Part 2: Gyroscopic Control of Robotic Smart Vehicles Using SE(3)

Abstract

Abstract This paper deploys the Moving Frame Method (MFM) for the analysis of the gyroscopic-induced pitch of a car; and in the context of a senior design project. While there is a research and development component, the primary focus of this and the companion paper (Part 1) is pedagogical reform to ensure student engagement. First, this paper presents the primary goals of the MFM: to bridge the chasm between engineering mathematics and real-world problems. To this end, this paper presents the underlying MFM theory, discussing aspects of Lie Group theory and associated Lie Algebra, distilled to the simplicity of matrix multiplications. In the project, the undergraduate students accounted for the dual mass system of the spinning disks, precessing gimbals and the mass of the car. It modeled the lift of the car, while avoiding its yaw. It presents a modification of the Runge-Kutta numerical integration scheme to conduct the simulation. It shows design trade-offs, and a comparison between MFM model and experimental results. It presents the motivational questions raised, and how this the MFM empowers insight into the modeling process. The paper then segues into a discussion of how the MFM motivated the manufacturing of the components of the car, the coding of the 3D simulations, and the understanding of machine motion, and motivated international student collaboration. Finally, it closes with the assertion that to inspire engineering students, various interventions might not work as well as modernizing the mathematics.