mạng sẽ được ánh xạ tới các kết nối giữa các đơn vị AB, AC, AD, AE, như thể hiện trong hình (b). Tương tự như vậy, ba khe cắm tiếp theo sẽ được ánh xạ tới các kết nối giữa các đơn vị BC, BD, và BE, CD tiếp theo hai đến, và C-E, và cuối cùng để DE. Bằng cách sử dụng các mảng theo cách này, | 276 Self-Organizing Maps PP Figure This illustration shows the sequence of responses from the phonotopic map resulting from the spoken Finnish word humppila. Do not bother to look up the meaning of this word in your Finnish-English dictionary humppila is the name of a place. Source Reprinted with permission from TeuvoKohonen The neural phonetic typewriter. IEEE Computer March 1988. 1988 IEEE. mechanism thus the torques that cause a particular motion must be known in advance. Figure illustrates the simple two-dimensional robot-arm model used in this example. For a particular starting position x and a particular desired end-effector velocity Udesired. the required torques can be found from T A x Udesired where T is the vector Tỵ. T 1 The tensor quantity A here simply a twodimensional matrix is determined by the details of the arm and its configuration. Ritter and Schulten use Kohonen s SOM algorithm to learn the A x quantities. A mechanism for learning the A tensors would be useful in a real environment where aging effects and wear might alter the dynamics of the arm over time. The first part of the method is virtually identical to the two-dimensional mapping example discussed in Section . Recall that in that example units - Torque itself is a vector quantity defined as the time-rate of change of the angular momentum vector. Our vector T is a composite of the magnitudes of two torque vectors T and T- . The directions of T and 7-2 can be accounted for by their signs T 0 implies a counterclockwise rotation of the joint and T 0 implies a clockwise rotation. Applications of Self-Organizing Maps 277 R d Figure This figure shows a schematic of a simple robot arm and its space of permitted movement. The arm consists of two massless segments of length and with unit point masses at its distal joint d and its end effector e. The end effector begins at some randomly selected location x within the region R. The joint angles are 01 and 02- The .
