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Tham khảo tài liệu 'sensors and methods for robots 1996 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 5 Dead-Reckoning 141 Thus the orientation error in Figure 5.9b is of Type B. In an actual run Type A and Type B errors will of course occur together. The problem is therefore how to distinguish between Type A and Type B errors and how to compute correction factors for these errors from the measured final position errors of the robot in the UMBmark test. This question will be addressed next. Figure 5.9a shows the contribution of Type A errors. We recall that Type A errors are caused mostly by Eb. We also recall that Type A errors cause too much or too little turning at the corners of the square path. The unknown amount of erroneous rotation in each nominal 90-degree turn is denoted as a and measured in rad . Figure 5.9b shows the contribution of Type B errors. We recall that Type B errors are caused mostly by the ratio between wheel diameters Ed. We also recall that Type B errors cause a slightly curved path instead of a straight one during the four straight legs of the square path. Because of the curved motion the robot will have gained an incremental orientation error denoted at the end of each straight leg. We omit here the derivation of expressions for a and which can be found from simple geometric relations in Figure 5.9 see Borenstein and Feng 1995a for a detailed derivation . Here we just present the results Xc.g. cw xc.g. ccw 180 4L B 5.9 solves for a in and xc.g. cw xc.g. ccw -4L 180 5.10 B solves for in . Using simple geometric relations the radius of curvature R of the curved path of Figure 5.9b can be found as R -L 2- sin 2 5.11 Once the radius R is computed it is easy to determine the ratio between the two wheel diameters that caused the robot to travel on a curved instead of a straight path E DR R b 2 d Dl R - b 2 5.12 Similarly one can compute the wheelbase error Eb. Since the wheelbase b is directly proportional to the actual amount of rotation one can use the proportion 142 Part II Systems and Methods for Mobile Robot Positioning b actual 90