This lab introduces some of the basic geometry and algebra that forms the framework for studying motion control from shape change. The problem of parallel parking a car can be interpreted as a motion control problem using shape change. Consider a simplified model of a car where we consider only one independent wheel (think of a unicycle). This wheel can roll along to drive the car forward or backward and it can turn about the vertical axis for steering. In this case, there are two shape variables: one is the roll angle and the other is the turn angle. The goal in performing a parallel park is to use an appropriate sequence of shape changes (driving and steering) to effect the required net sideways motion.

To get warmed up for the lab, try below to manually perform the parallel parking maneuver with the unicycle model of the car. There are buttons for forward and reverse driving and for clockwise and counterclockwise steering.

At the end of this lab, the parallel park maneuver is performed under automatic control. The prescription for the automatic control is based on the framework introduced in the lab. By the end of the lab, you may also want to come back to this page and try out the parallel park maneuver again to see if the mathematical framework which you will have learned can be used to improve your manual control strategy!

You need the Flash 6 plug-in to play with the car. Internet Explorer automatically instralls the plug in, or you may install it following the link: http://www.macromedia.com/shockwave/download/index.cgi? P1_Prod_Version=ShockwaveFlash&P2_Platform=Win32. Click inside the Flash window to activate controls.

If the Flash application isn't working on your computer you can use the old version of car parking applet below:

Your browser is not Java capable.

Try to parallel park the car by clicking the appropriate button to steer and drive the car into the spot on the right side of the screen. Red rectangles represent other parked cars; try not to touch them. To reset the car to its original orientation press the button marked "Reset". The coordinates of a point on the graph can be obtained by clicking anywhere on the graph. The x and y coordinates will be displayed in the lower left hand side of the applet. To zoom in or zoom out, click the appropriate button.