So welcome to Module 5 of the course, Control of Mobile Robots. So far the first 2 modules were kind of introductions to the topic and the previous 2 modules they went rather deeply into the issue of, control the sign for linear time in variant systems. And we ended the last module on a high note. Which showed that we could do rather remarkable things, like make a humanoid robot wave in, exciting ways. Using, control of linear time in variant systems. Now, unfortunately, the world isn't that easy. And especially, the robotic world is not that easy. So this entire module is devoted to how do we take Module 4. And make it cope with the realities of the world in which robots are embedded. Then in Module 6, we're actually going to go full force robotics, 100%. And this module can be thought of as the glue module between linear systems and actual robotics. And in fact, the title of this lecture is, Switches Everywhere, because so far the modules, or models have been the same all the time, and in fact, because the models are the same, we design a size fits all type of controller. the way we've kind of messed with the controllers, is by changing the, the, reference values to some desired angles for the.... this humanoid robot, or desired velocities and angular velocities for the segue robot. But, it's certainly not always true that the models never change in the real world. And, this is never true in robotics, unfortunately. In fact, if you recall, what we talked about in module 2. We talked about something called behavior based control. Where the robot switches between different modes of operation, or behaviors, in response to what the world throws at you. You see an obstacle, you switch to avoid that obstacle. If you, need to go recharge you switch to a, let's look for outlets behavior. So what we need to do is somehow come to grips, or terms with this reality. And that is how we're going to start this module. The first thing to note is that in the world there are switches everywhere. So here, over on our left, is a bipedal walking robot. Well, bipedal walking robots have a leg that's swinging, has one dynamics, and then bam, the ro, the leg is on the ground, now the dynamics changed. So because of the fact that the dynamics changes. Depending on whether or not you're in the swing face, or the stance face. The dynamics is different. Here, I drew a cartoon of a bouncing ball. Well, it has 2 modes. It's in the air, [SOUND]. And then it bounces. Something new happens. The b-, the ball gets squished, and then it releases again. So, there. We have switches. I actually included this wonderful picture of locusts because I have actually worked on locusts. These locusts don't bother anyone during what's called a solitary mode. And then something happens and they switch to a gregarious mode where they lump together and devastate harvests everywhere. and this is a transition that occurs because of a lack of food, for instance. But in the, all of these cases, these are naturally occurring switches that our models have to take into account. Now, from a robotics point of view, it may be slightly more relevant to look at switches by design instead of doing it by necessity. So here is a gear box to a car. We're switching between different gears because we want the car to run more smoothly at different RPM's. so we're switching the dynamics not because we have to but because it's better. Here, this is a, a cockpit. It's supposed to be representing an autopilot on an aircraft where you're switching between cruise climb turn land takeoff modes. So, instead of designing 1 controller that takes me from Atlanta, Georgia to Stockholm, Sweden. You have a bunch of different controllers that you're switching through in order to do this. And at the bottom here, we have a sensor network. Where, in order to preserve power, you're turning sensors on and off on purpose. So, you're switching by design, rather by necessity. And, in robotics. Everywhere it switches by design. This is our south driving Georgia Tech car that switches between different behaviors depending on what's happening in the world. Here's a mobile robot that switches between behaviors depending or not, whether or not there are obstacles, I wish we worked on snake robotics. We're switching between different modes, depending on what is going on in the environment. This is a friend in now, this is the sensor network, and this is the aerial robot that we've seen, and we're going to see more of. In all of these cases, we're going to have to switch in order to respond to what the world throw's our way. Now, there are some issues that we need to deal with. Issue number one is really how do we model these switches? How do we model systems that aren't staying the same all the time. Well, the other question then, of course, is if these models change, what about stability? What about the performance? Can we go with our old methods to try to understand this? Well, this all boils down to the fact, that T does not go to infinity, within a single mode. Meaning you are not staying in 1 mode forever, and stability is defined what happens when T goes to infinity, but T does not go to infinity in the in, individual mode. So, we somewhat need to understand that. We also have issues of compositionality. This is fancy speak for saying, if I have multiple modes and multiple controllers, how do I put them together? What is the way in which they fit together like Lego pieces in a big Lego drawing. And, most importantly, are there traps? Are there issues that arise because of these switches that we don't fully know how to deal with. Now, this module will deal with all of this, and more. And in the next lecture, we're going to start with the first question which is, how do we really model hybrid or switched systems in a systematic and coherent way?
