In this research we are trying to find a mobile robot control method for corridor navigation and wall following in a partially known environment, when obstacles trajectory is unknown or information about it is incomplete, and the environment consists of st ationary obstacles. Gathering information of the robot travelling is based on IR sensors. The aim of the robot is to select avoidance maneuvers to avoid collision with obstacles. Introduction Mobile robots are increasingly being used to perform tasks in un known environments. The potential of robots to undertake such tasks lies in their ability to intelligently and efficiently locate and interact with objects in their environment. Various methods for controlling mobile robot systems have been developed which are generally classified into two categories: global planning and local control. Many works, based on the complete knowledge of the robot and the environment, use a global planning method such as artificial potential fields, connectivity graph, cell decom position, etc. These methods build some paths (set of sub -goals) which are free of obstacles. The local methods are mainly used in an unknown environment. They could be called reactive strategies and are completely based on sensory information. The environ ments where robots are used can be categorized as dynamic or time varying or static. In these environments, there are several stationary or moving objects. Common examples of these environments will be manufacturing industry with machinery parts as the moving objects, an office or a museum where the moving objects will be humans or a road - system where the moving objects will be the vehicles. The robot has to negotiate and avoid these obstacles while moving towards its destination. If mobile robots are to be used to solve various problems, it is necessary that they be able to autonomously compute a safe trajectory. Mobile robots have been used as museum guides and office assistants. They have also been used for search and rescue operations and for exploration of hazardous environments. For these systems it becomes important that the robot finds an autonomous path with least chance of collision with any objects and humans. While navigating in a crowded environment, a dynamic obstacle can block the path of the r obot. The robot must stop its motion until the obstacle moves away. So, for three decades, many algorithms have been developed to solve the mobile robot navigations with specific conditions. Modeling through the bond graph There exist different methods to obtain the equations of motion of physical systems. One way for deriving a mathematical model of systems is the usage of bond graphs [ 1-9]. The aim of this section is to give a general view of bond graphs. Bond graphs that provide a systematic way of des cribing physical systems and their corresponding dynamics are introduced by Karnopp [ 1], and extensions appear in [ 10-19]. The main idea, introduced in [ 1, 2], is that the representation of geometric considerations by bond graph transformers leads to conse rvation of energy. This enables bond graphs to be created from geometric transformation without concerning about the power conservation since it automatically implies the forces corresponding to the velocities. Graphical representation of physical systems that explain the dynamic behavior of the system is called bond graph. Bond graphs are independent of the domain. It means that they explain physical systems in different energy domains in the same manner. The main concept of bond graphs based on energy and energy exchange. Bond graph splits complicated systems into simple subsystems. These subsystems can be in different domains of energy. Analyzing these subsystems, the bond graph provides the system model. This model can be used for simulation and study th e dynamic behavior of the system. In general, subsystems are connected by means of engineering links (mechanical shafts, electrical wires, etc.). Through these links’ energy transfers between subsystems. Utilizing energy as the exchange variable for a mode l yields to the use of two co -variables in each energy domain which are commonly called effort (e) and flow (f), where energy . These variables are also called power variables. They have a different meaning in different physical domains (mechanical, elect rical, hydraulic, thermal, chemical systems). The power is a product of these two variables. Modeling assumptions Mass, rigidity, and linearity of components, and so forth. The result of these assumptions can sometimes lead to mathematical formulation prob lems. In this system 8 energy storage elements end up in derivative causality. Angular velocity of center of mass of the robot assumes to be positive in clock wise mode otherwise it is negative. Linear velocities of tires must be positive relative to cente r of mass. Description of Robot This mobile robot contains two wheels with radius R1 which run by two D.C. motors independently. Also, there exist two power sources which obtain the power of the robot. Meanwhile to reduce angular velocity which each D.C. motor give a set of gears used. Fig. 1 gives a scheme of the robot, components and variables which used in this report. a=10cm w V a=10cm Fig. 1 Scheme of the robot Mobile robots are mechanical devices capable of moving in an environment with a certain degree of autonomy. Autonomous navigation is associated to the availability of external sensors that capture information of the environment through visual images or distance or proximity measurements. In this robot there are eight sensors that do distance measurements, which set in the structure of robot as shown in Fig. 2. To control this robot, to find its way through the corridor and avoid collision with obstacl es, the algorithm which used in this project is finding the linear and angular velocities of center of mass of the robot then finding necessary inputs corresponding to these velocities, in addition required data for modulated transformer are stored in two 16 by 16 matrices (Table 1& 2) and also state space equations found by using bond graph. Fig.2 Position of the Sensors Table 1 A B C D 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 A1 A2 A2 A2 A2 A2 A2 A3 A6 A3 A2 A3 A4 A4 0 0 0 1 A1 A2 A2 A2 A2 A2 A2 A5 A6 A6 A2 A2 A5 A5 A5 A8 0 0 1 0 A2 A5 A5 A5 A2 A2 A2 A2 A2 A2 A2 A2 A2 A2 A5 A8 0 0 1 1 A6 A2 A2 A2 A2 A2 A2 A5 A2 A2 A2 A5 A2 A2 A5 A8 0 1 0 0 A3 A3 A3 A3 A3 A3 A3 A4 A3 A3 A3 A4 A3 A4 A4 A7 0 1 0 1 A2 A2 A2 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A4 A7 0 1 1 0 A1 A2 A2 A2 A2 A2 A2 A3 A6 A3 A2 A3 A4 A4 0 1 1 1 A2 A2 A2 A2 A3 A3 A3 A2 A3 A2 A9 A9 A3 A9 A9 A9 1 0 0 0 A1 A3 A2 A5 A2 A2 A2 A5 A2 A6 A2 A5 A2 A2 A5 A8 1 0 0 1 A1 A2 A2 A2 A3 A2 A2 A3 A6 A3 A2 A3 A3 A3 1 0 1 0 A2 A3 A3 A2 A2 A2 A2 A2 A2 A2 A2 A2 A2 A2 A5 A8 1 0 1 1 A2 A2 A2 A2 A3 A2 A2 A2 A3 A6 A2 A2 A2 A9 A9 A9 1 1 0 0 A6 A3 A3 A3 A3 A3 A3 A4 A3 A3 A3 A3 A3 A4 A4 A8 1 1 0 1 A3 A2 A2 A3 A3 A3 A3 A9 A3 A6 A3 A9 A3 A3 A3 A9 1 1 1 0 A3 A2 A2 A2 A3 A9 A2 A9 A3 A3 A2 A9 A3 A9 A3 A9 1 1 1 1 A1 A2 A2 A2 A2 A2 A3 A3 A6 A3 A9 A3 A9 A9 A9 Table 2 Modulate of transformers for each state State Angle( Deg ) Velocity of mass center ( rpm ) m1 m2 A1 0 30 0.5 0.5 A2 -15 10 0.0512 0.282 A3 15 10 0.2821 0.0512 A4 30 10 0.33 0.0034 A5 -30 10 0.0034 0.33 A6 0 10 0.167 0.167 A7 90 18 0.5828 0.0172 A8 -90 18 0.0172 0.5828 A9 0 0 0 0 Source: Fictitious data, for illustration purposes only setting R(radius of tire)=2.5cm, a=10cm To derive the state equations the bond graph method used. The distinct velocities are found from dynamic equation of motion of the mobile robot (which explain in appendix) and using these relations and applying a power sign convention to construct the bond graph of the system which shown in Fig.3. By doing the sequential causal assignment procedure to above bond graph and propagate it the result is a completely augment bond gra ph which shown in Fig.4 Fig. 3 bond graph model of the system Fig. 4 bond graph model of the system - causality According to the causal bond graph, the order of the system is 4 because of 4 integer able elements, so states of system become (P3, P7, P19, and P38), and also e1 and e2 are two source of effort act as inputs. Linear and angular velocities are the output if the system. The formulation always starts by writing the rate of change of a state variable equals an effort and flow. We then use causality to track the efforts and flow through the bond graph. The formulation procedures are attached in appendix the result is shown in Matrix form (state space realization ). The definitions of the variables are attached in appendix.         +         − −+−−− =     24011 34 7231 72 22 32 16 4 51 3 27 34 10000001 381973 200 00 00 0 381973 meme Ir IRRTR IRRTRIT Ir PPPP PPPP             −=     PPPP yy aI IaRRRI 381973 010010 0 19 723119 21 Simulation results by 20SIM For simulation of the system instead of real parameter m1 and m2 we use any arbitrary signal for inputs and by attaching observer to the outputs elements we can find the response of system to any arbitrary inputs. Therefore, using the redundancy of the system, both the translational and rotational motion of the object are controlled by the modulate transformers. These results shown in Fig. 5 and Fig. 6 and also the Continuous -time equations demonst rated by 20SIM are attached in appendix. Fig. 5 bond graph model of the system in 20SIM Fig.6 results of modeling through bond graph by 20SIM. Conclusion The results shows that we can control the translational and rotational velocities of center of mass of mobile robot by using bond graph model, and applying proper inputs corresponded to each state that robot will face. With regard to state space equations, system is LTI so we can control it by PID controller.