We propose a dynamic controller for position tracking of a point-mass load attached to an omnidirectional aerial vehicle by means of a cable. Both the load and the aerial vehicle are subject to unknown wind forces. We model the dynamics of the slung-load system and put it into canonical form, i.e., a form which is independent of the system's physical parameters. Following a backstepping strategy, we design a dynamic control law for the canonical system that contains four estimators, since each of the two wind disturbances has two separate effects: an effect on the linear acceleration and another on the angular acceleration. Loosely speaking, the difference between the wind forces is an input-additive disturbance, while the wind force on the load is not, which makes removing the wind force on the load nontrivial. We identify conditions on the desired position trajectory and on the wind on the load, which guarantee that a well-defined equilibrium trajectory exists. The designed controller guarantees simultaneously that the latter trajectory is asymptotically tracked and the cable remains taut, provided that the system is initialized in a suitable set. Simulations illustrate our results.

A real-time 3-D trajectory planner for the leader-following formation control of autonomous vehicles is proposed. The planner relies on the definition of a trailer body whose hinge point is rigidly attached to the leader and assigns each follower to a distinct point of such a trailer. Convergence results for the trailer body reference frame are presented based on Lyapunov analysis, which guarantee that the planning can be independently implemented by n followers, with a common leader, as they asymptotically behave as n points of a unique trailer body. As such, the need for communication among followers is dispensable. The proposed strategy is divided into trajectory planning and trajectory tracking, the first problem being vehicle-independent. Experimental results obtained with quadrotor vehicles are presented, which demonstrate the richness and suitability of the planned trajectories.

This work focuses on the modeling, control and analysis of a bar, tethered to two unmanned aerial vehicles, which is required to stabilize around a desired pose. We derive the equations of motion of the system, we close the loop by equipping each UAV with a PID control law, and finally we linearize the closed-loop vector field around some equilibrium points of interest. When requiring the bar to stay on the horizontal plane and under no normal stress, we verify that the bar's motion is decomposable into three decoupled motions, namely a longitudinal, a lateral and a vertical: for a symmetric system, each of those motions is further decomposed into two decoupled sub-motions, one linear and one angular; for an asymmetric system, we provide relations on the UAVs' gains that compensate for the system asymmetries and which decouple the linear sub-motions from the angular sub-motions. From this analysis, we provide conditions, based on the system's physical parameters, that describe good and bad types of asymmetries. Finally, when requiring the bar to pitch or to be under normal stress, we verify that there is a coupling between the longitudinal and the vertical motions, and that a positive normal stress (tension) has a positive effect on the stability, while a negative normal stress (compression) has a negative effect on the stability.

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.

Denna avhandling inspirerades av AEROWORKS, ett europeiskt forskningsprojekt vars huvudsakliga syfte var att distribuera flera heterogena obemannade flygplan i miljöer med begränsat mänskligt ingripande. Avhandlingen undersöker kontroll av flygplan för lasttransport, vilket är en viktig tillämpning vid till exempel inspektion och underhåll av åldringsinfrastrukturer.

Därutöver fokuserar avhandlingen på kontroll av multi-agent system där agenter ska uppnå ett gemensamt mål, som exempelvis vid samarbete för transporter av gemensam last. I den första delen av avhandlingen fokuserar vi på kontroll av tryckdrivna system. Ett tryckdrivet system liknar ett flerrotorsystem där en tryckingång är tillgänglig i flera riktningar, vilket vi kan rotera med en momentinmatning. I ett första steg utvecklar vi regulatorer för det tryckdrivna systemet genom att tillämpa icke-linjär reglerteknik. I ett andra och sista steg omvandlar vi {ett fysiskt system} med en lämplig koordinatändring i det tryckdrivna systemet, vilket möjliggör att använda de styrenheter som utformats i det första steget.

Bland de fysiska system som undersöks betonar vi flygtransporter med hängande last där en last är kopplad till ett luftfordon, samt där en last är kopplad till två luftfordon. En annan nyckelidé, som används i hela avhandlingen, är geometrisk reglerteknik där man försöker utforma regulatorer som är oberoende av användarval. Detta innebär att när ett experiment utförs och en användare väljer en referensram, är applikationen av en geometrisk regulator okänslig inför valet av referensram. En icke-geometrisk regulator däremot ger olika resultat beroende på vilken ram som väljs. Experiment och simuleringar illustrerar prestandan för de föreslagna kontrollstrategierna för olika mekaniska system.

I den andra delen av denna avhandling fokuserar vi på global stabilisering av mekaniska system, i motsats till den första delen, där i mindre utsträckning global till lokal stabilisering var tillräcklig. För non-contractible sets, som återfinns genomgående i avhandlingen, existerar dock inte en global stabil asymptotiskt jämviktspunkt under en kontinuerlig reglersignal. Vi tar särskilt i beaktning en fast pendel som vi önskar stabilisera globalt vid en specifik önskad konfiguration. För att uppnå det ovan beskrivna skapar vi ett diagram mellan flera stabiliserande kontinuerliga reglersignaler och växlar mellan dessa för att uppnå den önskade jämvikten med en global samlingsregion. Detta har vi validerat i simuleringar.

I den sista delen av avhandlingen undersöker vi ett multi-agent system som består av rotationsmatriser, och vi utformar regulatorer som garanterar asymptotisk ofullständig synkronisering. Framför allt utvecklar vi decentraliserade vridmomentregulatorer för agenterna. När riktningarna som ska synkroniseras är huvudaxlarna kan vi föreslå regulatorsignaler för vridmoment som inte kräver vridmoment-inmatning i alla riktningar, utan endast i riktningarna ortogonala respektive huvudaxel. Slutligen presenteras simuleringar som illustrerar resultatet av den föreslagna reglerstrategin.

We consider a system composed of a bar tethered to two unmanned aerial vehicles (UAVs), where the cables behave as rigid links under tensile forces, and with the control objective of stabilizing the bar's pose around a desired pose. Each UAV is equipped with a PID control law, and we verify that the bar's motion is decomposable into three decoupled motions, namely a longitudinal, a lateral and a vertical. We then provide relations between the UAVs' gains, which, if satisfied, allows us to decompose each of those motions into two cascaded motions; the latter relations between the UAVs' gains are found so as to counteract the system asymmetries, such as the different cable lengths and the different UAVs' weights. Finally, we provide conditions, based on the system's physical parameters, that describe good and bad types of asymmetries. We present experiments that demonstrate the stabilization of the bar's pose.

We propose a control law for stabilization of a bar tethered to two aerial vehicles, and provide conditions on the control law's gains that guarantee exponential stability of the equilibrium. Given the proposed control law, we analyze the stability of the equilibrium for two cases, specifically, for a bar of known and unknown mass. We provide lower bounds on the attitude gains of the UAVs' attitude inner loop that guarantee exponential stability of the equilibrium. We also include an integral action term in the control law, so as to compensate for battery drainage and model mismatches, and we provide a lower bound on the integral gain that guarantees stability of the equilibrium. We present an experiment that demonstrates the stabilization and that validates the robustness of the proposed control law.

We model a point mass load tethered to two aerial vehicles, and propose a control strategy that guarantees that the load tracks a desired position trajectory. Our framework consists in designing an input and a state transformation which converts the quadrotors-load system into three decoupled subsystems: one concerning the position of the load, with dynamics similar to those of an under-actuated aerial vehicle; one concerning the angle between the cables, with double integrator dynamics; and another concerning the yaw motion of the plane formed by the cables, also with double integrator dynamics. Once the decoupling is done, controllers from the literature can be leveraged, which we take advantage of when controlling the subsystem with dynamics similar to those of an under-actuated aerial vehicle. Simulations are presented which validate the proposed algorithm.

In this paper we study a family of controllers that guarantees attitude synchronization for a network of agents in the unit sphere domain, i.e.,S-2. We propose distributed continuous controllers for elements whose dynamics are controllable, i.e., control with torque as command, and which can be implemented by each individual agent without the need of a common global orientation frame among the network, i.e., it requires only local information that can be measured by each individual agent from its own orientation frame. The controllers are constructed as functions of distance functions in S-2, and we provide conditions on those distance functions that guarantee that i) a synchronized network of agents is locally asymptotically stable for an arbitrary connected network graph; ii) a synchronized network is asymptotically achieved for almost all initial conditions in a tree network graph. When performing synchronization along a principal axis, we propose controllers that do not require full torque, but rather torque orthogonal to that principal axis; while for synchronization along other axes, the proposed controllers require full torque. We also study the equilibria configurations that come with specific types of network graphs. The proposed strategies can be used in attitude synchronization of swarms of under actuated rigid bodies, such as satellites.

In this paper, a trajectory planner for n autonomous vehicles following a common leader is presented, with the planning being accomplished in real time and in a three dimensional setting. The trajectory planner is designed such that n follower vehicles behave as n distinct points of a unique two dimensional trailer attached to a single leader vehicle. We prove that for a wide range of initial conditions the trailer reference frame converges to a unique solution, meaning that convergence to a fixed formation of n + 1 vehicles is guaranteed and each follower can plan its trajectory independently from its peers, thereby reducing the need for communication among vehicles. Bounds on the planned velocity and acceleration, provide conditions for the feasibility of the planned trajectory. An experimental validation of the planner's behavior is presented with quadrotor vehicles, demonstrating the richness of the planned trajectories.

We consider a system composed of a bar tethered to two aerial vehicles, and develop a controller for pose tracking of the bar, i.e., a controller for position and attitude tracking. Our first control step is to provide an input and a state transformations which convert the system vector field into one that highlights the cascaded structure of the problem. We then design a controller for the transformed system by exploring that cascaded structure. There are three main contributions: i) we provide bounds on the linear and angular acceleration of the bar that guarantee well-posedness of the controller, and such bounds can be used when selecting the gains and saturations of bounded controllers for both three dimensional and unit vector double integrators; ii) the proposed control law includes a degree of freedom which can be used to regulate the relative position between the aerial vehicles; and iii) the proposed control law for the throttle guarantees that the cascaded structure of the problem is preserved. Simulations are presented which validate the proposed algorithm.