Background:
Normally, the input to the quadrotor control scheme is considered to be the force produced by each propeller. However, this is a simplifying assumption for several reasons. Actually, we control the spinning velocity of the propeller (although supposing to control it instantaneously and perfectly is also an approximation).
The amount of force produced by the propeller is computed based on an identified model that links the propeller velocity to the produced force. Model errors at this stage translate into errors between the commanded control force and the actual input force produced. Moreover, external disturbances such as wind, the presence of walls, etc., affect the model that links the propeller velocity and force. For this reason, closing the loop of the control of UAVs on the propeller force would be beneficial. The force would become a state of the system, while the input is the propeller commanded velocity or PWM. To so do, it is necessary to measure online the force produced by each propeller using additional sensors.
Assignment Description:
This assignment supposes to have a strain gauge on each arm of a quadrotor. Strain gauges measure a deflection angle (they introduce elasticity in the system), but we are interested in understanding how it is possible to measure the propeller forces. The assignment starts from the linearized dynamic equations of a multi-rotor embedding elastic elements (i.e., passive revolute joints modeling the presence of embedded elastic sensors in the arms). In the model, propeller forces are part of the state. The input is the commanded velocity or PWM given to the propellers. The speed of each propeller might be measured or not.
The assignment includes the following steps:
- Studying the Observability of such a system.
- Finding a suitable change of coordinates that decouple the dynamic
equations of the system. - State estimation (including force estimation)
- Parameter estimation (e.g., the time constant of a first-order relation
between the PWM and the propeller actual velocity) - Possibly, designing, and testing in a simulation environment, a controller
(like an MPC) that exploits the new measurements to improve the tracking
control of the drone.