordance to equations (44), (45) and (46) are presented in Table 7 224 CONTEMPORARY ROBOTICS - Challenges and Solutions Configuration Initial Final emax ē σ emax ē σ v 0.122 -0 .059 0.034 0.067 -0 .003 0.027 Three vn 0.124 -0 .055 0.032 0.051 0.016 0.023 wheeled 1.699 -0 .046 0.546... configuration and allow for future enhancements both at controller and mechanical configuration level This study will enable effective full comparison of three and four wheeled systems 8 References Astrom, K & Wittenmark, B (1 984 ), Computer Controlled System – Theory and Design, Prentice-Hall, Information and System Sciences Series, 1 984 Campion, G.; Bastin, G & Dandrea-Novel, B (1996), Structural properties and. .. 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Modeling and AssessingofOmni-directionalRobotswithThree and FourWheels 207 Modeling and AssessingofOmni-directionalRobotswithThree and Four Wheels HélderP.Oliveira,ArmandoJ.Sousa,A.PauloMoreira and PauloJ.Costa X. Heidelberg New York, ISBN 3-5 4 0-6 397 5-6 , Germany. Kameš J. (20 08) . Alternativní palivo – vodík. Published by Czech Technical University in Prague, ISBN 97 8- 8 0-2 5 4-1 68 6-0 , Prague, Czech Republic Ltd., ISBN 97 8- 0 -4 7 0 -8 485 7-9 , Chichester, England. Pukrushpan, J. T.; Stefanopoulou, A. G., Peng, H. (2004). Control of fuel cell power systems: principles, modeling, analysis and feedback