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  • 自由度机器人运动学分析自由度机器人运动学分析自由度机器人运动学分析
  • 六自由度机器人运动学正反解求解过程,十分详细,机器人运动学
  • 六自由度机器人运动学求解及工作空间分析,张文君,丁华锋,随着机器人技术的不断发展,智能化、自动化程度的不断提高,各种用途的机器人在生产、科研等多个领域获得广泛应用。本文研究了一
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  • 六自由度机器人的运动学分析阶段:讨论了机器人运动学的数学基础。介绍了机器人的空间描述和坐标变换,利用Denavit和Hartenberg于1955年提出的D-H参数法来描述相邻连杆之间的坐标方向和参数,讨论了机器人逆运动学的...
  • 六自由度IRB2400机器人运动学分析及轨迹规划 ,陈超,李俊,以IRB2400机器人为研究对象,采用D-H坐标变换法建立机器人的坐标连杆系,完成机器人正运动学和逆运动学分析,在此基础上采用三次多�
  • clear clc % theta d a alpha sigma L(1)=Link([0 0 150 pi/2 0]); L(2)=Link([0 0 760 0 0]); L(3)=Link([0 0 0 pi/2 0]);...robot.plot([0 pi/3 pi/3 0 pi/3])%输入一定参数后机器人图形 hold on;
  • 六自由度机器人结构设计、运动学分析及仿真.pdf
  • 平面二自由度机器人运动学分析

    千次阅读 2017-07-30 18:33:00
    1 %运动学正解 2 function [x, y, c] = planar_robot_forward_kinematics(L1, L2, theta1, theta2) 3 x = L1 * cos(theta1) + L2 * cos(theta1 + theta2); 4 y = L1 * sin(theta1) + L2 * sin(theta1 ...

    1 %运动学正解
    2 function [x, y, c] = planar_robot_forward_kinematics(L1, L2, theta1, theta2)
    3 x = L1 * cos(theta1) + L2 * cos(theta1 + theta2);
    4 y = L1 * sin(theta1) + L2 * sin(theta1 + theta2);
    5 c = theta1 + theta2;
    6 end
     1 %运动学逆解
     2 function [theta1, theta2] = planar_robot_inverse_kinematics(L1, L2, x, y, handcoor)
     3 c2 = (x^2 + y^2 - L1^2 -L2^2) / (2 * L1 * L2);%若(x,y)在工作空间里,则c2必在[-1,1]里,但由于计算精度,c2的绝对值可能稍微大于1
     4 temp = 1 - c2^2;
     5 if(temp < 0)
     6     temp = 0;
     7 end
     8 if(handcoor == 0)   %right handcoor
     9     theta2 = atan2(sqrt(temp), c2);
    10 else    %left handcoor
    11     theta2 = atan2(-sqrt(temp), c2);
    12 end
    13 s2 = sin(theta2);
    14 theta1 = atan2(y, x) - atan2(L2 * s2, L1 + L2 * c2);
    15 end
    1 %画圆弧
    2 function draw_arc(x0, y0, r, theta1, theta2, options)
    3 deltaTheta = 0.1 * pi / 180;
    4 theta = theta1 : deltaTheta : theta2;
    5 x = x0 + r * cos(theta);
    6 y = y0 + r * sin(theta);
    7 plot(x, y, 'LineStyle', options.LineStyle, 'Color', options.Color, 'LineWidth', options.LineWidth);
    8 axis equal;
    9 end
     1 %画工作空间
     2 function draw_planar_robot_workspace(L1, L2, thetaLimit1, thetaLimit2, handcoor)
     3 thetaL1 = thetaLimit1(1);
     4 thetaU1 = thetaLimit1(2);
     5 thetaL2 = thetaLimit2(1);
     6 thetaU2 = thetaLimit2(2);
     7 
     8 hold on;
     9 if(handcoor == 0) %right handcoor
    10     options.LineStyle = '-';
    11     options.Color='g';
    12     options.LineWidth = 3;
    13     
    14     x0 = 0;
    15     y0 = 0;
    16     r = sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaU2));
    17     alpha = acos((r^2 + L1^2 - L2^2) / (2 * r * L1));
    18     thetaStart = thetaL1 + alpha;
    19     thetaEnd = thetaU1 + alpha;
    20     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    21     
    22     x0 = 0;
    23     y0 = 0;
    24     r = L1 + L2;
    25     thetaStart = thetaL1;
    26     thetaEnd = thetaU1;
    27     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    28     
    29     x0 = L1 * cos(thetaU1);
    30     y0 = L1 * sin(thetaU1);
    31     r = L2;
    32     thetaStart = thetaU1;
    33     thetaEnd = thetaU1 + thetaU2;
    34     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    35     
    36     x0 = L1 * cos(thetaL1);
    37     y0 = L1 * sin(thetaL1);
    38     r = L2;
    39     thetaStart = thetaL1;
    40     thetaEnd = thetaL1 + thetaU2;
    41     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    42     
    43     title('Workspace in right handcoor', 'fontsize', 16);
    44 else  %left handcoor
    45     options.LineStyle = '-';
    46     options.Color='b';
    47     options.LineWidth = 3;
    48     
    49     x0 = 0;
    50     y0 = 0;
    51     r = sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaL2));
    52     alpha = acos((r^2 + L1^2 - L2^2) / (2 * r * L1));
    53     thetaStart = thetaL1 - alpha;
    54     thetaEnd = thetaU1 - alpha;
    55     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    56     
    57     x0 = 0;
    58     y0 = 0;
    59     r = L1 + L2;
    60     thetaStart = thetaL1;
    61     thetaEnd = thetaU1;
    62     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    63     
    64     x0 = L1 * cos(thetaU1);
    65     y0 = L1 * sin(thetaU1);
    66     r = L2;
    67     thetaStart = thetaU1 + thetaL2;
    68     thetaEnd = thetaU1;
    69     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    70     
    71     x0 = L1 * cos(thetaL1);
    72     y0 = L1 * sin(thetaL1);
    73     r = L2;
    74     thetaStart = thetaL1 + thetaL2;
    75     thetaEnd = thetaL1;
    76     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    77     title('Workspace in left handcoor', 'fontsize', 16);
    78 end
    79 set(gcf, 'color', 'w');
    80 axis off;
    81 end
      1 %画工作空间草图
      2 function draw_planar_robot_workspace_sketch(L1, L2, thetaLimit1, thetaLimit2, handcoor)
      3 
      4 thetaL1 = thetaLimit1(1);
      5 thetaU1 = thetaLimit1(2);
      6 thetaL2 = thetaLimit2(1);
      7 thetaU2 = thetaLimit2(2);
      8 
      9 hold on;
     10 if(handcoor == 0) %right handcoor
     11     options.LineStyle = '-';
     12     options.Color='g';
     13     options.LineWidth = 3;
     14     
     15     x0 = 0;
     16     y0 = 0;
     17     r = sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaU2));
     18     alpha = acos((r^2 + L1^2 - L2^2) / (2 * r * L1));
     19     thetaStart = thetaL1 + alpha;
     20     thetaEnd = thetaU1 + alpha;
     21     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
     22     
     23     x0 = 0;
     24     y0 = 0;
     25     r = L1 + L2;
     26     thetaStart = thetaL1;
     27     thetaEnd = thetaU1;
     28     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
     29     
     30     x0 = L1 * cos(thetaU1);
     31     y0 = L1 * sin(thetaU1);
     32     r = L2;
     33     thetaStart = thetaU1;
     34     thetaEnd = thetaU1 + thetaU2;
     35     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
     36     
     37     x0 = L1 * cos(thetaL1);
     38     y0 = L1 * sin(thetaL1);
     39     r = L2;
     40     thetaStart = thetaL1;
     41     thetaEnd = thetaL1 + thetaU2;
     42     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
     43     
     44     %-------------
     45     options.LineStyle = '--';
     46     options.Color='r';
     47     options.LineWidth = 0.5;
     48     
     49     x0 = 0;
     50     y0 = 0;
     51     r = sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaU2));
     52     thetaStart = 0;
     53     thetaEnd = 2 * pi;
     54     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
     55     
     56     r = L1 + L2;
     57     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
     58     
     59     x0 = L1 * cos(thetaU1);
     60     y0 = L1 * sin(thetaU1);
     61     r = L2;
     62     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
     63     
     64     x0 = L1 * cos(thetaL1);
     65     y0 = L1 * sin(thetaL1);
     66     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
     67     
     68     xA1 = L1 * cos(thetaL1);
     69     yA1 = L1 * sin(thetaL1);
     70     xB1 = xA1 + L2 * cos(thetaL1 + thetaU2);
     71     yB1 = yA1 + L2 * sin(thetaL1 + thetaU2);
     72     xA2 = L1 * cos(thetaU1);
     73     yA2 = L1 * sin(thetaU1);
     74     xB2 = xA2 + L2 * cos(thetaU1 + thetaU2);
     75     yB2 = yA2 + L2 * sin(thetaU1 + thetaU2);
     76     xC1 = (L1 + L2) * cos(thetaL1);
     77     yC1 = (L1 + L2) * sin(thetaL1);
     78     xC2 = (L1 + L2) * cos(thetaU1);
     79     yC2 = (L1 + L2) * sin(thetaU1);
     80     
     81     plot([0, xA1, xB1], [0, yA1, yB1], 'lineStyle', '-', 'color', 'k', 'lineWidth', 3);
     82     plot([0, xA2, xB2], [0, yA2, yB2], 'lineStyle', ':', 'color', 'k', 'lineWidth', 3);
     83     
     84     fontsize = 15;
     85     delta = 25;
     86     text(0, 0, 'O', 'Fontsize', fontsize);
     87     text(xA1, yA1 - delta, 'A_1', 'fontsize', fontsize);
     88     text(xB1, yB1 - delta, 'B_1', 'fontsize', fontsize);
     89     text(xA2, yA2 + delta, 'A_2', 'fontsize', fontsize);
     90     text(xB2, yB2 - delta, 'B_2', 'fontsize', fontsize);
     91     text(xC1, yC1, 'C_1', 'fontsize', fontsize);
     92     text(xC2, yC2, 'C_2', 'fontsize', fontsize);
     93     title('Workspace sketch in right handcoor', 'fontsize', 16);
     94     
     95 else  %left handcoor
     96     options.LineStyle = '-';
     97     options.Color='b';
     98     options.LineWidth = 3;
     99     
    100     x0 = 0;
    101     y0 = 0;
    102     r = sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaL2));
    103     alpha = acos((r^2 + L1^2 - L2^2) / (2 * r * L1));
    104     thetaStart = thetaL1 - alpha;
    105     thetaEnd = thetaU1 - alpha;
    106     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    107     
    108     x0 = 0;
    109     y0 = 0;
    110     r = L1 + L2;
    111     thetaStart = thetaL1;
    112     thetaEnd = thetaU1;
    113     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    114     
    115     x0 = L1 * cos(thetaU1);
    116     y0 = L1 * sin(thetaU1);
    117     r = L2;
    118     thetaStart = thetaU1 + thetaL2;
    119     thetaEnd = thetaU1;
    120     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    121     
    122     x0 = L1 * cos(thetaL1);
    123     y0 = L1 * sin(thetaL1);
    124     r = L2;
    125     thetaStart = thetaL1 + thetaL2;
    126     thetaEnd = thetaL1;
    127     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    128     
    129     %-------------
    130     options.LineStyle = '--';
    131     options.Color='r';
    132     options.LineWidth = 0.5;
    133     
    134     x0 = 0;
    135     y0 = 0;
    136     r = sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaL2));
    137     thetaStart = 0;
    138     thetaEnd = 2 * pi;
    139     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    140     
    141     r = L1 + L2;
    142     draw_arc(x0, y0, r, thetaStart, thetaEnd, options)
    143     
    144     x0 = L1 * cos(thetaU1);
    145     y0 = L1 * sin(thetaU1);
    146     r = L2;
    147     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    148     
    149     x0 = L1 * cos(thetaL1);
    150     y0 = L1 * sin(thetaL1);
    151     draw_arc(x0, y0, r, thetaStart, thetaEnd, options);
    152     
    153     xA1 = L1 * cos(thetaL1);
    154     yA1 = L1 * sin(thetaL1);
    155     xB1 = xA1 + L2 * cos(thetaL1 + thetaL2);
    156     yB1 = yA1 + L2 * sin(thetaL1 + thetaL2);
    157     xA2 = L1 * cos(thetaU1);
    158     yA2 = L1 * sin(thetaU1);
    159     xB2 = xA2 + L2 * cos(thetaU1 + thetaL2);
    160     yB2 = yA2 + L2 * sin(thetaU1 + thetaL2);
    161     xC1 = (L1 + L2) * cos(thetaL1);
    162     yC1 = (L1 + L2) * sin(thetaL1);
    163     xC2 = (L1 + L2) * cos(thetaU1);
    164     yC2 = (L1 + L2) * sin(thetaU1);
    165     
    166     plot([0, xA1, xB1], [0, yA1, yB1], 'lineStyle', '-', 'color', 'k', 'lineWidth', 3);
    167     plot([0, xA2, xB2], [0, yA2, yB2], 'lineStyle', ':', 'color', 'k', 'lineWidth', 3);
    168     
    169     fontsize = 15;
    170     delta = 25;
    171     text(0, 0, 'O', 'fontsize', fontsize);
    172     text(xA1, yA1 - delta, 'A_1', 'fontsize', fontsize);
    173     text(xB1, yB1 + delta, 'B_1', 'fontsize', fontsize);
    174     text(xA2, yA2 + delta, 'A_2', 'fontsize', fontsize);
    175     text(xB2, yB2 - delta, 'B_2', 'fontsize', fontsize);
    176     text(xC1, yC1, 'C_1', 'fontsize', fontsize);
    177     text(xC2, yC2, 'C_2', 'fontsize', fontsize);
    178     title('Workspace sketch in left handcoor', 'fontsize', 16);
    179 end
    180 set(gcf, 'color', 'w');
    181 axis off;
    182 end
     1 %求边界点
     2 function p = solve_planar_robot_boundary_point( L1, L2, thetaLimit1, thetaLimit2, handcoor, x0, y0, s)
     3 
     4 thetaL1 = thetaLimit1(1);
     5 thetaU1 = thetaLimit1(2);
     6 thetaL2 = thetaLimit2(1);
     7 thetaU2 = thetaLimit2(2);
     8 
     9 xA1 = L1 * cos(thetaL1);
    10 yA1 = L1 * sin(thetaL1);
    11 xA2 = L1 * cos(thetaU1);
    12 yA2 = L1 * sin(thetaU1);
    13 xC1 = (L1 + L2) * cos(thetaL1);
    14 yC1 = (L1 + L2) * sin(thetaL1);
    15 xC2 = (L1 + L2) * cos(thetaU1);
    16 yC2 = (L1 + L2) * sin(thetaU1);
    17 
    18 if(handcoor == 0) %right handcoor
    19     r = [sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaU2)), L1 + L2, L2, L2];
    20     xB1 = xA1 + L2 * cos(thetaL1 + thetaU2);
    21     yB1 = yA1 + L2 * sin(thetaL1 + thetaU2);
    22     xB2 = xA2 + L2 * cos(thetaU1 + thetaU2);
    23     yB2 = yA2 + L2 * sin(thetaU1 + thetaU2);
    24     pp = [xB1, yB1, xB2, yB2; xC1, yC1, xC2, yC2; xC2, yC2, xB2, yB2; xC1, yC1, xB1, yB1];
    25 else  %left handcoor
    26     r = [sqrt(L1 * L1 + L2 * L2 + 2 * L1 * L2 * cos(thetaL2)), L1 + L2, L2, L2];
    27     xB1 = xA1 + L2 * cos(thetaL1 + thetaL2);
    28     yB1 = yA1 + L2 * sin(thetaL1 + thetaL2);
    29     xB2 = xA2 + L2 * cos(thetaU1 + thetaL2);
    30     yB2 = yA2 + L2 * sin(thetaU1 + thetaL2);
    31     pp = [xB1, yB1, xB2, yB2; xC1, yC1, xC2, yC2; xB2, yB2, xC2, yC2; xB1, yB1, xC1, yC1];
    32 end
    33 xc = [0, 0, L1 * cos(thetaU1), L1 * cos(thetaL1)];
    34 yc = [0, 0, L1 * sin(thetaU1), L1 * sin(thetaL1)];
    35 
    36 p = zeros(8,2);
    37 k = 0;
    38 if(abs(s(1) - 0) < eps)
    39     temp = r.^2 - (x0 - xc).^2;
    40     for i = 1 : 4
    41         if(temp(i) >= 0)
    42             xp1 = x0;
    43             yp1 = yc(i) + sqrt(temp(i));
    44             xp2 = x0;
    45             yp2 = yc(i) - sqrt(temp(i));
    46             if(dot([xp1 - x0; yp1 - y0], s) > 0 && (pp(i, 3) - xp1) * (pp(i, 2) - yp1) - (pp(i, 1) - xp1) * (pp(i, 4) - yp1) > 0)
    47                 k = k + 1;
    48                 p(k, :) = [xp1, yp1];
    49             end
    50             if(dot([xp2 - x0; yp2 - y0], s) > 0 && (pp(i, 3) - xp2) * (pp(i, 2) - yp2) - (pp(i, 1) - xp2) * (pp(i, 4) - yp2) > 0)
    51                 k = k + 1;
    52                 p(k, :) = [xp2, yp2];
    53             end
    54         end
    55     end
    56 else
    57     a = (s(2) / s(1))^2 + 1;
    58     b = 2 * (s(2) / s(1)) * (y0 - yc - x0 * (s(2) / s(1))) - 2 * xc;
    59     c = xc.^2 - r.^2 - 2 * y0 * yc + y0^2 + yc.^2 + (s(2) / s(1))^2 * x0^2 + 2 * (s(2) / s(1)) * x0 * (yc - y0);
    60     delta = b.^2 - 4 * a * c;
    61     for i = 1 : 4
    62         if(delta(i) >= 0)
    63             x = roots([a b(i) c(i)]);
    64             xp1 = x(1);
    65             yp1 = s(2) / s(1) * (x(1) - x0) + y0;
    66             xp2 = x(2);
    67             yp2 = s(2) / s(1) * (x(2) - x0) + y0;
    68             if(dot([xp1 - x0; yp1 - y0], s) > 0 && (pp(i, 3) - xp1) * (pp(i, 2) - yp1) - (pp(i, 1) - xp1) * (pp(i, 4) - yp1) > 0)
    69                 k = k + 1;
    70                 p(k, :) = [xp1, yp1];
    71             end
    72             if(dot([xp2 - x0; yp2 - y0], s) > 0 && (pp(i, 3) - xp2) * (pp(i, 2) - yp2) - (pp(i, 1) - xp2) * (pp(i, 4) - yp2) > 0)
    73                 k = k + 1;
    74                 p(k, :) = [xp2, yp2];
    75             end
    76         end
    77     end
    78 end
    79 
    80 distance = sqrt((p(1 : k, 1) - x0).^2 + (p(1 : k, 2) - y0).^2);
    81 [~, index] = min(distance);
    82 p = p(index, :);
    83 end
     1 %画工作空间(示例)
     2 clc;
     3 clear;
     4 close all;
     5 L1 = 200;
     6 L2 = 200;
     7 thetaLimit1 = [-135, 135] * pi / 180;
     8 thetaLimit2 = [-145, 145] * pi / 180;
     9 
    10 figure(1);
    11 handcoor = 0;
    12 draw_planar_robot_workspace(L1, L2, thetaLimit1, thetaLimit2, handcoor)
    13 figure(2);
    14 handcoor = 1;
    15 draw_planar_robot_workspace(L1, L2, thetaLimit1, thetaLimit2, handcoor)
    16 
    17 figure(3);
    18 handcoor = 0;
    19 draw_planar_robot_workspace_sketch(L1, L2, thetaLimit1, thetaLimit2, handcoor)
    20 figure(4);
    21 handcoor = 1;
    22 draw_planar_robot_workspace_sketch(L1, L2, thetaLimit1, thetaLimit2, handcoor)
     1 %求边界点(示例)
     2 clc;
     3 clear;
     4 close all;
     5 L1 = 200;
     6 L2 = 200;
     7 thetaLimit1 = [-135, 135] * pi / 180;
     8 thetaLimit2 = [-145, 145] * pi / 180;
     9 
    10 figure(1);
    11 handcoor = 1;
    12 draw_planar_robot_workspace(L1, L2, thetaLimit1, thetaLimit2, handcoor);
    13 while (1)
    14     [x0, y0] = ginput(1);
    15     [x1, y1] = ginput(1);
    16     s = [x1 - x0; y1 - y0];
    17     p = solve_planar_robot_boundary_point(L1, L2, thetaLimit1, thetaLimit2, handcoor, x0, y0, s);
    18     plot([x0, p(1)], [y0, p(2)], '--o')
    19 end

     

    转载于:https://www.cnblogs.com/gxb31415926/p/7259897.html

    展开全文
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