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| ece4560:biped:04rrinvkin [2022/10/23 20:31] – typos | ece4560:biped:04rrinvkin [2023/03/06 10:31] (current) – external edit 127.0.0.1 |
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| <code>[ traj_alpha ] = rr_inv_kin( obj, a_traj_ws, a_time, a_ref_frame, a_ee_frame )</code> | <code>[ traj_alpha ] = rr_inv_kin( obj, a_traj_ws, a_time, a_ref_frame, a_ee_frame )</code> |
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| This method will take a desired (workspace) trajectory of your (selected) foot frame, relative to the **TORSO** frame, and produce a joint trajectory to accomplish it. | This method will take a desired (workspace) trajectory of your (selected) foot frame, relative to the **TORSO** frame, and produces a joint trajectory to accomplish it. |
| The same assumptions, from #1, hold for inputs ''a_ref_frame'' and ''a_ee_frame''. ''a_traj_ws'' represents the foot frame trajectory (with respect to the ''a_ref_frame'' = **TORSO** frame). This is a $3 \times T$ matrix, [ $x$ ; $y$ ; $\theta$ ], where $T$ is the number of waypoints comprising your trajectory and $x$, $y$, $\theta$, here, are $1 \times T$ vectors. ''a_time'' is a $1 \times T$ vector holding timestamps associated with each waypoint in ''a_traj_ws''. The output, ''traj_alpha'', then, is a $3 \times T$ vector that should look something like [ $\alpha_{hip}$ ; $\alpha_{knee}$ ; $\alpha_{ankle}$ ] where $\alpha_{hip}$, $\alpha_{knee}$ and $\alpha_{ankle}$ are $1 \times T$ vectors containing joint trajectories for each joint that is capable of affecting motion of the selected foot frame. | The same assumptions, from #1, hold for inputs ''a_ref_frame'' and ''a_ee_frame''. ''a_traj_ws'' represents the foot frame trajectory (with respect to the ''a_ref_frame'' = **TORSO** frame). This is a $3 \times T$ matrix, [ $x$ ; $y$ ; $\theta$ ], where $T$ is the number of waypoints comprising your trajectory and $x$, $y$, $\theta$, here, are $1 \times T$ vectors. ''a_time'' is a $1 \times T$ vector holding timestamps associated with each waypoint in ''a_traj_ws''. The output, ''traj_alpha'', then, is a $3 \times T$ vector that should look something like [ $\alpha_{hip}$ ; $\alpha_{knee}$ ; $\alpha_{ankle}$ ] where $\alpha_{hip}$, $\alpha_{knee}$ and $\alpha_{ankle}$ are $1 \times T$ vectors containing joint trajectories for each joint that is capable of affecting motion of the selected foot frame. |
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| Generate the following: | Generate the following: |
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| **a.** Plots of each relevant joint angle vs. time (ie. 3 plots) | **( a )** Plots of each relevant joint angle vs. time (ie. 3 plots) |
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| **b.** Plot of $x$-$y$ foot position over time. For 3 different time instants, overlay a visualization of the foot frame on this plot. | **( b )** Plot of $x$-$y$ foot position over time. For 3 different time instants, overlay a visualization of the foot frame on this plot. |
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| **c.** Overlay, onto the plot from **3(b)**, the $x$-$y$ foot position over time (again, relative to the **TORSO** frame or assuming **TORSO** frame is locked to and aligned with the spatial/origin axes) produced by the resolved rate inverse kinematics joint trajectory, ''traj_alpha''. You will have to perform forward kinematics (eg. using ''fwd_kinematics( ... )'') to obtain the the actual accomplished foot frame trajectory. | **( c )** Overlay the $x$-$y$ foot position over time (again, relative to the **TORSO** frame or assuming **TORSO** frame is locked to and aligned with the spatial/origin axes) produced by the resolved rate inverse kinematics joint trajectory, ''traj_alpha''. You will have to perform forward kinematics (eg. using ''fwd_kinematics( ... )'') to obtain the the actual accomplished foot frame trajectory. |
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| **4.** Use ''animateTrajectory( ... )'' to produce an animation of your resolved rate inverse kinematics joint trajectory, ''traj_alpha''. | **4.** Use ''animateTrajectory( ... )'' to produce an animation of your resolved rate inverse kinematics joint trajectory, ''traj_alpha''. |
