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| ece4560:lynx6:05resratepos [2017/11/16 18:36] – pvela | ece4560:lynx6:05resratepos [2023/12/03 12:03] (current) – classes |
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| Here, the Lynx6 manipulator Jacobian (using your link lengths) will be used to follow a trajectory. Basically, given $\alpha(0)$ and the body manipulator Jacobian, one can use resolved rate trajectory generation to follow a given desired trajectory. | Here, the Lynx6 manipulator Jacobian (using your link lengths) will be used to follow a trajectory. Basically, given $\alpha(0)$ and the body manipulator Jacobian, one can use resolved rate trajectory generation to follow a given desired trajectory. |
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| For this problem, attempt to generate a trajectory from the initial position $Pos(g_i) = d_i$ (given in previous [[ECE4560:lynx6:07splines|spline problem]]) that moves with a constant body velocity $\xi$ to the final location $Pos(g_f) = d_f$ in the same amount of time as given for the [[ECE4560:lynx6:07splines|spline problem]]. Since the initial joint values $\alpha$ were known, the start condition is known. The trajectory should then flow according to the linear velocity $v$ (in the world frame) for the allotted time. Of course, this velocity should be converted from the world frame to the body frame via the inverse transformation $[g_e(\alpha(t))]^{-1}$ as the manipulator moves. Turn in the time varying signal $\xi(t)$ that gets computed along the | For this problem, attempt to generate a trajectory from the initial position $Pos(g_i) = d_i$ (given in previous [[ECE4560:lynx6:07splines|spline problem]]) that moves to the final location $Pos(g_f) = d_f$ in the same amount of time as given for the [[ECE4560:lynx6:07splines|spline problem]]. Since the initial joint values $\alpha$ were known, the start condition is known. The trajectory should then flow according to the linear velocity $v$ (in the world frame) for the allotted time such that it ends up at $d_f$. To work for the manipulator (body) Jacobian, this velocity should be converted from the world frame to the body frame via the inverse transformation $[g_e(\alpha(t))]^{-1}$ as the manipulator moves. Turn in the time varying signal $\xi(t)$ that gets computed along the trajectory for the constant velocity path (in world frame) to follow (the angular velocity should be zero, so turning in the linear body velocity is sufficient). |
| trajectory for the constant velocity path (in world frame) to follow. | |
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| Using the [[ECE4560:piktul:05resratepos|past resolved rate trajectory generation code]] for ''piktul'' as an example, add the necessary functions that will do so for the ''lynx6''. | Using the [[ECE4560:piktul:05resratepos|past resolved rate trajectory generation code]] for ''piktul'' as an example, add the necessary functions that will do so for the ''lynx6''. |
| 1. Let's check to see if the manipulator is really following the trajectory. Plot the end-effector position as a function of time, as well as the straight line path. They should be close, if not equal. Plot both the position as a function of time, as well as the position as a parametric plot. | 1. Let's check to see if the manipulator is really following the trajectory. Plot the end-effector position as a function of time, as well as the straight line path. They should be close, if not equal. Plot both the position as a function of time, as well as the position as a parametric plot. |
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| 2. Demo the ''lynx6'' manipulator following the desired end-effector position trajectory. | 2. Plot the joint angles versus time. |
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| | 3. As requested, make sure to turn in the desired body velocity versus time. The body velocity can be provided as two plots, one for the linear velocity and one for the angular velocity. Plotting together can be troublesome since the units differ (unless ``plotyy``` is used and the plot styles vary). However, the angular velocity should be zero, thus turning in only the linear velocity is sufficient. |
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| | 4. Demo the ''lynx6'' manipulator following the desired end-effector position trajectory. |
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| === Testing ==== | === Testing ==== |
