Part 1: Gyroscopic Control of Robotic Smart Vehicles Using SO(3)

Abstract

Abstract In response to challenges faced in engineering education, this paper presents the Moving Frame Method (MFM) as an alternative to the existing pedagogies. This paper, and a companion paper, present the MFM for the analysis of rigid single-bodies, in the context of an international collaborative senior design project between two engineering schools: The Cooper Union in New York, NY and The Western Norway University of Applied Sciences in Bergen, Norway. Students at Cooper Union analyzed the smart vehicle as a single-body problem; a second team in Norway used the same method to model the problem as a multi-body. Both teams modeled the gyroscopic lift effect using the foundational theory of the MFM. This first paper presents the underlying theory of how the MFM uses the Special Orthogonal Group, SO(3), to model the problem of gyroscopic lift of a smart vehicle. It presents the underlying theory: motion of a reference frame in terms of the reference frame; and the various properties of SO(3) and its associated algebra as applied to a new, undergraduate approach to dynamics. The paper presents two design alternatives to lift a vehicle, the first one uses two gyroscopes and the second a single reaction wheel. The modeling and analysis process led to the design that employs a single reaction wheel. Next, it examines the model-generated estimates for torque generated and subsequent motion of the car. After analysis using the initial model, the Cooper Union Team pivoted a design approach before entering the rapid prototyping phase of the project. Then, it discusses the manufacturing process for the final version of the car and the construction of a test enclosure for ensuring safety by containing the heavy reaction wheel spinning at high speeds. Finally, it describes the testing of the car, which involves measurement of angular impulse due to a braking event. The results from initial experiments on the prototype validate the model and confirm that the car can lift itself using the selected method.