1 

Fast optimizationbased control and estimation using operator splitting methods
The size of modern technological systems has grown significantly and the need for fast, online optimizationbased control is a necessity. The complexity of these systems along with the need for increased accuracy in the computed outcome dictate the usage of optimization methods for the computation of the solution. Besides this, new data arrive in real time and in fast rates, that have to be incorporated efficiently in the control policy under design.
Exploiting the stateoftheart, multicore, computing architectures, we can achieve fast online solutions of optimal control problems by splitting a large problem into several smaller ones that can be solved in parallel. In this thesis, we apply an operator splitting technique to a generic convex optimal control problem. The resulting algorithm alternates between a quadratic regulator iteration, and a step in which singleperiod optimization problems are solved in parallel. Depending on the constraints and nonquadratic objective terms, these singleperiod problems can be solved extremely quickly, or even analytically in many cases. In the timeinvariant case, precomputing the gain matrices in the quadratic regulator problem gives another speedup, as well as an algorithm that requires no division, and is therefore suitable for implementation with fixedpoint processor. The method is demonstrated on several examples arising in different application areas. Furthermore, we develop an extension to this algorithm so that it can handle more generic optimal control problems and propose a different decomposition approach that achieves an even higher level of parallelization.

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2 

Scheduling the Refuelling Activities of Multiple Heterogeneous Autonomous Mobile Robots
When a team of autonomous mobile robots (MRs) has to perform a mission of a duration that exceeds their energy capacities, the mission can only be fulfilled if the MRs are resupplied. Nowadays most MRs are powered by batteries, which can either be recharged, or replaced. Since it is not necessary that the MRs are battery powered, we will use the general term refuelling instead of recharging. In general there are two options for MRs to refuel themselves: by travelling to a fuelling station (FS) that is situated at a fixed location, or rendezvousing with a mobile fuelling station (MFS). When multiple MRs operate in the same environment, it is desired that the MRs share the available FSs instead of each MR having its own dedicated FS. Sharing the FSs will reduce the purchase and maintenance costs, and less space will be needed for the placement of FSs. The FSs considered during this thesis, can only refuel a single robot at a time. This raises the need for properly scheduling the refuelling activities, such that the FSs are shared in an efficient manner, and depletion of the MRs can be prevented. This thesis presents several methods to schedule the refuelling activities of multiple heterogeneous autonomous MRs. The scheduling is focused on the selection of the refuel events, and the allocation of the FSs as a shared resource. The following problem is considered: For an environment which contains an arbitrary number of FSs, and MRs, the refuelling activities should be scheduled in such a way that the overall mission time is minimized. Each mission entails an assignment of a unique set of waypoints for each MR which have to be visited in a predetermined order, in order to complete the mission. The total mission is accomplished when the last MR is completely refuelled, after visiting its last waypoint. Scheduling the refuelling activities using a timebased metric is complicated compared to a distancebased metric. Since a FS can refuel only a single MR at a time, the duration that each MR spends refuelling, and the ordering in which the MRs are refuelling have to be taken into account. Furthermore since the MRs share the FSs, each refuel event of one MR can affect all future refuel events of all other MRs. Global optimal solutions for this problem can be found by using a centralized approach as shown in this thesis. However, since all refuel events of all MRs can influence each other, the complexity increases very quickly when the problem size increases. In order to obtain a global optimum, all possible refuel events have to be taken into account. Due to the computational complexity, the problem size that can be solved by this approach is limited. In order to solve larger scale problems, a tradeoff has been made between computation time and solution quality. A distributed, and hierarchical architecture are proposed, in order to distribute the computations and decision making over the robotic team. The core of the distributed approach is that MRs make individual decisions based on local knowledge. The decision making of the hierarchical approach is done for individuals or clusters of MRs. Simulation case studies indicate that these decentralized approaches can be used to solve large scale problems in realtime, at the cost of a suboptimal solution.

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3 

Predictive control for residential capacity controlled heat pumps in a smart grid scenario

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4 

Distributed ConnectivityAware Multirobot Exploration
Networks of mobile robots enable us to explore areas quickly and without danger to human operators. To execute this task successfully, communication between the robots in the network is imperative. In this thesis, we link communication between robots to network integrity, where network integrity is defined as the ability of the network to communicate its acquired data to all robots in the network and to the human operator.
We first introduce a greedy exploration algorithm which will be used as the basis of this connectivityaware exploration algorithm. Then, we propose two different algorithms that each aim to maintain network integrity by using relaying robots:
 The Laplacian algorithm aims to keep the graph of robots connected, which means that the graph Laplacian has a positive Fiedler value. The relaying robots actively maintain network integrity while the exploration robots execute the greedy exploration task.
 The Data Transmission Rate (DTR) algorithm aims to preserve enough bandwidth for the exploration robots. All robots simultaneously attempt to preserve this bandwidth, and through artificial potential functions a control law is devised to allow for exploration.
We present simulation results based on a series of scenarios, which involve exploration of a rectangular obstaclefree area. From the results, we conclude that the DTR algorithm performs significantly better in terms of exploration time and size of the explored area. Still, many improvements can be made to the DTR algorithm, such as incorporating obstacle avoidance and finding realistic parameters for the signal strength function used in the algorithm.

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5 

Transportation of Cable Suspended Load using Unmanned Aerial Vehicles: A Realtime Model Predictive Control approach
Unmanned Aerial Vehicles (UAV) have received an increasing amount of attention recently with many applications being actively investigated across the globe, and several related open research questions being actively pursued. Possible applications include search and rescue, disaster relief, environmental monitoring and surveillance, transportation, and construction. Transportation of cable suspended payloads using Unmanned Aerial Vehicles is one such application which is the topic of this research. Autonomous transportation of objects using UAV can contribute to the safe and reliable supply of food and medicine in remote or disasteraffected areas and even in commercial delivery of goods.
The stateoftheart approaches towards the slung load transportation either develop nonlinear feedback control laws to stabilize the system to a predefined trajectory or employ open loop offline trajectory planning schemes to generate optimal control inputs to the system. Most of these techniques often rely on availability of an accurate model of the system backed up with simulation results. Very few results exist which target experimental validation of the proposed method. Based on the findings of the previously conducted literature survey, it appears that the application of closed loop online trajectory generation and control schemes to transport a slung payload in swing free manner remains unanswered. The work in this thesis sets off to answer the research questions in this direction and address the issues that come along with experimental validation. Model Predictive Control (MPC) is a promising framework, which provides the means to tackle both the trajectory generation problem and the feedback control problem in an unified manner. As a result, it forms the most important component of this thesis.
Specific research problem that is addressed in this thesis is to transport a cable suspended load using quadrotor from one point to another, while minimizing the swing through the use of Linear Time Invariant MPC techniques. A nonlinear dynamic model for the quadrotorslung load system is obtained and the structure within the system dynamics is exploited to decide the control strategy. Two different MPC formulations viz. MPC with integral action and MPC with deltau formulation are simulated and compared to Linear Quadratic control with integral action which acts as a benchmark controller. Backed with simulation results, it is shown through experimental validation that it is possible to control the swing of cable suspended load using linear control techniques. MPC being an computationally expensive task, stateoftheart fast optimization solvers such as FORCES PRO is used to achieve online implementation of MPC for the quadrotorslung load system. To this end, a new software framework for implementation of MPC is developed which establishes a wireless link with the quadrotor resulting in a realtime networked control loop.

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6 

Mobile robot swarming using radio signal strength measurements and deadreckoning
The mobile robots considered in this thesis are six legged "Zebro" robots. These mobile robots will use Radio Signal Strength (RSS) measurements to determine the distances towards other mobile robots and radio beacons placed in the surroundings. A combination of distance measurements and deadreckoning is used to perform a localization of the relative positions of the other mobile robots in the neighbourhood. The focus of the localization algorithm is to deal with a bad performance of the distance estimation, because this will result in uncertain position estimations. With knowledge about the bad performance of the localization an according suitable swarm algorithm is designed. This swarm algorithm is will also be used to test how valuable the position estimations can be as an addition to already existing swarm algorithms.

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7 

SLAMming with Spheros: An impactbased approach to Simultaneous Localization and Mapping
The Simultaneous Localization and Mapping (SLAM) problem for mobile robots aims at consistently building a map of an unknown environment while simultaneously determining its position within this map. From a controltheoretic viewpoint, it is somehow analogous to simultaneously estimating the states and output map of the system. In the robotics community, SLAM is arguably considered a solved problem on a theoretical and conceptual level, but still it requires considerable maturity on a practical level. The stateoftheart SLAM algorithms require computationally powerful processors, expensive sensors with dense feature extraction and multiple sensors for uncertainty reduction. An approach to the SLAM problem using minimal sensing information is still lacking in both theoretical and practical aspects.
In this context, this M.Sc. thesis aims to study and implement a special type of SLAM solely using the impact information from a spherical mobile robot called Sphero (developed by Orbotix). Such impact data is available from the robot's onboard IMU, however the impact angle and odometry information are subject to significant drift. Thus, the SLAM problem will be restricted to a rectilinear environment in order to allow for calibration and correction of such accumulated IMU errors (assuming that impacts with walls are sufficiently frequent).
The impactbased SLAM is an observable estimation problem with downside of a poor robot pose distribution. An accurate representation of the pose distribution is a particle set, with the resulting estimation technique as particle filter. Suitable map representations for the impactbased SLAM problem are formulated and studied, and the most efficient one is implemented. A probabilistic formulation is laid out for the SLAM problem using robot motion model and map representation, and associated challenges are studied for developing an efficient algorithm.
The resulting SLAM algorithm uses a RaoBlackwellized particle filter which is computationally efficient and robust to data association errors. The issue of inconsistency is discussed for the developed SLAM algorithm and suitable modifications are proposed over the developed algorithm for ensuring consistency. SLAM is extended to multiple robots as a mapmerging problem since multiple robots can build a perceptually rich map with a lower exploration time.

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8 

Rigid Formation Control using Hovercrafts: A Spatial Model Predictive Control Approach
The steady increase in volume of goods to be transported over land and water has necessitated the development of efficient and alternative methods of transportation. In current practices considerable amount of transportation delay is caused due to switching between different modes of transportation resulting in economic losses. Another difficulty in the transportation sector arises when handling extremely large objects, such as wind turbines and cargo containers. In order to overcome these difficulties, an alternative method of transportation has been proposed recently. The proposed alternative method consists of the development of a formation control framework using hovercrafts. Formation control is a widely researched topic due its potential benefits in reducing the system cost, structure flexibility and improving the efficiency of the overall system.
Stateoftheart methods for formation control are focused towards developing a controller to track a predefined trajectory, and the trajectory generation is an additional problem which is addressed offline. A path tracking formation control framework is an area which has received less attention in the literature and can have possible improvements. Hence, this thesis work answers the research question of generating a feasible path for a set of initial and final conditions, and tracking the generated path.
Model Predictive Controller (MPC) is a promising framework, because of its constraint handling capabilities. Hence, it accounts for the major component of this thesis. A new framework for formation control is proposed which uses spatialdomain parametrization instead of the conventional timedomain parametrization. MPC being a computationally expensive task, the proposed framework reduces the number of decision variables and constraint evaluations which can help to achieve the desired Real Time performance.
The specific research question addressed in this thesis work is to develop a path tracking formation control framework while minimising the absolute and relative position error for each vehicle in the formation. A nonlinear dynamic model for the hovercraft is obtained using first principles and its structure is used to design an optimization based controller. An Optimal Control Problem (OCP) is formulated which is solved using direct collocation method. In this method a continuous problem is discretized into a number of collocation points, and the resulting problem is solved using stateoftheart Nonlinear Program solvers such as, SNOPT and NPSOL. The performance of the proposed framework is illustrated using numerical simulations.

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9 

Regressionbased inverter control for power flow and voltage regulation
Rapid and substantial voltage changes can occur in distribution networks with a high pen etration of photovoltaic (PV) systems, due to their unpredictable nature. Electronic power inverters are capable of delivering fast reactive power support to maintain customer voltages within operating tolerances and reduce system losses in distribution feeders. While optimization based paradigms have been proposed to control the reactive power output of inverters, these methods typically rely on the presence of an extensive and fast communication infrastructure which is currently not in place and would be expensive to build. On the other hand, approaches that utilize completely local data require the design of a relation between local measurements and inverter output (i.e. a VoltVAr curve). These relationships are often naively designed and typically do not yield optimal results. In this work, a systematic and data driven approach is presented to determine PV inverter output as a function of locally obtained measurements in a manner that obtains near optimal results. First, a network model and historic information are used to compute globally optimal settings a posteriori for all controllable inverters in the network. Subsequently, a regression approach is used to find a function for each inverter that maps the solely local historical data to an approximation of the globally optimal inverter output. The resulting functions are then employed as decentralized controllers of the inverters and approximate the globally optimal reactive power outputs based on local measurements only. Simulation results on real feeder models demonstrate that this method achieves near optimal results when performing voltage and capacityconstrained loss minimization and voltage flattening. This method paves the way to an efficient voltage optimization scheme in which legacy control equipment collaborates with existing inverters to facilitate safe operation of distribution networks with higher levels of distributed generation.

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10 

Optimal Control for Race Car Minimum Time Maneuvering
Minimizing the time needed to travel a prescribed distance is the main development goal in motorsports. In racing car development, simulations are used to predict the effect of design parameter changes on vehicle performance. If approached as an optimal trajectory planning problem, a maneuver simulation can be used to determine not only the maneuver time, but also to identify the performance limitations on the system. This thesis describes the development and implementation of an optimal trajectory planning method using optimal control for short maneuvers. The requirements and modeling decisions are based on the application of the method to example problems related to TC design.
The model for the method is based on a study of steadystate acceleration limits and stability. The rigid twotrack model resulting from this study includes lateral and longitudinal load transfer, a nonlinear tire model, a limitedslip differential and aerodynamic downforce. An important contribution is the omission of wheel rotational velocities from the model, reducing the number of states by four and relaxing the requirements on the discretization interval. Possible misuse of this formulation is prevented by a constraint representing wheel rotational stability limitations. The formulation is validated by comparison to a reference model which includes wheel rotational velocities.
The optimal trajectory planning method is formulated as an optimal control problem. The cost function is the maneuver time, and the constraints consist of the system dynamics and maneuver boundaries. The timebased dynamics are transformed into spatial dynamics, and a curvilinear coordinate system is used.
The optimal control problem is discretized using a full collocation method, and the state and input trajectories are parametrized in terms of Bspline coefficients. The resulting problem is solved using a NLP solver. Interiorpoint solver IPOPT and SQP solver SNOPT are compared on various small problems. For this application IPOPT appears to be superior over SNOPT. The first order derivative information of the constraints required for IPOPT is approximated using sparsefinite differences, and the cost function gradient is calculated analytically. The precision of the method is assessed in a study of maneuver time dependency on mass. It appears that precision is mainly affected by convergence of the solver to various local minima. As such, the use of distancedependent constraints and warmstart are employed for improving precision.
The optimal trajectory for a hairpin with various radii is studied in detail. Special attention is paid to tire friction potential utilization and vehicle stability according the Lyapunov's First Method. For the given parameters it is shown that the optimal solution involves instances of overdriving either the front or rear axle. It is also shown that the vehicle is openloop locally unstable on intervals along the optimal trajectory.
In another simulation study, the reaction of the control inputs to temporary reductions in tireroad friction and perturbations to the yaw rate and body slip angle on turnexit are evaluated. The most important result of this study is that the longitudinal control was found to be the primary means for rejecting such disturbances. The study also showed that steering angle changes are used as additional means for disturbance rejection if the perturbation is large enough to saturate the reduction of longitudinal control.
The sensitivity of maneuver time and optimal trajectory to vehicle mass is studied by the use of socalled sensitivity differentials. This is done using a welldeveloped theoretical framework for parametric sensitivity for barrier methods, implemented in the software package sIPOPT. The sensitivity study can be seen as a proof of concept of the sensitivity differential approach for the race car MTM application.

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11 

Distributed Estimation and Control for Robotic Networks
Mobile robots that communicate and cooperate to achieve a common task have been the subject of an increasing research interest in recent years. These possibly heterogeneous groups of robots communicate locally via a communication network and therefore are usually referred to as robotic networks. Their potential applications are diverse and encompass monitoring, exploration, search and rescue, and disaster relief. From a research standpoint, in this thesis we consider specific aspects related to the foundations of robotic network algorithmic development: distributed estimation, control, and optimization.
The word “distributed” refers to situations in which the cooperating robots have a limited, local knowledge of the environment and of the group, as opposed to a “centralized” scenario, where all the robots have access to the complete information. The typical challenge in distributed systems is to achieve similar results (in terms of performance of the estimation, control, or optimization task) with respect to a centralized system without extensive communication among the cooperating robots.
In this thesis we develop effective distributed estimation, control, and optimization algorithms tailored to the distributed nature of robotic networks. These algorithms strive for limiting the local communication among the mobile robots, in order to be applicable in practical situations. In particular, we focus on issues related to nonlinearities of the dynamical model of the robots and their sensors, to the connectivity of the communication graph through which the robots interact, and to fast feasible solutions for the common (estimation or control) objective.

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12 

Distributed model predictive controller design based on distributed optimization

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13 

Realtime receding horizon trajectory generation for long heavy vehicle combinations on highways
The socalled Adouble long heavy vehicle combination is a 32 meter long and up to 80 tonnes heavy doubletrailer truck widely used in Canada and Australia today, and will be more abundant on the road also in Europe in the near future. They have the potential to decrease road transport cost, traffic congestion and generate lower emissions than current road freight transport. However, an undesired effect of the added towed units is the increase in difficulty to maneuver truck on roads and in busy traffic. The increasing complexity for truck drivers to handle trivial tasks like lane changing call for advanced driver assistance functions.
The development of advanced assistance systems or potentially autonomous functioning trucks can improve traffic safety, allowing for further increase in use of long combination trucks. This thesis work focuses on one crucial element of such driver assistance systems, the ability to plan a safe and smooth trajectory and generate control signals for the low level actuators. Based on the measured vehiclestate, the road curvature and measurements of surrounding vehicles, a (sub)optimal steering action and cruise control reference velocity ought to be generated.
A receding horizon optimal control problem (OCP) is formulated, with a nonlinear singletrack vehicle prediction model for the Adouble combination. The OCP is designed to capture the main highway driving tasks of lane keeping, lane changing and collision avoidance. A direct multipleshooting solution strategy to this OCP is implemented using the automatic codegeneration functionality of the ACADO toolkit. Results of closedloop simulations are presented for the control of both the vehicle prediction model and a highfidelity vehicle model, developed and validated by Volvo Group Truck Technology. Because of the computational performance advantages of the RealTime Iteration algorithm and the automatic codegeneration for the solution scheme, realtime performance is achieved for the optimizationbased receding horizon trajectory generator for the Adouble combination.

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14 

Design of a position determination system for a ship’s hull maintenance robot
Positioning and localization are key topics associated with the control and operation of robotic vehicles. This holds in particular for robots functioning in a challenging environment, such as the ship’s hull maintenance robot developed by Fleet Cleaner. As the industry standard techniques are limited due to constraints imposed by the harbor and ship’s hull as operating area, solving this positioning problem is not trivial. Therefore, the main objective of this thesis is: “design a position determination system for a ship’s hull maintenance robot”. The objective is accomplished by completing three phases: conceptual design, embodiment design, and proof of concept.
The conceptual design approach focuses on the selection of optimal measuring principles, based on the characteristic constraints and requirements of the system. The solution is found to be a combination of both absolute and relative positioning methods, using the principles of: underwater acoustics, depth sensing, inertial sensing, and wheel encoding. For the embodiment design the implementation parameters for customizing the inertial, depth, and acoustic subsystem to the application are considered. This leads to the proposed set of design choices: a local reference system of acoustic beacons attached to the ship’s hull, where acoustic oneway communication between the robot and beacons provide information of the robot’s absolute position in intervals; using inertial velocity and orientation to compute the relative displacement between intervals; a pressurebased sensor for determining depth. A proof of concept is obtained by combining the sensors into a test platform. The setup, built with some assumptions and concessions, contains the basics of essential methodologies for position estimation. Evaluation is based on measurements obtained from two settings (i.e., a water crate and the 3mE towing tank), both aimed at simulating harbor environment. The basic principles are verified and the design proven to work in a laboratory setting.
Based on findings throughout the project, suggestions are formulated for improvement by scaling and integrating components, while adding robustness to the estimation methods. Also further testing in a more controlled and structured way (i.e., using the towing tank cart) is required to quantify the performance. Following up on these recommendations will lead to the realization of the complete full scale positioning system for the ship’s hull maintenance robot.

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