To simplify the control of their autonomous underwater vehicle, Juan Rojas and Nathan Liebrecht of the Autonomous Robotic Vehicle Project at the University of Alberta join Connell D'Souza of MathWorks® to talk about using MATLAB® to design, simulate, and implement a Linear-Quadratic Regulator (LQR) controller for their vehicle.
Juan and Nathan start by explaining, at a high level, the theory behind an LQR Controller. LQR Controllers are based on optimal control theory which
allows
the submarine to perform complex maneuvers. This allows them to supply a target state, which the controller, using the state estimator, converts to percent-of-effort motor commands. They also discuss the benefits of an LQR over a PID controller for their vehicle.
Juan and Nathan then demonstrate their workflow for designing this system. They use MATLAB and the Symbolic Math Toolbox™ to symbolically solve the system equations and linearize them. The
ccode
function is then used to convert these symbolic expressions to C code, which is then pasted into a Python script that runs on their vehicle. Juan also demonstrates using MATLAB to simulate the behavior of this controller in
an ROS-enabled
simulation platform.
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