Hi there, my name is Luis Rodrigues. Welcome to this module on trajectory generation for dense thermomobility. It's a pleasure for me to be talking about these very exciting subject. It's a subject of my own research. Before we start, I would like you to know a little bit more about myself. I'm a professor at the Department of Electrical and Computer Engineering of Concordia University. I started my studies in electrical engineering. I did my bachelor's degree in electrical engineering, and also my master's in electrical engineering. In my master's, I was working on underwater robotics; trajectory generation and control of an underwater robotic vehicle to deploy a lab at the bottom of the ocean. I got very much interested in hydrodynamics and I had a passion for aircrafts, so I decided to go to the Department of Aeronautics and Astronautics at Stanford University for my PhD. My PhD is in aeronautics and astronautics, and ever since, I've been completely in love with aerospace, and I've been working mainly in control systems, navigation systems, and trajectory optimization. That's my background, and we'll start this lecture by some remarks about the scene in advanced air mobility in the province of Quebec in Canada where I teach. Then we'll move into the more detailed trajectory generation and flight control. The major players in the province of Quebec in aerospace in general, and in particular in advanced advance air mobility are universities and companies. Companies, they have some consortiums together and there's some research consortiums that put together companies and universities. It's a very vibrant ecosystem in Quebec. Quebec in particular, Montreal is the capital of aerospace in Canada, and it's probably one of the few cities where you can build an airplane from A to Z around Montreal and probably within 40 kilometers from Montreal. It's one of the top three cities in the world in aerospace after Toulouse and Washington State, Seattle. In terms of universities, so as I said universities and consortiums of companies and also consortiums of companies with universities. In terms of universities, Montreal is a city that has several universities. There's four universities in Montreal. The Concordia University where I work, there's McGill, there's a Coal Polytechnique, which is part of the university at the Montreal, and there's ETS as well in engineering. Those four universities plus the University Laval in Quebec city, and Universite de Sherbrooke. They got together and they formed what is called the Montreal Aerospace Institutes, MAI. That's one of the major players in Quebec which involves is called Montreal Aerospace Institutes, but involves two universities that are outside of Montreal, as I said, Sherbrooke is about 80 kilometers away from Montreal, and Quebec CD, which is the capital of the province of Quebec. Then there's also a collection of universities, which are all called Universite du Quebec, which means Quebec universities. Similar to for example what you find in California, University of California. Then you have the universities at different cities in the province. That's called the Reseau de l'Universite du Quebec, and there's 10 universities in this network. This is from the side of the universities. All universities from the MAI are actively doing research in aerospace and in particular, some of them in air mobility, and also there's one of the universities in the Reseau de l'Universite du Quebec at [inaudible], that has a research chair in aerospace in project management. This is from the universities' side. Then there's a vibrant ecosystem of companies in Montreal. The companies actually formed a consortium called Aero Montreal, and it's a consortium with the board of directors with 35 members, and all major companies are involved into this consortium. Then there's a consortium for research that puts together universities and companies. All the projects in this consortium involve two companies and two universities. The key idea is that these are larger projects in aerospace that involve collaboration of at least two universities and at least two companies. That consortium is called the Consortium de recherche et d'innovation en aerospatiale au Quebec. The acronym is CRIAQ. Then in Canada there's also the Canadian Advanced Air Mobility Consortium or CAAM. There's several other entities that are working in air mobility. Montreal houses headquarters of IATA, which is the representative of the airlines, and also houses the headquarters of ICAO, the International Civil Organization, which focuses on regulations, but they also have teams that work on research projects. One of which is the Ambular Project, which is a project that focuses on the design of an ambulance that can be either manned or unmanned, so if you want, it would be a drone ambulance. This design you can see in the slide right now. That's basically the ecosystem in Montreal and Quebec and in Canada in aerospace in general, in particular in air mobility. Now, air mobility will focus mainly on what is called vertical takeoff and landing aircraft, so VTOL is the acronym for vertical takeoff and landing. They look like helicopters really, but they are electric. There are concerns with both noise and definitely also the emissions to the atmosphere. These vehicles are supposed to go green and be electric vehicles. But the first design, they look like helicopters a bit. The first design of a helicopter, which was called actually an copter, was many years ago by Leonardo da Vinci, who lived in Italy from 1452. He was born in Italy and died in France in 1519. That's what you see here, his sketched in the slide. Then we moved from that design to a more very recent resign of Bell Flight, which is a Textron company that has a headquarters also in Mirabel in Quebec in Montreal. What you see here is the Nexus vertical takeoff and landing. We can see the difference from the 15th century up to now on the designs of these air vehicles. This photo is courtesy of the Wings Magazine article, which is entitled Bell Unveils 4EX Concept at the CES, " in 2020.