机器人热仿真利器matlab机器人工具箱演示matlabrobotics-toolbox-demo.

文件名称: 机器人热仿真利器matlab机器人工具箱演示matlabrobotics-toolbox-demo.pdf

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详细说明：一、rtdemo机器人工具箱演示 2 二、transfermations坐标转换 2 三、Trajectory齐次方程 8 四、forward kinematics 运动学正解 12 四、Animation 动画 18 五、Inverse Kinematics运动学逆解 23 六、 Jacobians雅可比---矩阵与速度 32 七、Inverse Dynamics逆向动力学 45 八、Forward Dynamics正向动力学 52% Homogeneous transformations describe the relationships between Cartesian coordinate frames in terms of translation and orientation % A pure translation of 0.5m in the x direction is represented by trans(0.5,0.0,0.0) ans= 1.0000 0 0 0.5000 1.0000 0 000 010000 0 1.0000 % a rotation of 90degrees about the y axis by roty(pi/ 2) ans三 0.0000 1.0000 0 1.0000 0 0 1.0000 0 0.0000 0 0 01.0000 %and a rotation of -90degrees about the Z axis by rotz(- pi/2) ans= 0.0000 1.0000 0 0 1.00000.0000 0 0 01.0000 0 1.0000 these may be concatenated by multiplication t=transl(0.5, 0.0, 0.0 ) roty(pi /2)*rotz(-pi/2) t 0.00000.00001.000005000 -1.0000 0.0000 0 0 0.0000-1.00000.0000 0 0 1.0000 % %If this transformation represented the origin of a new coordinate frame with respect to the world frame origin(0, 0, 0), that new origin would be given by t*[0001] ans 0.5000 0 1.0000 pause any key to continue the orientation of the new coordinate frame may be expressed in terms of % Euler angles tr2eul(t) ans= 0 15708-1.5708 % %or roll/pitch/yaw angles tr2rpy(t ans 1.57080.0000-1.5708 pause any key to continue % %It is important to note that tranform multiplication is in general not %commutative as shown by the following example rotx( pi/2 )*rotz(-pi/8 ans 0.92390.3827 0 0 0.00000.0000-1.0000 0.3827092390.0000 0 0 0 1.0000 rotz (- pi/)*rotx (pi/2 ans 0.92390.0000-0.3827 0 0.38270000009239 01.00000.0000 0 1.0000 %% pause any key to continue echo off 三、 Trajectory齐次方程 The path will move the robot from its zero angle pose to the upright (on %READY) pose %First create a time vector, completing the motion in 2 seconds with a sample interval of 56ms t=[0:056:2] pause hit any key to continue %a polynomial trajectory between the 2 poses is computed using jtrajo q= jtrajlqz, gr, t) pause hit any key to continue For this particular trajectory most of the motion is done by joints 2 and 3, and this can be conveniently plotted using standard matlab operations subplot(2, 1, 1) plot(t, q(:, 2)) title( theta) xlabel( Time(s)); ylabel joint 2(rad) subplot(2, 1, 2) (t,q(:3) xlabel('time(s)) ylabel(joint 3(rad)) pause hit any key to continue Fi File Edit View Insert Tools Desktop Lindow Help 己日边回·日国口回 Theta 1.5 002040608 Time(s) m-1 1.5 002040608 Time(s) We can also look at the velocity and acceleration profiles We could %differentiate the angle trajectory using diff, but more accurate results can be obtained by requesting that jtrajo return angular velocity and acceleration as follows [a, gd, add]= jtrajlqz, gr, t) which can then be plotted as before subplot(2, 1, 1) plot(t, ad(:, 2) title( velocity) xlabel( Time (s)) ylabel Joint 2 vel(rad/s)") subplot(2, 1, 2 plot(t, qd(: 3) xlabel(Time(s)) ylabel joint 3 vel (rad/s), pause 2)

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