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So, when you do control design you always have a number of parameters that need to
be tweaked and tuned. And there's really no way of selecting these parameters
without actually testing what's going on. So, we have seen how to design now goal to
goal behaviors but we haven't really picked parameters in the PID regulator.
So, what we're going to do now is take what we have done and actually simulate
it. And for that, we're going to use our in-house GRITS robot simulator, which is a
MATLAB-based simulator. It's based on a Khepera [inaudible] differential drive
mobile robots with infrared range sensors around it, so it can detect things in the
environment and odometry is obtained using wheel encoders. and I should point out
that I will be using this simulator quite a lot in this course. and you can actually
download it for free at this address and you can either download it as a standalone
executable, which means you'll be able to run it and interact with the user
interface, or you can download the entire MATLAB package. Now, I will not require
that you use if for the course, but if you want to play around with different control
designs on a robot, this is a very good simulator to start with. So, let's
actually see what it would do. So, I'm going to move over to MATLAB and start up
the simulator. And what we're going to see here is, this is the robot, it's pointing
in some direction. I have placed a goal at negative 1, 1 so it's going to go
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backwards in this direction to get to the goal. So, let's see what it's actually
doing. So, I'm going to start playing this. The robot is turning, turning and,
as you can see here, the blue line is the, is the actual heading and the dotted line,
the red line, is the desired heading. And here, we have quite a bit of overshoot.
So, this is not a particularly good control the sign actually that's going on
because we're overshooting even though we now seem to be stabilizing towards the
direction in which we want to go. So, instead of going in this direction, let'
s, let's see if we can do something better to the, the control parameters. So, I'm
going to open up the file where we define the PID controller. So, I have a p gain, a
proportional gain of 10, an integral gain of 10 and no d gain. Well, the integral
gain of 10 seems rather excessive to me. So, I'm rather brutally going to say, why
don't we make it 0? We're not caring about getting exactly there. So, let's turn it
down to zero and actually see what happens. So, if we do that and close this
window here, and this window, let's see what happens, let's start it off again.
Well, now, let's, let's start the simulator and now, it should go again to
negative 1, 1. And hopefully, we'll we will have cured the robot of its annoying
overshoot. And look at this step response. See how the desired heading goes up to, or
the actual heading goes up to the desired heading quite nicely and then stabilizes
to where we wanted. So now, in simulation, we have verified that this particular
choice of control parameters is, is at least not entirely useless. which is a
good way to start when you actually go on a real robot. So now, let's stop this
simulation business and move on to the actual robot. So, now that we've seen how
to think about control design for building a go to goal behavior, and we even
simulated it with varying degrees of success, let's actually now put it on an
actual robot. So, I'm here with again, JP, who is the master of ceremony and a
Khepera 3 differential drive mobile robot. And we're going to be running exactly the
same code as we did in the simulator. All we're doing is flipping a switch so we're
actually running it on the robot instead of on the simulator. And this differential
drive robot will know where it is based solely on the edometric information it's
getting from the wheel encoders, and its task is, is to make it from here over to
this turquoise gold point here. And a simple PID regulator is enforced and we're
going to use the same parameters as in the simulation With a p of 10, an i gain of 0
and a d gain of 0, so its a pure P-regulator. And without further ado, JP,
let's see how the computer does. ,, , And as you can see the turn was nice, there
are very few or little oscillation here and the Khepera is making it very nicely
all the way to the turquoise goal point. So, we will call that a success.
Dr. Magnus EgerstedtProfessor
