4 Gimbal IMU Non-linear Control Scheme
Standard Inertial Measurement Units (IMUs) have 3 gimbals and are susceptible to a condition known as gimbal lock. Adding an additional gimbal creates a redundant axis of control that can be manipulated to avoid a gimbal lock condition. Additionally, attitude control of the stable platform mounted at the center of the guidance system is highly non-linear. So I set out to develop a nonlinear control scheme based on Lyapunov functions for a 4 gimbal IMU.
Simulink Setup
The Simulink setup is shown on the left and it highlights the main portions of this system: real-world affects of friction and motor saturation, a 4 gimbal plant, an integrator, and a plotting function.
Gimbal Motion Simulation
The whole purpose of this project was to develop a control scheme to keep the platform (the purple gimbal) stationary with respect to inertial space. As you can see in the GIF, this approach has merit: there is little motion of the platform while the other gimbals move around it.
One improvement I would make on this project is to add the kinetic energy of the outer gimbal (blue) to the Lyapunov function. The control scheme attempts to minimize the value of the Lyapunov function. Currently only the kinetic energy of the platform is considered, which is why the blue gimbal picks up speed over time.