# Modeling and Parametric Selection

The second main goal of this Special Problems course was to model the various versions of the Open Rover. There are three version of Open Rover: 4 wheels(two hub motors, two passive motors), 4 wheels all hub motors, and 6 wheels all powered. The main requirement difference between the 4 wheeled and 6 wheeled rover was to give an additional option for applications that would require higher torques e.g. hauling a large load or climbing more difficult terrain. The 4 wheeled model with only two hub motors is the proof of concept that will be constructed. Only two hub motors are available for the PoC. Coming into this project, there was no true guiding principle that would dictate the Rover’s dimensions. The general idea was to have sizing similar to a push mower. Multiple metrics were extracted from the PhD thesis of Thomas THÜER. Theta of static stability is the maximum angle in which the stability margin becomes zero. The x(longitudinal) and y(lateral) variables are independent of each other and stability is calculated based on the geometry of the center of gravity compared to the points where the wheels contact the ground. The formula is as follows:

**ThetaSS = atan(Xrear/z)**

**Longitudinal and lateral stability figured taken from Thomas THÜER PhD thesis ^{1}**

Xrear can be exchanged for Yleft/right, and both are half of the width and length respectively because the vehicle has a symmetrical center of gravity on both the x and y axis. Therefore, the wider and longer the Rover is at a specific height, the more stable it is. There is an arbitrary factor of, from a practical standpoint, how large the Rover be.

A three dimensional graph was created to give a better view of how the Theta of static stability changes with varying dimensions.

The first model had a length of 1 meter and a width of 0.5 meters. To maximize the Rover’s stability in both the x and y, 0.75 meters was selected. Cost and practicality are limiting factors in making the rover any larger. For the target applications, the general size of a yard lawn mow used as a guiding principle. This improved the combined static stability as the table below shows:

The initial design of the 4 wheeled Rover was going to be a static frame. By adding a simple pivot point to the front pair of wheels, the stability of the Rover is improved by allowing all of the wheels to maintain contact with the ground.

A six wheel model was designed for applications that would require higher torque. For the sake of reusability and consistency, the back suspension was replicated on each side of the main chassis for two independent boogie suspensions. This continues the dynamic of allowing all wheels to be in contact with the ground as an obstacle is traversed. The main frame expanded to 1.0 meters in length to allow enough clearance between the rear wheels and the middle wheels in the boogie. The ExoMars rover was inspiration for this suspension configuration.^{2}

Footnotes: