| Summary: | Mecanum wheels are often used in vehicle/robotics applications where agility is a top priority, since they can be used to translate the vehicle in any direction on the ground as well as rotate around any center point. However, the standard placement and orientation of these wheels is quite rigidly adhered to in common practice, causing little to no flexibility and variation in this aspect of the vehicle's design. This thesis shows how the use of mecanum wheels need not fall under such constraints that are currently so widespread. Design considerations for arbitrary arrangements of mecanum wheels are presented, as well as some motivations for deviating from standard configurations. A system for controlling a vehicle with an unconventional arrangement of mecanum wheels is developed, proving that the wheel's rotational axes and relative placement need not align in any specific way. Furthermore, equations are derived and presented that permit for the control of any number of mecanum wheels in any arbitrary configuration on the vehicle. This control is possible for the user simply by measuring a few key details about the vehicle's wheels: for each wheel, the location of the wheel in the vehicle's coordinate frame, the positive-signal direction of the motors, and the angle of the wheel's diagonal rollers. To prove the results, a random arrangement of wheels is generated and assembled on a robot, which is successfully controlled using the framework described in this thesis. Also, an example is given of a robot which uses the methodology described to compete very successfully in an MIT robotics class competition.
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