This repository has been created for the project of the master course "Computational Control" with Dr. Saverio Bolognani. The project is a simulation of the SpaceX Falcon 9 vertical landing phase its purpose is to develop a controller to land the rocket.
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$(x,y)$ : the 2D position of the rocket center of mass [m] -
$(\dot{x},\dot{y})$ : the velocity of the rocket [m/s] -
$\theta$ : the angle of the rocket [rad] -
$\dot{\theta }$ : the angular velocity of the rocket [rad/s] -
$c_{L}, c_{R}$ : binary variables indicating wether the left or right legs are in contact with the environment, respectively (equal to 0 otherwise)
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$F_{E}$ : the thrust produced by the main engine in Newtons, acting directly on the rocket body at the point where the nozzle pivots -
$F_{S}$ : the thrust produced by the side gas thrusters in Newtons, defined as the difference$F_{L}-F_{R}$ , acting at a distance$l_{2}$ from the rocket center of mass -
$\phi$ : the angle of the nozzle with respect to the rocket body in radians, which changes the direction of$F_{E}$ . It can be discontinuous and it has instant response up to the 60 fps frame rate of our model
Even though a PID controller works well under "easy" initial states, it fails for more complex scenarios. Therefore, I chose to use a tracking MPC for the following reasons:
- Constraints handling: the incorporation of the constraints during the design of the MPC provides a safe operation of the rocket within its boundaries
- Trajectory optimization: the fact that the MPC optimizes the trajectory over a finite time horizon at each time step results in smoother and more accurate tracking
- Nonlinear System Handling: even though the tracking MPC uses a linear model of the rocket, it is still more robust to nonlinearities than the PID controller
