Geometric Control of Thrust Propelled Systems

Sammanfattning: This thesis was motivated and inspired by the AEROWORKS project, a European research project, whose main goal was to deploy multiple heterogeneous unmanned aerial vehicles in environments where human intervention is restricted.In particular, this thesis focuses on control of aerial vehicles for the purposes of cargo transportation, an application of interest, for example, in inspection and maintenance of aging infrastructures.This thesis also focuses on control of multi-agent systems, where agents are required to accomplish some common goal, such as collaborating on transporting a common cargo. In the first part of this thesis, we focus on control of thrust-propelled systems.A thrust-propelled system is similar to a multi-rotor system, where a thrust input is available along some direction, which we can rotate by means of a torque input.In a first step, we develop controllers for the thrust-propelled system, by application of nonlinear control techniques.In a second and final step, we convert a physical system, by means of an appropriate change of coordinates, into the thrust-propelled system form, at which point we are able to leverage the controllers designed in the first step.Among the physical systems considered in this thesis, we highlight slung-load transportation, where a point-mass cargo is tethered to a single aerial vehicle, and slung-bar transportation, where a bar cargo is tethered to two aerial vehicles.Another key idea, exploited throughout this thesis, is that of geometric control, where one attempts to design controllers that are independent of the user choices.For example, when performing an experiment, a user picks a reference frame, and the application of a geometric controller is insensitive to that choice.On the contrary, a non-geometric controller yields different results depending on which frame is chosen.Experiments and simulations illustrate the performance of the proposed control strategies.In the second part of this thesis, we focus on global stabilization of mechanical systems, in contrast with the first part, where almost global and/or local stabilization sufficed.However, for non-contractible sets, which are pervasive throughout this thesis, a globally asymptotically stable equilibrium point does not exist under a continuous control law.In particular, we consider a rigid-body pendulum, which we wish to globally stabilize at some desired configuration.To accomplish the latter, we create a graph between several stabilizing continuous control laws, and switch among them so as to provide the desired equilibrium with a global region of attraction, which we validate in simulations.In the final part of this thesis, we consider a multi-agent system composed of rotation matrices, and we design controllers that guarantee asymptotic incomplete synchronization.In particular, we develop decentralized torque controllers for the agents, and when the directions to be synchronized are principal axes, we are able to propose torque control laws that do not require torque input in all bodies directions, but rather only in the body directions orthogonal to the respective principal axis.Simulations are then presented which illustrate the performance of the proposed control strategy.