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prelab4

# prelab4 - ECE194D...

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ECE 194D Prelab 4: Due Thursday, April 21, 2011 at 5pm (in dropbox) Spring 2011 Page 1 of 3 Prelab 4: Omnibot trajectory planning and feedforward control This prelab involves 3 goals: 1) Planning kinematics for wheel rotations of the omnibot, to move the “body” of the vehicle as desired, 2) determining how “quickly” to play back these trajectories over time, and 3) designing a feedforward element to your controller, to compensate for both linear and nonlinear dynamics of the motor system. The prelab involves both paper calculations and generation of MATLAB code. Even if your code does not work perfectly, it should help enormously for you to have worked out some of the issues in planning and control ahead of time. You will need to build off of your code this week to prepare for Lab 5, as well, so don’t fall behind! Problem 1) Derive the Jacobian matrix that relates joint velocities, ݍሶ ൌ ሾݍሶ ݍሶ ݍሶ (i.e., wheel rotations,) to velocities of the center of body of the vehicle chassis, ߦ ൌ ሾ ݔሶ ݕሶ ߶ , where the subscript I indicates that coordinates are with respect to the global (aka “inertial”) reference frame. (Recall the Jacobian is defined by: ߦ ൌܬݍሶ .) For full credit, your derivation should include steps such as 1A through 1C below; parts 1D and 1E are required MATLAB. Pages 47-60 in the Siegwart handout (from Lecture 7) may be helpful; equation (3.19) has the

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prelab4 - ECE194D...

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