quiz3solutions

quiz3solutions - CMPE 8 NAME: Fall 2009 Quiz 3 Test Time:...

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Unformatted text preview: CMPE 8 NAME: Fall 2009 Quiz 3 Test Time: 8:05—8:35 AM . E 1. (5 points) Our robot has position variables a: and y, and orientation variable 9. The control inputs are the translational speed u and rotational speed '0. Write the discrete— tim‘eéidfg‘namic model of the robot, which shows how the position and orientation 4 * \offighe robmo \{Iolve in time, as a function of the translational and rotational Speeds. 3rd, y A x xi; x 2. For the dynamic model of the robot above, (a) (5 points) Compute the equilibrium position(s) and orientation(s) (513*,y*,6*). Also, determine the commanded speeds (in, 12*) that are required for the robot to be at equilibrium: ’ (b) (5 pornts)" of any equilibrium point (93*, y*, 6*)? 3. (10 points) Write a function in Matlab whose output is a plot of an orbit for the model xk+1 2 56k — acos(sck) + blog(a:i). (1) Define the function to have four INPUT arguments: the parameters a and b, the initial value :31 and the orbit length N. Name the file NewFun . m. The orbit should be plotted versus iteration number (So, :51 at 1, $2 at 2, ...., and mN at N). 10. 4. (5 points) Write the Matlab command that you would enter in the workspace to create an orbit for the model (1), starting from $1 = 0.12, with a = 2, b = 3 and N = 500. ...
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quiz3solutions - CMPE 8 NAME: Fall 2009 Quiz 3 Test Time:...

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