This dissertation explores the development of sophisticated distributed layered control algorithms focused on the navigation, planning, and control of multi-agent quadrupedal robots collaborating in uncertain environments. Quadrupedal robots are high-dimensional, complex systems that are inherently unstable, posing significant challenges in designing predictive control laws. Template models offer a solution by providing a bridging layer of reduced-order models with fewer state variables and linearized dynamics. However, this approach compromises the agility and full potential of these sophisticated machines, as template models may fail to capture the intricate nonlinear dynamics of quadrupedal robots. Furthermore, in multi-robot systems (MRS) where numerous robots operate concurrently, it becomes crucial to develop strategies embedding collision safety mechanisms. One approach involves embedding Euclidean distance constraints in the predictive control formulation. While effective, this method significantly complicates the optimal control (OC) problem and increases computational overhead. To mitigate these challenges, this dissertation explores hierarchical and distributed control frameworks, focusing on developing real-time feasible controllers that guarantee collision avoidance while preserving the agility of these hardware platforms by utilizing fully nonlinear template models. In particular, this research investigates a multi-layered framework consisting of potential fields at the high-level layer, a distributed nonlinear model predictive control (DNMPC) based middle-level layer responsible for uncertainty mitigation, and full-order nonlinear controllers at the low-level layer. Additionally, the latter part of this dissertation examines the integration of safety-ensuring control barrier functions (CBFs) into the nonlinear model predictive control (NMPC) layer, thereby providing rigorous mathematical guarantees for collision avoidance. The crux of this research lies in addressing the following questions: How do we design layered control frameworks to guarantee optimal gait planning and collision avoidance while maintaining computational tractability? How do we mitigate uncertainty in the environment in real-time using safety-critical control algorithms? / Doctor of Philosophy / This dissertation investigates advanced control strategies for coordinating teams of quadrupedal robots in dynamic and uncertain environments. Quadrupedal robots present significant challenges in control and stability due to their complex, high-dimensional nature and inherent instability. Current approaches often employ simplified models for control, which, while computationally efficient, fail to fully capture the intricate dynamics of these sophisticated machines, thus limiting their agility and potential. Furthermore, in multi-robot systems, ensuring collision avoidance is a practically integral part of control. Conventional methods, including Euclidean distance constraints for collision avoidance, prove effective but substantially increase computational demands and complicate the optimal control problem. To address these challenges, this research explores a hierarchical, distributed control framework designed to guarantee collision-free navigation while maximizing the agility of quadrupedal platforms through the use of comprehensive nonlinear models. The proposed framework consists of three primary layers: a high-level layer utilizing potential fields for global path planning, a middle layer employing distributed nonlinear model predictive control for local navigation and uncertainty mitigation, and a low-level layer implementing full-order nonlinear controllers for precise motion execution. Additionally, this work examines the integration of control barrier functions into the predictive control layer, providing mathematical guarantees for collision avoidance. The core objectives of this research are twofold: first, to develop layered control frameworks that ensure optimal gait planning and collision avoidance while maintaining computational feasibility; and second, to create real-time algorithms capable of mitigating environmental uncertainties using safety-critical control methods. By addressing these fundamental questions, this dissertation aims to advance the field of multi-agent quadrupedal robotics, enhancing the capability of robotic teams to operate effectively in complex, unpredictable environments. The potential applications of this research extend to critical areas such as search and rescue operations, environmental monitoring, and exploration of hazardous terrains.

This compilation thesis presents an overarching framework on the utilization of nonlinear model predictive control(NMPC) for various applications in the context of Unmanned Aerial Vehicle (UAV) path planning and collision avoidance. Fast and novel optimization algorithms allow for NMPC formulations with high runtime requirement, as those posed by controlling UAVs, to also have sufficiently large prediction horizons as to in an efficient manner integrate collision avoidance in the form of set-exclusion constraints that constrain the available position-space of the robot. This allows for an elegant merging of set-point reference tracking with the collision avoidance problem, all integrated in the control layer of the UAV. The works included in this thesis presents the UAV modeling, cost functions, constraint definitions, as well as the utilized optimization framework. Additional contributions include the use case on multi-agent systems, how to classify and predict trajectories of moving (dynamic) obstacles, as well as obstacle prioritization when an aerial agent is in the precense of more obstacles, or other aerial agents, than can reasonably be defined in the NMPC formulation. For the cases of dynamic obstacles and for multi-agent distributed collision avoidance this thesis offers extensive experimental validation of the overall NMPC framework. These works push the limits of the State-of-the-Art regarding real-time real-life implementations of NMPC-based collision avoidance. The works also include a novel RRT-based exploration framework that combines path planning with exploration behavior. Here, a multi-path RRT * planner plans paths to multiple pseudo-random goals based on a sensor model and evaluates them based on the potential information gain, distance travelled, and the optimimal actuation along the paths.The actuation is solved for as as the solutions to a NMPC problem, implying that the nonlinear actuator-based and dynamically constrained UAV model is considered as part of the combined exploration plus path planning problem. To the authors best knowledge, this is the first time the optimal actuation has been considered in such a planning problem. For all of these applications, the utilized optimization framework is the Optimization Engine: a code-generation framework that generates a custom Rust-based solver from a specified model, cost function, and constraints. The Optimization Engine solves general nonlinear and nonconvex optimization problems, and in this thesis we offer extensive experimental validation of the utilized Proximal-Averaged Newton-type method for Optimal Control (PANOC) algorithm as well as both the integrated Penalty Method and Augmented Lagrangian Method for handling the nonlinear nonconvex constraints that result from collision avoidance problems.

Critical automated maneuvers for ships typically require a redundant set of thrusters. The motion control system hierarchy is commonly separated into several layers using a high-level motion controller and a thruster allocation (TA) algorithm. This allows for a modular design of the software where the high-level controller can be designed without comprehensive information on the thrusters, while detailed issues such as input saturation and rate limits are handled by the TA. However, for a certain set of thruster configurations this decoupling may result in poor control performance due to the limited knowledge in the high-level controller about the physical limitations of the ship and the behavior of the TA. This thesis investigates different approaches of improving the control performance, using nonlinear Model Predictive Control (MPC) as a foundation for the developed motion controllers due to its optimized solution and capability of satisfying constraints. First, a decoupled system is implemented and results are provided for two simple motion tasks showing problems related to the decoupling. Thereafter, two different approaches are taken to remedy the observed drawbacks. A nonlinear MPC controller is developed combining the motion controller and thruster allocation resulting in a more robust control system. Then, in order to keep the control system modularized, an investigation of possible ways to augment the decoupled system so as to achieve similar performance as the combined system is carried out. One proposed solution is a nonlinear MPC controller with time-varying constraints accounting for the current limitations of the thruster system. However, this did not always improve the control performance since the behavior of the TA still is unknown to the MPC controller.

This thesis explores the possibility of using an optimal control scheme called Model Predictive Control (MPC), to control climatization systems for electric vehicles. Some components of electric vehicles, for example the batteries and power electronics, are sensitive to temperature and for this reason it is important that their temperature is well regulated. Furthermore, like all vehicles, the cab also needs to be heated and cooled. One of the weaknesses of electric vehicles is their range, for this reason it is important that the temperature control is energy efficient. Once the range of electric vehicles is increased the down sides compared to traditional combustion engine vehicles decrease, which could lead to an increase in the usage of electric vehicles. This could in turn lead to a decrease of greenhouse gas emission in the transportation sector. With the help of MPC it is possible for the controller to take more factors into consideration when controlling the system than just temperature and in this thesis the power consumption and noise are also taken into consideration. A simple model where parts of the climate system’s circuits were seen as point masses was developed, with nonlinear heat transfers occurring between them, which in turn were controlled by actuators such as fans, pumps and valves. The model was created using Simulink and MATLAB, and the MPC toolbox was used to develop nonlinear MPC controllers to control the climate system. A standard nonlinear MPC, a nonlinear MPC with custom cost functions and a PI controller where all developed and compared in simulations of a cooling scenario. The controllers were designed to control the temperatures of the battery, power electronics and the cab of an electric vehicle. The results of the thesis indicate that MPC could reduce power consumption for the climate control system, it was however not possible to draw any final conclusions as the PI controller that the MPC controllers were compared to was not well optimized for the system. The MPC controllers could benefit from further work, most importantly by applying a more sophisticated tuning method to the controller weights. What was certain was that it is possible to apply this type of centralized controller to very complex systems and achieve robustness without external logic. Even with the controller keeping track of six different temperatures and controlling 15 actuators, the control loop runs much faster than real time on a modern computer which shows promise with regard to implementing it on an embedded system.

Docking maneuvers are a relevant part of the modern space mission, requiring precision and safety to ensure the success of the overall mission. This thesis proposes using a non-linear Model Predictive Control (MPC) as a controller with various constraints to ensure safe docking maneuvers for a satellite. This was done in MATLAB using as a model for the satellite the Sliders used by the Robotics Lab at Luleå University of Technology (LTU). The controller was tested first on the MATLAB model and then briefly on hardware.The main objective of this thesis is to develop and implement an MPC-based control strategy to achieve safe docking maneuvers between two satellites. Great attention has been paid to implementing constraints, such as collision avoidance, and hardware constraints, such as thrust limits, to ensure the safety and reliability of the process.Through the MATLAB simulations, it was possible to indicate that the introduced constraints contribute significantly to the safe execution of docking maneuvers, preventing collisions, andoptimizing fuel usage. The controller successfully adapts to unforeseen disturbances and uncertainties in real-time, showcasing its robustness and reliability in dynamic space environments.The hardware simulations have shown that the controller operates as expected but needs further tuning to adapt to the hardware uncertainties.In conclusion, this thesis comprehensively explores MPC-based control strategies with constraints for space docking maneuvers. The positive results underscore this approach’s potential to ensure the safety and reliability of future space missions, opening avenues for further research and application in autonomous space systems.

This thesis describes the theory of model predictive control and application of the theory to synchronous drives. It shows explicit and on-line solutions and compares the results with classical vector control structure.

This thesis describes the theory of model predictive control and application of the theory to synchronous drives. It shows explicit and on-line solutions and compares the results with classical vector control structure.