Rover Positioning

Background:  
The FIDO rover uses four systems to determine its location during surface operations.

• The rover uses wheel odometry as its primary positioning system. This is simply knowing how many times the wheels have rotated. The distance traveled can be calculated by multiplying the wheel's circumference by the number of rotations. Wheel odometry also includes knowing the angle through which the wheels have rotated when making a turn. In this way, the rover's heading relative to it's initial direction is known.

• A sun sensor is used to orient the rover's frame of reference to an absolute frame of reference. Since the Sun's position is a known quantity at all times, the rover's relative headings can be translated to an absolute direction.

• On-board gyroscopes are used to measure the rover's rate of pitch, yaw, and roll. This information is used to determine the rover's orientation, say if it is sitting at a slant, relative to it's beginning orientation. It is also possible to obtain position information from the gyroscope measurements. Since the gyroscopes measure the velocity of the pitch, yaw, and roll, integrating the measurements gives positional information (since velocity is the first derivative of position). But, the integration over time serves to magnify any errors. Errors are introduced into the measurements due to the gyroscopes themselves. Over time gyroscopes 'drift'. This drift can be roughly corrected for by testing the gyroscopes before launch and measuring the amount of drift with time, but errors will be introduced nonetheless.

• The accelerometers are used to determine the rover's attitude with respect to the local gravitational field. The accelerometer measurements are used to convert from the rover's frame of reference to that of the absolute frame of reference. And, since the hazard camera, belly camera, and sun sensor, are rigidly mounted to the rover, their attitude needs to be known. (Note: accelerometers are not used for determining the rover's exact position, since the required double integration would significantly magnify errors.)

All these measurements are tied together in what is called "State Fusion." That is the determination of the absolute position and attitude of the rover on the surface.

Activity: 
A graphing calculator and a CBL can be used for exploring the accelerations that occur around you, such as a car, an elevator, or a roller coaster. Acceleration is a change in velocity during a time interval. This change in velocity can either be a change in speed or a change in the direction of motion. Direction is indicated by the algebraic sign of the acceleration: a positive sign indicates increasing positive distances from the origin, while a negative sign indicates decreasing positive distances from the origin. For example, while riding in a car that leaves from a stop sign, you undergo positive acceleration. As the car slows to a stop, you experienece a negative acceleration.

Materials:

• TI-83+ calculator and CBL
• Vernier Software's PHYSICS program
• low-g accelerometer

Procedure:

1. Connect and turn on the calculator and CBL. Start the PHYSICS application.
2. Setup one LOW-G ACCELEROMETER using the stored calibration.
3. Use the manual TRIGGERING option to collect data. This allows you to disconnect the calculator from the CBL.
4. Orient the arrow in the direction you plan to take data (either horizontally or vertically) and zero the accelerometer.
5. Enter a data collection rate (usually 0.5 seconds between samples is adequate).
6. To begin data collection, disconnect the calculator and press the TRIGGER button on the CBL.
7. Once the CBL displays DONE, reconnect the calculator and use the RETRIEVE DATA option.
8. Time values (in seconds) will be stored in list #1 and accelerations (in m/s²) will be stored in list #2. An acceleration versus time graph will be displayed.

Analysis:

• Linear Acceleration on a Road - Lay the accelerometer on the dashboard of a car. Zero the accelerometer with the arrow pointed horizontally toward the front windshield and collect data for 30 seconds. Have the driver accelerate to a safe speed and then slow to a stop. Compare different cars and manual vs automatic transmissions.

• Centripetal Acceleration around a Corner - Lay the accelerometer on the dashboard of a car. Zero the accelerometer with the arrow point horizontally toward the driver's side window and collect data for 20 seconds. Have the driver make a wide, left-hand turn maintaining a constant rate of speed. Compare circular turns of different radii.

• Acceleration in an Elevator - Place the accelerometer against the wall of an elevator. Zero the accelerometer with its arrow pointing upward and collect data for the transit time of the elevator. Compare the motion of the elevator as it moves upward and downward.

• Acceleration of the Vertical Loop on a Roller Coaster - Secure the accelerometer inside a fanny pack around the rider's waist. Zero the accelerometer with the arrow pointed vertically upwards and collect data for 15 seconds. Compare the accelerations at the top, bottom, and sides of the loop.

Credits:

• Dr Ray Arvidson & staff, Washington University
• Texas Instruments
• Vernier Software

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