Towards autonomous navigation: nonlinear observers for simultaneous localization and mapping and secure formation control

Autonomous navigation is a basic ability for mobile robots. To do this, robots need sensors to detect their surroundings and their movement; actuators to move; and a cognitive system to reason and plan. In this thesis, I investigate two different problems related to autonomous navigation. The first problem is how to map and self-localize in an unknown environment when the sensors provide only incomplete information. Think of a camera, you can only measure relative angles in relation to objects, but not relative distances. This problem is hard to solve because the robot has less data to work with. In this thesis, I present new nonlinear observers as a solution and show their effectiveness through mathematical analysis, multiple simulations, and experiments with an autonomous drone. The second problem is about ensuring privacy and security when a fleet of robots is using third-party computers to perform computations. Think about cloud services. In this case, the fleet needs to maintain a certain shape while navigating. This problem is called secure formation control, and a previous work solved it by using a special encryption scheme together with a new quantizer. This method works because the encryption scheme permits to directly perform mathematical operations on the encrypted data. In this thesis, I analyze the effectiveness of this solution through mathematical analysis and simulation.