The Project of Autonomous Group of 2-wheeled Mobile Robots

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1 2th IFToMM World Congress, Besançon (France), June8-2, 27 The Project of utonomous Group of 2-wheeled Mobile Robots T. Buratowski * T.Uhl + G. Chmaj GH University of Science and Technology Cracow, POLND bstract-this work discusses the possibility of wheeled mobile robots design for cooperation in group of robots. The paper presents problems connected with the navigation. Navigation it is very complex problem especially for group of robots. This complex problem is connected with self-localization, path planning and maps creations. This paper presents several path planning algorithms for mobile robots. In the process of mechatronic design, three identical mobile robots have been manufactured. I. Introduction One of the basic problems connected with wheeled mobile robots is the choice of the appropriate navigational method. This refers to individual robots and also, in particular, the group of mobile robots. Navigation can be defined as an issue connected with systems control, defining their position and orientation as well as choosing appropriate trajectory. The consisting elements of mobile robots navigation are: self-localization, path planning and creating a map of the explored area. Each of the above enumerated elements is independent, however, the realization of the target navigation task of the mobile robot or the group of mobile robots depends on the correct construction of particular elements. Now the main problem in robotics is to control more than robot in the some time. We can distinguish a swarm of robots and a group of robots. If we talk about a swarm it means that we have more then robots to control. The group of robots consists of maximum robots. In this paper we are trying to present wheeled mobile robot project capable of cooperating in a group. We decided to build robots capable of communicating and sending data in the process of navigation. Those robots can be used in indoor localization. In those mechatronic systems we have several problems to solve. The first problem is connected with communication between robots, also to find robots' position by themselves is an essential problem but it's not easy to solve. If we take into consideration a possible scenario for a group of robots we can present it in Table I. * tburatow@agh.edu.pl tuhl@agh.edu.pl chmaj@.agh.edu.pl Scenario I The Robots starting point is known The obstacle position is known The target position is known Scenario II The Robots starting point is known The obstacle position is unknown The target position is known Scenario III The Robots starting point is unknown The obstacle position is unknown The target position is known Scenario IV The Robots starting point is unknown The obstacle position is unknown The target position is unknown TBLE I. The possible scenarios for the group of robots In our project we assumed that the group of robots must be able to operate in all scenarios presented in Table I. II. 2-Wheeled mobile robot description. Basic assumptions connected with kinematics model If we look in to the reference connected with 2- wheeled mobile robots, we can say that for indoor solutions this type of mechatronic systems is treated as nonholonomic [,2,]. This nonholonomic condition has been presented below and is connected with point in Fig. : yɺ = xɺ tan(θ) () lso we are assuming that there is no skid between wheel and the ground [2]. The basic elements of the model are: wheel unit drive of wheels and 2, selfadjusting supporting wheel and the frame of unit with all electronics. When describing motion phenomena for a complex system such as mobile 2-wheeled robot, it is

2 2th IFToMM World Congress, Besançon (France), June8-2, 27 beneficial to attach the coordinates system to the particular robot s elements. This mechatronic system have had 2DOF (degree of freedom) it means that our position should be presented by coordinates x,y and orientation is represented by angle Θ. In fig. has been presented the mode of calculation focused on the system of kinematics description [,2,]. Fig.. The mode of calculation connected with system kinematics description. System coordinates have been attached to the robot basic element. The system coordinates x y z is motionless and based. If our kinematics model is defined in this way it is possible to describe position and orientation any point on our robot. s an example characteristic points B and C connected with wheels can bee describe with the use of Denavit-Hartenberg notation as follow[2,]: T T B, C, cos( Θ) = cos( Θ) = cos( Θ) cos( Θ) x y + x l y + l l l cos( Θ) r Θ cos( ) r 2 Where l stands for a distance between points,b and and,c. lso parameters r,r 2 this are particular wheel radiuses. B. Basic assumptions connected with path planning The basic matter in the issue of the wheeled mobile robots (and not only) trajectory planning is describing basic definitions connected with an object moving in space. The basic law connected with trajectory planning may be defined as follows []: FS = W C ) () ( i Θ V c C is defined as: FS and trajectory c :[,] where c( ) p and start c( ) p t arg et If we take in to consideration kinematics constraints for our particular mobile robot presented above there are 2 possible schemes of motion on our defined surface [2,]. The first possible motion scheme is connected with metric L which is described as follows: ( x, y) : x + y = const () y C B x () (2) The second possible scheme of motion is described by metric L2 defined as: ( x, y) : x 2 + y 2 = const (6) If we present those metrics on graphical way we receive presentation described in Fig.2 : Fig.2. The graphical presentation of metrics connected with robot motion scheme. In this project L2 metric has been assumed. This mode of motion is the most efficient and will be used in the process of path planning. ccording to scheme of motion assumption in fig. robot movement has been presented. SUPPLY UNIT start targe start target Fig.. The possible movement for particular robot accumulators CONTROL UNIT U=2 [V] elements, [V] elements 8,2 [V] sensors connected with robot environment sonar, infrared, fotooptic sensors Sensors subunit NORTHSTR system camera charger subunit 2, GHz bluetooth transmission voltage conversion and stabilisation U=[V] U2=2[V] robot s controller computer subunit for data transmission BRM Fig. The Block diagram of 2-wheeled mobile robot MOTION UNIT ccording to a basic definition connected with robots, basic definition of those mechatronic systems describes

3 2th IFToMM World Congress, Besançon (France), June8-2, 27 them as autonomous devices owning units presented in fig.. The first unit is connected with power supply. In this unit we have accumulator, converters and charger. The Robot s controller still controls voltage level and sends the robot to the docking station. The MOTION UNIT is connected with mechanical construction and it is mobile platform equipped with wheels, two driven and one self-adjusted, and drives MXON -max 2 with planetary gear GP 2 and optic encoders HEDS. The CONTROL UNIT is the most complex. In this unit there are infrared, sonar and optic sensors controlled by sensors subunit ll those sensors are connected with robot environment. For sensors work the robot controller is based on TMEG28. dditionally the robot is equipped which embedded computer PCM7 which is responsible for data acquisition and managing control, because this mechatronic device should cooperate in group each robot wireless communication device based of Bluetooth technology. In this project hierarchical control system for particular robot has been assumed. The basic description connected with this kind of control has been presented in fig.. Managing control Off line regime situation in robot environment. It means that the received information is interpreted and appropriate action is taken. nother control level is called strategic and is responsible for dividing global tasks on series basic tasks. On this level path planning is calculated in cartesian coordinates. In this project we decided to create simple robot s language based on basic assumptions connected with path planning. For example if our robot should go straight meter command connected with robot motion is!nn/r. On tactical level of hierarchical control system robot position is mapping from cartesian on joint coordinates. On this level the control system is using sensor information (encoders) to estimate appropriate position. The main task of the control system on executive control is to drive control in order to execute tasks planned on strategic and tactical levels. In this project for managing, strategic control and robot s language embedded computer is responsible. Especially designed robot s controller is responsible for tactical and executive control. In our project each robot from the group of three is an agent. n agent [,6,7] is an animate entity that is capable of doing something on purpose. That definition is broad enough to include humans and other animals, the subjects of verbs that express actions, and the computerized robots. Strategic control BSE STTION (B) BSE STTION Robot language M B from M,S,S2 Tactical control ROBOTS ENVIRONMENT Executive control actuators sensors S2 M from S2 () S M from S (2) M S2 from S () M S from S2 () 2-wheeled mobile robot On line regime Fig. The hierarchical control system for mobile robot The managing control is the highest control level. It includes special algorithms and artificial intelligence elements based on swarm behavior. Those algorithms allow to compute sensor information and recognize SLVE 2 (S2) MSTER (M) SLVE (S)

4 2th IFToMM World Congress, Besançon (France), June8-2, 27 the basis of markers whose position is known by the robot e.g. NORTHSTR system. Fig.6 The scheme of wireless communication between robots In the presented group of robots each agent is equipped with ORCLE XE database installed in embedded computer. The database is a very important source of agent environment information. Each robot receives and sends information to another with the use of the scheme presented in fig.6. The communication master agent initiates communication and sends information from slave 2 to agent slave. Slave agent sends information about itself to the master agent. Master agent sends information from slave to the agent slave 2 and then slave 2 sends data about itself to the master. This is one cycle. fter the assumed cycle quantity master sends information about agents positions and obstacles to the base station. B Path planning There are several ways to calculate robot trajectory. In our software we implement two algorithms: - Simple path algorithm - Wavefront algorithm This part is going to presents how robot trajectory is calculated on the basis of Simple path algorithm. The Simple path algorithm was designed to provide simple way of building user trajectories. In fig.7 there is trajectory which was created by user and calculated by Simple path algorithm. III NVIGTION. Self-localization Self-localization of a robot in space consists in defining its position and orientation in reference to the base coordinates. Base coordinates should be understood as constant base coordinates. Defining position and orientation takes place on the basis of data connected with a robot s state parameters and the robot s state surroundings parameters as well as a proper interpretation of the data stored in the robot s memory. Generally we can say that there are several ways of a method of selflocalization classification. Examples of such methods are local and global methods[8]. Local methods consist in calculating the position and the orientation of a robot in reference to its prior localization, while global methods are based upon defining position and orientation without knowing the prior system localization. nother classification of self-localization methods is based upon the environment description. We may differentiate static environment, in which only the robot is moving and dynamic environment, in which other systems are also moving and the robot is able to detect this motion. s far as self-localization is concerned, a very important role is played by the methods of measuring the robot s position and one may differentiate relative methods (the measurements are done by means of sensors placed on the robot) to which we may include odometric methods consisting in calculating relative vehicle movement on the basis of the measurement of angle rotations of driven wheels, as well as inertial methods consisting in the usage of accelerometers, gyroscopes for speed and acceleration measurement. There also is a possibility of using absolute methods of measuring position and orientation of a robot in space, to which we may include recognizing artificial or natural markers, i.e. defining position and orientation on Fig.7 The trajectory created by user and checked by Simple path algorithm When user trajectory is ready, we have to find out that this trajectory is clear-cut and is appropriate with metric L2. It means we need to check every step in trajectory. For instance, fig.8 shows possible moves in robot trajectory. Fig.8 The possible next steps moves. Lets consider the possibility of next steps for those parts of robot trajectory. When we look at example in fig.8 where robot trajectory is straight, we have three possible moves for next robot step to expand trajectory and 2 which are corrected according to metric L2 but not expanding trajectory. Next example shows situation when robot is turning ninety degrees right. For this move we can find four steps, which are possible in the next move. Step marked by white dot is not considered due to reasons like above. Third example shows the part of robot trajectory where robot is moving through part of a circle. Here we also have four steps which are possible to reach in next robot step. The last example shows situation where robot was turned forty five degrees left and then it is moving straight. For the next step we can simply calculate five steps. Since, our robots can move in eight directions ( fig. ) we have to create, discussed above, masks consisting of next

5 2th IFToMM World Congress, Besançon (France), June8-2, 27 possible steps for other directions. When we consider this mask as regards to direction we quickly find out that there are sixteen masks which we have to consider to make our trajectory clear-cut. This masks are shown in fig.9. Lets consider how to create command trajectory trajectory which will be sent to the robot. First of all we have to number each cluster in robot area (each cluster has unique number). Fig.9 Masks included next possible steps. a) masks for straight move, b) masks for ninety degree turning, c) masks for moving through part of circle, d) masks for forty five degree move In example presented in fig.7, we number this area from to 9. Once robot area has numbered clusters we must insert each step of user trajectory to array which includes number of cluster where robot is going to move. In our case this array will be as shown below: [, 9, 7, 26,,,, 62, 7, 78, 86, 8, 8, 8, 82, 9, 99, 8, 6, 2, 2,, 8, 6]. To create command trajectory we start from left cluster marked by arrow in fig.7. For this cluster we create mask consist of next possible steps, then we calculate if next step of user trajectory is in this mask. If it is, we choose one command from movement mask (this mask includes robot command) shown in fig., If it is not in the mask, it means that user trajectory is incorrect. Fig. The movement mask. Which command we will choose depends on in which direction we have to move to reach step from mask. If this step is straight we choose N, if it is forty five degrees right we choose NE, if it is ninety degrees right we choose E. We have to remember that if we choose command which is connected with turning, we have to rotate the movement mask. This mask is rotated one time right when we choose NE command or two times right when we choose E command. For left side we apply the same calculation. From movement mask we use only five commands marked dark grey color. The other commands are not used because the robot does not have to turn one hundred thirty five degree because of step like this one would have been detected by previous mask. This algorithm has been applied to all steps in user trajectory. In our example command trajectory looks like below (we assume that one cluster has one centimeter in length): [N, N, NE, N, N, N, N, NW, N, N, W, N, N, N, E, NE, N, NW, N, N, N, N, N]. If we look on this array, we can say that this command trajectory is not optimal. Why? It is not good idea to sent to robot all this command separately. We can simple add all commands which say: go straight. s a matter of fact there is only one: N. fter adding all this commands our robot trajectory should look like below: [N2, NE, N, NW, N2, W, N, E, NE, N, NW, N]. Now, this trajectory looks much better, but we can do one more thing. For this command which are connected with robot turning we can check if next is N command (move straight). If it is, we can simple add this value to previous one connected with turning. fter this, our robot trajectory should look like below: [N2, NE, NW, W, E, NE2, NW6]. Now we are ready to send this trajectory to the robot. The second algorithm is called wavefront and is very efficient in robot s path planning. There are 2 types of this mode of path planning, first is connected with 2 dimensional area and second operating in dimensional space. For mobile robots solution first mode is used. The wavefront algorithm involves a breadth first search of the graph beginning at the destination point until it reaches the start point. In fig.9 exemplary robot or group of robots environment has been presented. 9 obstacle robot 2 target Fig.9 n exemplary robot s environment. First, obstacles are marked with a and your goal point is marked with a 2. You can optionally surround the entire world with s as well to tell your robot to avoid those squares, and/or "expand" the size of the obstacle to avoid collisions due to dead-reckoning errors. fter those operations our computational environment will look like this presented in fig

6 2th IFToMM World Congress, Besançon (France), June8-2, Fig. The computational robot s environment. To create the "wave" of values, begin at the destination, and assign a distance of to every square adjacent to the goal. Then assign a distance of to every square adjacent to the squares of distance. Continue to do this until you reach the start point. Once this is complete, you can simply follow the numbers in reverse order until you reach the goal (see fig. ), avoiding any square with the value. You are free to chose if you would like your robot to be able to move diagonally or just in directions, but obviously motion scheme in 8 directions is faster and more efficient Fig. The wavefront algorithm after implementation The discussed settings are enough when we are talking about robot trajectories. When we turn on robots there is couple of thing we have to check to make them ready to run. For instance we ought to wait for start services which are required to correct robots runs. Our software utilize Oracle database to store all information about obstacles, clusters and also running history, so services for which we have to wait are Oracle services. The project is still developed. To sum up current the robots gather information by means of sensors and pass them on the database. In the database this information is classified by means of SQL procedures. Than the data is passed on the particular robots. So the collaboration rule consist in the collective view of environment by which the robots are surrounded. Currently work are being carried out to find an algorithm which will divide the area of search to search for cluster of a different color. Now these points are indicated at random excluding the possibility of the robots trajectories crossing. In fig.2 has been presented group of robots designed and manufactured in our Departments of Robotics and Mechatronics except embedded computer and Bluetooth modules. In the above graph, the ones represent an obstacle. The goal and start points are labeled - 2 and - and all other squares are labeled according to their distance from the goal. possible path has been marked on grey in fig.. This is just one of the many paths that can be used to reach the goal, and any path that follows the descending numbers correctly will be acceptable. Fig.2 The group of robots. Fig.2 The wavefront algorithm after implementation in software. In our developing software we applied this algorithm to path planning for each of robot from the group. n exemplary path calculated on the basis of this algorithm has been presented in fig.2. IV. Conclusions Since, robots which are developed in our Department communicates by Bluetooth devices, we have to configure this devices. To configure Bluetooth devices, robot ports where commands are sent and other required settings the special software have been developed. The result of interpreting data connected with robots environment is a geometric map. Equipping the robot with the possibility of generating a map lets for effective trajectory planning and self-localization in space. References [] Buratowski T., Uhl T.: The Project and construction of group of wheeled mobile robots, Pomiary utomatyka Kontrola, Warszawa, nr, 26. [2] Buratowski T., Uhl T.: The fuzzy logic application in rapid prototyping of mechatronic systems, Proceedings of the Fourth International Workshop on Robot Motion and Control ROMOCO, Poznań 2. [] Buratowski T., Uhl T., śylski W.: The comparison of parallel and serial-parallel structures of mobile robot Pioneer 2DX state emulator, Proceedings of the Seventh Symposium on Robot Control SYROCO, Wroclaw, 2.

7 2th IFToMM World Congress, Besançon (France), June8-2, 27 [] Leonard J.J., Durrant-Whyte H. F.: Directed sonar sensing for mobile robot navigation, Hardcover, 92. [] Konishi M., Nishi T., Nakano K., and Sotobayashi K. : Evolutionary Routing Method for Multi Mobile Robots in Transportation. In Proceedings of the IEEE International Symposium on Intelligent Control, October 22. [6] bbass H.., Xuan H., McKay R.I.: New Method to Compose Computer Programs using Colonies of nts. InProceedings of the IEEE Congress on Evolutionary Computation, 22. [7] N. Baskar, R. Saravanan, P. sokan, and G. Prabhaharan. : nts Colony lgorithm pproach for Multi-Objective Optimisation of Surface Grinding Operations. dvanced Manufacturing Technology, 2. This work is supported by Polish State Committee for Scientific Research under contract T2C 6 29