The purpose of this project is to develop a method for learning and motion planning for robot arm. TRN(Topological Representing Network) is the key concept in this implementation. TRN is used to learn the movement of the robot arm. With the result of learning , motion planning can be done using diffusion algorithm. Also we can use the learning result to control the movement of robot arm. That is, given the coordinates as the input to TRN, TRN will generate the corresponding values to control the robot arm to move. Theoretically, the dimension of TRN can be arbitrary. This means the input to the TRN can be any dimensions and generate any dimension output. That is an advantage of TRN over some other kind of ANN. With diffusion algorithm, the path found from source to destination has the fewest number of movement, namely passing fewest intermediate neural nodes.