This paper investigates the rendezvous problem for the autonomous cooperative landing of an unmanned aerial vehicle (UAV) on an unmanned surface vehicle (USV). Such heterogeneous agents, with nonlinear dynamics, are dynamically decoupled but share a common cooperative rendezvous task. The underlying control scheme is based on distributed Model Predictive Control (MPC). The main contribution is a rendezvous algorithm with an online update rule of the rendezvous location. The algorithm only requires the agents to exchange information when they can not guarantee to rendezvous. Hence, the exchange of information occurs aperiodically, which reduces the necessary communication between the agents. Furthermore, we prove that the algorithm guarantees recursive feasibility. The simulation results illustrate the effectiveness of the proposed algorithm applied to the problem of autonomous cooperative landing.

This thesis investigates cooperative maneuvers for aerial vehicles autonomously landing on moving platforms. The objective has been to develop methods for safely performing such landings on real systems subject to a variety of disturbances, as well as physical and computational constraints. Two specific examples are considered: the landing of a fixed-wing drone on top of a moving ground carriage; and the landing of a quadcopter on the deck of a boat. The maneuvers are executed in a cooperative manner where both vehicles are allowed to take actions to reach their common objective, while avoiding safety based spatial constraints. Applications of such systems can be found in, for example, autonomous deliveries, emergency landings, and in search and rescue missions. Particular challenges of cooperative landing maneuvers include the heterogeneous and nonlinear dynamics, the coupled control, the sensitivity to disturbances, and the safety criticality of performing a high-velocity landing maneuver.

In this thesis, a cooperative landing algorithm based on Model Predictive Control (MPC) that includes spatial safety constraints for avoiding dangerous regions is developed. MPC offers many advantages for the autonomous landing problem, with its ability to explicitly consider dynamic equations, constraints, and disturbances directly in the computation of the control inputs. It is shown that the cooperative landing MPC can be decoupled into a horizontal and a vertical sub-problem. This result makes the optimization problems significantly less computationally demandingand facilitates the real-time implementation. The autonomous landing maneuver is further improved by the employment of a variable horizon. The variable-horizon MPC framework lets the finite horizon length become a part of the optimization problem, and makes it possible to always extend the horizon to the end of the landing maneuver. An algorithm for variable horizon MPC that can be implemented to real-time systems is derived by the use of efficient update rules, and by taking into account the similarities between the multiple optimization problems that we have to solve in each sampling period. The algorithm is fast enough to be used even in time-critical systems with long horizons. Furthermore, the solution time of the variable-horizon MPC decreases as the target gets closer. This means that the computational demand becomes smaller in the most critical part of the landing maneuver.

The algorithms are derived for two different landing systems, and are subsequently implemented in realistic simulations and in real-world outdoors flight tests through the WASP research arena. The results demonstrate both that the controllers are practically implementable on real systems with computational limitations, and that the suggested controller can successfully be used to perform the cooperative landing under the influence of external disturbances and under the constraint of various safety requirements.

Denna avhandling behandlar kooperativa och autonoma landningar av drönare på mobila landingsplattformar, och undersöker hur sådana landningar effektivt kan implementeras på verkliga system som påverkas av externa störningar och som samtidigt arbetar under fysiska och beräkningsmässiga begränsningar. Två exempel betraktas särskilt: först landingen av ett autonomt flygplan på en markfarkost, därefter landning av en quadcopter på en båt. Landningarna utförs kooperativt,vilket innebär att båda fordonen har möjlighet att påverka systemet för att fullborda landningen. Denna typ av system har applikationer bland annat inom autonoma leveranser, nödlandningar, samt inom eftersöknings- och räddningsuppdrag. Forskningen motiveras av ett behov av effektiva och säkra autonoma landingsmanövrar, för fordon med heterogen och komplex dynamik som samtidigt måste uppfylla ett antal säkerhetsvillkor.

Reglermetoden som appliceras är modell-prediktiv reglerteknik (MPC), en optimeringsbaserad metod där ett optimalt reglerproblem med ändlig horisont löses under varje samplingsperiod. Denna metod tillför till det autonoma landningsproblemet fördelar såsom explicit hantering av systemdynamik, samt direkt inkludering av störningshantering och bivillkor vid beräkning av insignaler. På så sätt kan vi direkt i optimeringslösaren hantera säkerhetsvillkor och externa störningar. Det visas i avhandlingen hur lösningstiden för optimeringen kan effektiviseras genom att separera den horisontella och den vertikala dynamiken till två subproblem som löses sekvensiellt. Därefter härleds en ny algoritm för variabel-horisont MPC, där horisonten tillåts variera som en del av optimeringsproblemet i MPC-regulatorn. Algoritmen använder sig av effektiva uppdateringsregler och tar hänsyn till de likheter som finns i strukturen på de flertalet optimeringsproblem som löses under varje samplingstid. Vi visar dels att algoritmen är tillräckligt effektiv för att implementeras på system även med långa horisonter, och även att lösningstiden går ner när manövern går mot sitt slutskede. Detta betyder att kraven på systemets beräkningskraft minskar under den mest kritiska delen.

Algoritmen implementeras för två olika landingssystem, för att därefter tillämpas och utvärderas i både realistiska simuleringsmiljöer under olika typer av störningar, samt med flygtester på en verklig plattform genom WASPs forskningsarena. Resultaten visar dels att reglermetoden ger önskade resultat med avseende både på störningshantering och uppfyllande av bivillkor från säkerhetskrav, och dels att algoritmen är praktiskt implementerbar även på system med begränsad beräkningskraft.

Motivated by applications in autonomous UAV landings on moving platforms, this paper proposes a Variable Horizon Model Predictive Control (VH-MPC) algorithm for cooperative rendezvous problems. Compared to existing VH-MPC, for which the associated computations are extensive which makes implementation on real-time UAV-platform systems most difficult, the look-ahead horizon in our VH-MPC algorithm adapts to the distance and time left to reach the rendezvous state in a computationally tractable manner. Our main contribution is the derivation of these efficient horizon-update rules. More specifically, the computational concerns in standard MPC for rendezvous maneuvers stem from that for the MPC to find a feasible solution, the look-ahead time needs to be long enough to ensure that a complete trajectory to the target set exists (i.e., the position and point in time where the two agents should meet). However, choosing a too long horizon results in expensive computations. A variable horizon can be used to find a horizon that is just long enough to make the control problem feasible, while reducing the computational complexity as the target set gets closer. To validate our proposed VH-MPC scheme, we conduct several experiments both in a realistic simulation environment (FlightGear-JSBSim, which includes nonlinear and complex dynamical effects), and in outdoors experiments with a quadrotor. Our experiments demonstrate i) the prohibitive computational cost of standard MPC, and ii) successful real-time computations of feasible trajectories and control inputs for an autonomous cooperative landing (fixed-wing UAV landing on an unmanned sea-surface vehicle), while satisfying important spatial safety-constraints (e.g., zones around the landing platform to avoid). Our experiments establish the feasibility of important future real-world applications in, e.g., sea rescue missions with fixed-wing drones and autonomous sea vessels.

A research arena (WARA-PS) for sensing, data fusion, user interaction, planning and control of collaborative autonomous aerial and surface vehicles in public safety applications is presented. The objective is to demonstrate scientific discoveries and to generate new directions for future research on autonomous systems for societal challenges. The enabler is a computational infrastructure with a core system architecture for industrial and academic collaboration. This includes a control and command system together with a framework for planning and executing tasks for unmanned surface vehicles and aerial vehicles. The motivating application for the demonstration is marine search and rescue operations. A state-of-art delegation framework for the mission planning together with three specific applications is also presented. The first one concerns model predictive control for cooperative rendezvous of autonomous unmanned aerial and surface vehicles. The second project is about learning to make safe real-time decisions under uncertainty for autonomous vehicles, and the third one is on robust terrain-aided navigation through sensor fusion and virtual reality tele-operation to support a GPS-free positioning system in marine environments. The research results have been experimentally evaluated and demonstrated to industry and public sector audiences at a marine test facility. It would be most difficult to do experiments on this large scale without the WARA-PS research arena. Furthermore, these demonstrator activities have resulted in effective research dissemination with high public visibility, business impact and new research collaborations between academia and industry. 

We design, implement and test two control algorithms for autonomously landing a drone on an autonomous boat. The first algorithm uses distributed model predictive control (DMPC), while the second combines a cascade controller with DMPC. The algorithms are implemented on a real drone, while the boat's motion is simulated, and their performance is compared to a centralized model predictive controller. Field experiments are performed, where all algorithms show an ability to land while avoiding violation of the safety constraints. The two distributed algorithms further show the ability to use longer prediction horizons than the centralized model predictive controller, especially in the cascade case, and also demonstrate improved robustness towards breaks in communication.

Cooperation is increasingly being applied in the control of interconnected multi-agent systems, and it introduces many benefits. In particular, cooperation can improve the efficiency of many types of missions, and adds flexibility and robustness against external disturbances or unknown obstacles. This thesis investigates cooperative maneuvers for aerial vehicles autonomously landing on moving platforms, and how to safely and robustly perform such landings on a real system subject to a variety of disturbances and physical and computational constraints. Two specific examples are considered: the landing of a fixed-wing drone on top of a moving ground carriage; and the landing of a quadcopter on a boat. The maneuvers are executed in a cooperative manner where both vehicles are allowed to take actions to reach their common objective while avoiding safety based spatial constraints. Applications of such systems can be found in, for example, autonomous deliveries, emergency landings, and search and rescue missions. Particular challenges of cooperative landing maneuvers include the heterogeneous and nonlinear dynamics, the coupled control, the sensitivity to disturbances, and the safety criticality of performing a high-velocity landing maneuver.

The thesis suggests the design of a cooperative control algorithm for performing autonomous and cooperative landings. The algorithm is based on model predictive control, an optimization-based method where at every sampling instant a finite-horizon optimal control problem is solved. The advantages of applying this control method in this setting arise from its ability to include explicit dynamic equations, constraints, and disturbances directly in the computation of the control inputs. It is shown how the resulting optimization problem of the autonomous landing controller can be decoupled into a horizontal and a vertical sub-problem, a finding which significantly increases the efficiency of the algorithm. The algorithm is derived for two different autonomous landing systems, which are subsequently implemented in realistic simulations and on a drone for real-world flight tests. The results demonstrate both that the controller is practically implementable on real systems with computational limitations, and that the suggested controller can successfully be used to perform the cooperative landing under the influence of external disturbances and under the constraint of various safety requirements.

Samarbete tillämpas i allt högre utsträckning vid reglering av sammankopplade multiagentsystem, vilket medför både ökad robusthet och flexibilitet mot yttre störningar, samt att många typer av uppgifter kan utföras mer effektivt. Denna licentiatavhandling behandlar kooperativa och autonoma landningar av drönare på mobila landingsplatformar, och undersöker hur sådana landningar kan implementeras på ett verkligt system som påverkas av externa störningar och som samtidigt arbetar under fysiska och beräkningsmässiga begränsningar. Två exempel betraktas särskilt: först landingen av ett autonomt flygplan på en bil, därefter landning av en quadcopter på en båt. Landningarna utförs kooperativt, vilket innebär att båda fordonen har möjlighet att påverka systemet för att fullborda landningen. Denna typ av system har applikationer bland annat inom autonoma leveranser, nödlandningar, samt inom eftersöknings- och räddningsuppdrag. Forskningen motiveras av ett behov av effektiva och säkra autonoma landingsmanövrar, för fordon med heterogen och komplex dynamik som samtidigt måste uppfylla en mängd säkerhetsvillkor.

I avhandlingen härleds  kooperativa regleralgoritmer för landningsmanövern. Reglermetoden som appliceras är modell-prediktiv reglerteknik, en optimeringsbaserad metod under vilken ett optimalt reglerproblem med ändlig horisont löses  varje samplingsperiod. Denna metod tillför här fördelar såsom explicit hantering av systemdynamik, och direkt inkludering av störningshantering och bivillkor vid beräkning av insignaler. På så sätt kan vi direkt i optimeringslösaren hantera säkerhetsvillkor och externa störningar. Det visas även hur lösningstiden för optimeringen kan effektiviseras genom att separera den horisontella och den vertikala dynamiken till två subproblem som löses sekvensiellt. Algoritmen implementeras därefter för två olika landingssystem, för att därefter tillämpas och utvärderas i realistiska simuleringsmiljöer med olika typer av störningar, samt med flygtester på en verklig plattform. Resultaten visar dels att reglermetoden ger önskade resultat med avseende både på störningshantering och uppfyllande av bivillkor från säkerhetskrav, och dels att algoritmen är praktiskt implementerbar även på system med begränsad beräkningskraft.

This paper presents a Model Predictive Control approach for autonomous landing of a quadcopter on the deck of a moving boat. The research is motivated by a large-scale demonstrator arena equipped with autonomous boats and drones that should collaborate to perform various tasks related to search and rescue missions. The landing maneuver is executed in a cooperative manner where both the boat and the drone take actions to reach their common objective. The maneuver is designed to be feasible under a range of conditions, including scenarios where the boat is moving across the water or when it is subjected to disturbances such as waves and winds. During the landing, the vehicles must also consider various safety constraints for landing safely and efficiently. The algorithms are implemented both in hardware-in-the-loop simulations, where we demonstrate some of the different scenarios that the algorithm is expected to handle, as well as on a real boat-drone system, on which initial tests have been carried out.

In this paper we develop a simulation setup for testing and analyzing cooperative maneuvers and corresponding control algorithms. We also find feasible initial sets using backwards reachable set computations for the cooperative control problem, which we then test using the simulation setup. The particular example considered is a cooperative rendezvous between a fixed-wing unmanned aerial vehicle and a unmanned ground vehicle. The open-source software FlightGear and JSBSim are used for the vehicle dynamics, enabling testing of algorithms in a realistic environment. The aircraft models include nonlinear, state-dependent dynamics, making it possible to capture complex behaviors like stall and spin. Moreover, environmental effects such as wind gusts and turbulence are directly integrated into the simulations. From the simulations we get a comprehensive understanding of the controller performance and feasibility when tested in a real-time scenario. Results from several landing simulations are presented, and demonstrate that the MPC solution for the cooperative rendezvous problem is a promising method also for use in complex, safety-critical systems.

Unmanned stratospheric aircraft capable of staying aloft for long periods of time have become a topic of interest in the past years. Several problems are still to be solved to allow for a profitable commercial use of such aircraft. The inherent lightweight design leads to fragile structures with low payload capacities and a high wind sensitivity. The weather dependence significantly reduces the system's operational availability. To address these drawbacks a novel landing system is proposed in this paper. The landing gear can be removed from the aircraft and a ground-based mobile landing platform is introduced. The main technical challenges consist in the precise relative state estimation and cooperative control of the involved vehicles. A reliable simulation model of the overall system was developed and a number of simulation experiments performed before the actual landing was attempted with an experimental system setup. Multiple successful landing experiments demonstrate the validity of the proposed system.

This paper considers the problem of controlling a fixed-wing unmanned aerial vehicle and a cooperating unmanned ground vehicle to rendezvous by making the aerial vehicle land on top the ground vehicle. Both vehicles are actively taking part in the control effort, where they coordinate positions and velocities to complete the landing. The rendezvous time and the terminal state are kept free to increase the flexibility of the solution. There are two main challenges with this maneuver. First, the controller must force the system to stay within a safe set such that the aerial vehicle approaches the ground vehicle directly from above. Second, the rendezvous must occur within some finite distance. A model predictive control algorithm is proposed to achieve these objectives. The choice is motivated by recent experimental results showing how the landing safety and efficiency could benefit from including safety margins already in the computation of the control inputs. A controller, which steers the agents towards rendezvous and which indirectly provides safety guarantees through non-convex optimization constraints, is derived. Simulations are provided showing the ability of the controller to plan a safe trajectory online, even under the disturbance of wind gusts.