Description
Goal
This week, you will design a control system that makes a 2D quadrotor (a “bi-rotor”) deliver ten
packages as fast as possible. You will implement your control system by modifying the script:
hw10_ControlLoopTemplate.m
You will test your control system with the script:
hw10_Simulation.m
Instructions on exactly how to do these two things will be posted to piazza.
Model
The dynamics of the robot are:
mq¨1 = − (fR + fL) sin q3
mq¨2 = (fR + fL) cos q3 − mg
Jq¨3 = w (fR − fL)
(1)
where
• m is the mass;
• J is the moment of inertia about the center of mass;
• w is the spar length;
• (q1, q2) is the position of the center of mass of the robot;
• q3 is the angle of the robot from horizontal (in radians);
• fR and fL are the forces supplied by the right and left rotor, respectively.
To “hover” means to achieve zero motion at q3 = 0, which—by examination of (2)—can only be
achieved when fR + fL = mg. Near hover, the dynamics can be linearly approximated by
mq¨1 = −mgq3
mq¨2 = (fR + fL) − mg
Jq¨3 = w (fR − fL)
(2)
You now have a linear set of ODEs, which you can proceed to put in state space form and use as
the basis for control design. As you will see in hw10_ControlLoopTemplate.m, you have access to
a noisy measurement of position (q1, q2) and a not-so-noisy measurement of angular velocity ˙q3.
It is of course possible to define a set of outputs that correspond to these measurements, to put
these outputs in state space form, and to use them as the basis for an observer. Note that rotors
cannot produce negative thrust. So fR and fL will be bounded below by 0 (and bounded above by
simdata.params.fmax). This fact may be important when implementing your observer.
1
Three Tasks
Your control system has three tasks:
• To pick up packages by hovering near the point pFrom.
• To deliver packages by hovering near the point pTo.
Note that pTo is only non-empty when the robot has a package to deliver. Note also that
packages have mass. When the robot has a package—i.e., when pTo is non-empty—both its
mass and its moment of inertia increase from m and J to m + mpackage and J + Jpackage.
Your control design will need to take this fact into account (e.g., by switching between a “no
package” design and a “yes package” design, or by using integral action).
• To recharge the robot’s battery, when necessary, by hovering near the point pBattery.
Note that the level of charge γ in the battery, when it is not recharging, satisfies
γ˙ = kbattery
f
2
R + f
2
L
In other words, the charge decreases faster when the rotors are producing more thrust. You’ll
want to make sure you don’t let your robot run out of charge.
Note that all three of these tasks require you to hover near a point. A good strategy might be to
design one control system that can hover near any given point, and then just switch the point.
What to Turn In
You may work, if you like, with one partner. The two of you should submit the following:
• A single MATLAB script to replace hw10_ControlLoopTemplate.m, with your final control
system. You must call this script hw10_NAME1_NAME2.m, where “NAME1” and “NAME2” are
replaced with the first five letters of your first name (in capitals) followed by the first letter
of your last name (in capitals) and—if you are working in a group—your teammate. Details
on how to submit your code will be posted to piazza.
• A brief description of your design process. If you use state space methods, this process should
at least include the following:
– Derivation of a state space model of the system (starting from what is described above).
– Analysis of controllability and observability.
– Design of controller and observer, either by eigenvalue placement or by optimality.
– Simulation results, and their use to refine or validate your control system.
If you use classical methods, the design process should at least include the following:
– A block diagram model of the system.
– Analysis of time response.
– Analysis of frequency response.
– Simulation results, and their use to refine or validate your control system.
Please be very concise. A formal report is not required.
As discussed in class, we will have a contest in class on the due date. Details of this contest—and
of opportunities for extra credit—will be posted online.