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During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. In this thesis, the objective is not only to find feasible solutions to a motion planning problem, but solutions that also optimize some kind of performance measure. From a control perspective, the resulting problem is an instance of an optimal control problem. In this thesis, the focus is to further develop optimal control algorithms such that they be can used to obtain improved solutions to motion planning problems. This is achieved by combining ideas from automatic control, numerical optimization and robotics. First, a systematic approach for computing local solutions to motion planning problems in challenging environments is presented. The solutions are computed by combining homotopy methods and numerical optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms both a state-of-the-art numerical optimal control method based on standard initialization strategies and a state-of-the-art optimizing sampling-based planner based on random sampling. Second, a framework for automatically generating motion primitives for lattice-based motion planners is proposed. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the algorithm not only automatically optimizes the motions connecting pre-defined boundary conditions, but also simultaneously optimizes the terminal state constraints as well. In addition to handling static a priori known system parameters such as platform dimensions, the framework also allows for fast automatic re-optimization of motion primitives if the system parameters change while the system is in use. Furthermore, the proposed framework is extended to also allow for an optimization of discretization parameters, that are are used by the lattice-based motion planner to define a state-space discretization. This enables an optimized selection of these parameters for a specific system instance. Finally, a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems is presented. The main idea is to combine the strengths of sampling-based path planners and numerical optimal control. The lattice-based path planner is applied to the problem in a first step using a discretized search space, where system dynamics and objective function are chosen to coincide with those used in a second numerical optimal control step. This novel tight combination of a sampling-based path planner and numerical optimal control makes, in a structured way, benefit of the former method’s ability to solve combinatorial parts of the problem and the latter method’s ability to obtain locally optimal solutions not constrained to a discretized search space. The proposed approach is shown in several practically relevant path planning problems to provide improvements in terms of computation time, numerical reliability, and objective function value.

One of the most common advanced control strategies used in industry today is Model Predictive Control (MPC), and some reasons for its success are that it can handle multivariable systems and constraints on states and control inputs in a structured way. At each time-step in the MPC control loop the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line. There exist several optimization methods to solve the CFTOC problem, where two common types are interior-point (IP) methods and active-set (AS) methods. In both these types of methods, the main computational effort is known to be the computation of the search directions, which boils down to solving a sequence of Newton-system-like equations. These systems of equations correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performance IP and AS methods for CFTOC problems rely on efficient algorithms for solving the UFTOC problems. The solution to a UFTOC problem is computed by solving the corresponding Karush-Kuhn-Tucker (KKT) system, which is often done using generic sparsity exploiting algorithms or Riccati recursions. When an AS method is used to compute the solution to the CFTOC problem, the system of equations that is solved to obtain the solution to a UFTOC problem is only changed by a low-rank modification of the system of equations in the previous iteration. This structured change is often exploited in AS methods to improve performance in terms of computation time. Traditionally, this has not been possible to exploit when Riccati recursions are used to solve the UFTOC problems, but in this thesis, an algorithm for performing low-rank modifications of the Riccati recursion is presented. In recent years, parallel hardware has become more commonly available, and the use of parallel algorithms for solving the CFTOC problem and the underlying UFTOC problem has increased. Some existing parallel algorithms for computing the solution to this type of problems obtain the solution iteratively, and these methods may require many iterations to converge. Some other parallel algorithms compute the solution directly (non-iteratively) by solving parts of the system of equations in parallel, followed by a serial solution of a dense system of equations without the sparse structure of the MPC problem. In this thesis, two parallel algorithms that compute the solution directly (non-iteratively) in parallel are presented. These algorithms can be used in both IP and AS methods, and they exploit the sparse structure of the MPC problem such that no dense system of equations needs to be solved serially. Furthermore, one of the proposed parallel algorithms exploits the special structure of the MPC problem even in the parallel computations, which improves performance in terms of computation time even more. By using these algorithms, it is possible to obtain logarithmic complexity growth in the prediction horizon length.

The control-theoretic notion of controllability captures the ability to guide a systems behavior toward a desired state with a suitable choice of inputs. Controllability of complex networks such as traffic networks, gene regulatory networks, power grids etc. brings many opportunities. It could for instance enable improved efficiency in the functioning of a network or lead to that entirely new applicative possibilities emerge. However, when control theory is applied to complex networks like these, several challenges arise. This thesis consider some of these challenges, in particular we investigate how control inputs should be placed in order to render a given network controllable at a minimum cost, taking as cost function either the number of control inputs or the energy that they must exert. We assume that each control input targets only one node (called a driver node) and is either unconstrained or unilateral. A unilateral control input is one that can assume either positive or negative values but not both. Motivated by the many applications where unilateral controls are common, we reformulate classical controllability results for this particular case into a more computationally-efficient form that enables a large scale analysis. We show that the unilateral controllability problem is to a high degree structural and derive theoretical lower bounds on the minimal number of unilateral control inputs from topological properties of the network, similar to the bounds that exists for the minimal number of unconstrained control inputs. Moreover, an algorithm is developed that constructs a near minimal number of control inputs for a given network. When evaluated on various categories of random networks as well as a number of real-world networks, the algorithm often achieves the theoretical lower bounds. A network can be controllable in theory but not in practice when completely unreasonable amounts of control energy are required to steer it in some direction. For unconstrained control inputs we show that the control energy depends on the time constants of the modes of the network, and that the closer the eigenvalues are to the imaginary axis of the complex plane, the less energy is required for control. We also investigate the problem of placing driver nodes such that the control energy requirements are minimized (assuming that theoretical controllability is not an issue). For the special case with networks having all purely imaginary eigenvalues, several constructive algorithms for driver node placement are developed. In order to understand what determines the control energy in the general case with arbitrary eigenvalues, we define two centrality measures for the nodes based on energy flow considerations: the first centrality reflects the network impact of a node and the second the ability to control it indirectly. It turns out that whether a node is suitable as driver node or not largely depends on these two qualities. By combining the centralities into node rankings we obtain driver node placements that significantly reduce the control energy requirements and thereby improve the “practical degree of controllability”. / <p>Minor corrections are made in the electronic version of the thesis (Abstract). / Mindre korreigeringar är gjorda i den elektroniska versionen av avhandlingen (i Abstract).</p>

Mines, construction sites, road construction and quarries are examples of applications where construction equipment are used. In a production chain consisting of several construction machines working together, the work needs to be optimised and coordinated to achieve an environmental friendly, energy efficient and productive production. Recent rapid development within positioning services, telematics and human machine interfaces (HMI) opens up for control of individual machines and optimisation of transport missions where several construction machines co-operate. The production chain on a work site can be split up in different sub-tasks of which some can be transport missions. Taking off in a transport mission where one wheel loader ("loader" hereinafter) and two articulated haulers ("haulers" hereinafter) co-operate to transport material at a set production rate [ton/h], a method for fuel optimal control is developed. On the mission level, optimal cycle times for individual sub-tasks such as wheel loader loading, hauler transport and hauler return, are established through the usage of Pareto fronts. The haulers Pareto fronts are built through the development of a Dynamic Programming (DP) algorithm that trades fuel consumption versus cycle time for a road stretch by means of a time penalty constant. Through varying the time penalty constant n number of times, discrete fuel consumption - cycle time values can be achieved, forming the Pareto front. At a later stage, the same DP algorithm is used to generate fuel optimal vehicle speed and gear trajectories that are used as control signals for the haulers. Input to the DP algorithm is the distance to be travelled, road inclination, rolling resistance coefficient and a max speed limit to avoid unrealistic optimisation results. Thus, a method to describe the road and detect the road related data is needed to enable the optimisation. A map module is built utilising an extended Kalman Filter, Rauch-Tung-Striebel smoother and sensor fusion to merge data and estimate parameters not observable by sensors. The map module uses a model of the vehicle, sensor signals from a GPS or GNSS sensor and machine sensors to establish a map of the road. The wheel loader Pareto front is based on data developed in previous research combined with Volvo in-house data. The developed optimisation algorithms are implemented on a PC and in an interactive computer tablet based system. A human machine interface is created for the tablet, guiding the operators to follow the optimal control signals, which is speed for the haulers and cycle time for the loader. To evaluate the performance of the system it is tested in real working conditions. The contributions develop algorithms, set up a demo mission control system and carry out experiments. Altogether rendering in a platform that can be used as a base for a future design of an off-road transport mission control system.

No description available.

<p>The aim of the thesis is to develop and describe WRAP’s capabilities in handling the WiMAX standard as defined in IEEE 802.16e related to traffic capacity calculations. WRAP International has developed the software WRAP for spectrum management and radio network planning. WRAP includes various technical calculation functions that are applied for design and analysis tasks with the purpose of achieving the desired quality of service within radio communication networks, navigation and radar systems. WRAP already includes functions for radio wave calculations to establish for instance coverage; best server maps etc, as well as traffic calculations for cellular networks (2G) using channel-orientated calculations that are modeled by Erlang B and Erlang C formulas. Since WiMAX supports multiple broadband data services including voice, video, web data, interactive network gaming and streaming media so there is a need to build a tool for the estimation of WiMAX traffic capacity calculations. Some methods and algorithms are analyzed and a tool has been built to ease the network planner’s job. It works based upon the calculations and algorithm presented in the report. Total number of users and data rate supported by a base station is calculated and total number of base stations, required for the coverage of a specific area is determined. This new tool is compatible with WRAP’s current functions.</p>

<p>På moderna missiler ställs inte bara krav på nedslagsposition utan i allt högre grad även på nedslagsvinkel. För hårt bepansrade mål är vinkeln kritisk då det finns risk att missilen studsar om den kommer in allt för flackt. Samtidigt ökar träffprestandan då en optimal nedslagsvinkel och nedslagsposition används. Med anledning av detta föreslås en styrlag för att reglera missilen efter på förhand genererade referensbanor i vilka nedslagsposition och nedslagsvinkel kan specifieras. Styrlagen är indelad i två huvuddelar och inleds med en optimal styrlag för att reglera ut navigationsfel från tidigare faser och ta missilen till referensbanan. Därefter tar en banföljningsalgoritm vid för att följa referensbanan, vilken konstruerats som interpolerade referenspunkter. </p><p>Styrlagen har implementerats i en befintlig simulator bestående av en missilmodell och en omvärldsmiljö. I denna simulator har prestanda för styrlagen jämförts för ett flertal olika fall med en befintlig styrlag. </p><p>Simuleringsresultaten visar att en mycket god positions- och vinkelnogrannhet erhålls vid navigationsfel upp till en viss gräns. Därefter räcker inte den tillgängliga accelerationen till, med positionsfel som följd.</p>

<p>Från Sjövärnskåren division syd, underavdelning Blekinge, inkom en förfrågan om att göra en undersökning och projektering till ett digitalt maskinövervakningssystem.</p><p>Syftet med maskinövervakningssystemet är att det ska vara lättare för de som tränas ombord att ta till sig maskineriets kondition. Detta kommer att bidra till att minska underhållskostnaderna genom att förbättra övervakningen under drift, för att undvika oönskade driftfall, och dels att förbättra driftsdokumentationen som underlag för beslut om underhållsåtgärder/-intervaller.</p><p>Projektet innebar en föreberedande undersökning av vilken utrustning som behövs till det nya systemet samt för att få en kostnadsram åt Sjövärnskåren.</p><p>Vi träffades i Karlskrona för att komma överens om vilka maskinparametrar som skulle presenteras. Därefter påbörjades förundersökning och dokumentationsgenomgång för att ta reda på vilka givare det var samt vad för signal de gav till det befintliga övervakningssystemet. Detta visade sig bli en stor del av projektet som tog mycket tid. Vi var och mätte signalerna från givarna på fartyget utan att komma fram till slutsats. Efter att ha pratat med varv och underhållsenheter som fartyget varit i kontakt med under sin tid i försvaret, hittade vi en källa som var mycket kunnig i området. Denne uppgav muntligen information som innebar att givarna skulle ge standardsignal, 4-20 mA.</p><p>Projektet fortskred med denna information och offertunderlag gjordes och skickades ut till olika företag som hade produkter som kunde klara av uppgiften.</p><p>Det inkom tre system som skulle klara av uppgiften. Alla dessa innebär omfattande programmeringsarbete för att få controllern att hantera och presentera informationen som det är tänkt. Samtliga system programmeras med funktionsblock (FB) eller strukturerad text, (ST). Även för den insatte i dessa språk kommer det att bli en ansenlig mängd programmeringstimmar.</p> / <p>This exam work was initiated by a request from Sjövärnskåren division Syd. They wanted to implement a newer, computer based system with graphical display, an engine monitoring system which was ment to provide the engineer on watch with data from the engines. The object for this is to reduce the maintenance costs through improved monitoring while running and to improve documentation which later on the maintenance measures is based on.</p><p>The project was an initial study which conclusions and recommendations on systems suited for the task is to give Sjövärnskåren an economical frame.</p><p>We met up in Karlskrona on the ship and had a discussion about which parameters that should be presented. After that we started to go through the documentation and perform onsite surveys to conclude what signals the transmitters put out to the existing monitoring system.</p><p>This was a delicate task, information about the transmitters was lacking in the documentation.</p><p>The onsite measures gave no vital information. We talked to the shipyards and maintenance units that the ship had been in contact with during its time in the navy. We came in contact with a man that had been working with this ship, and he gave us information that told us that the transmitters were of standard type, 4-20 mA.</p><p>With this information, the project pursued and we invited tenders to give us systems that could cope with the task.</p><p>We had three tenders thar supplied us with systems. All of theese meant considerable programmingwork to get the monitoring system up and running.</p>

Efficient drive cycle simulation of longitudinal vehicle propulsion models is an important aid for design and analysis of power trains. Tools on the market today mainly use two different methods for such simulations, forward dynamic or quasi-static inverse simulation. Here known theory for stable inversion of non linear systems is used in order to combine the fast simulation times of the quasi-static inverse simulation with the ability of including transient dynamics as in the forward dynamic simulation. The stable inversion technique with a new implicit driver model together forms a new concept, inverse dynamic simulation. This technique is demonstrated feasible for vehicle propulsion simulation and specifically on three powertrain applications that include important dynamics that can not be handled using quasi-static inverse simulation. The extensions are engine dynamics, drive line dynamics, and gas flow dynamics for diesel engines, which also are selected to represent important properties such as zero dynamics, resonances, and non-minimum phase systems. It is shown that inverse dynamic simulation is easy to set up, gives short simulation times, and gives consistent results for design space exploration. This makes inverse dynamic simulation a suitable method to use for drive cycle simulation, especially in situations requiring many simulations, such as optimization over design space, powertrain configuration optimization, or development of powertrain control strategies. Optimal vehicle propulsion control is developed with special focus on heavy trucks used for long haulage. The power to mass ratio for a typical heavy duty truck makes even moderate road slopes significant in the sense that it is impossible to keep a constant cruising speed. This gives an interesting problem how to control vehicle speed such that fuel consumption is minimized. Todays telematic systems together with three dimensional roadmaps can provide the vehicle control system with information of the road topography. This enables intelligent cruise controllers that utilize this information to control engine fueling and gear shifting such that an optimal speed trajectory is obtained. First the optimal control problem is solved numerically by dynamic programming, giving a controller with real time capabilities that can be used on-line in the vehicles control system. Simulations of such a system on authentic road profiles show that it has potential for significant fuel savings. To achieve knowledge about the underlying physics that affects the optimal solution, the optimal control problem is solved in detail and analytical expressions for the conditions of optimality are derived. Those expressions are then used to find optimal solutions on constructed test road profiles. Such test cases point out the typical behavior of an optimal solution and also which parameters that are decisive for the fuel minimization problem, and also how they quantitatively influence the behavior. It is for example shown that small non-linearities in the engine torque characteristics have significant effect on the optimal control strategy. The solutions for the non linear engine model have a smoother character but also require longer prediction horizons. For optimal gear ratio control it is shown that the maximum fueling function is essential for the solution. For example, in the case of a continuously variable transmission it is shown that the gear ratio never is chosen such that engine speed exceeds the speed of maximum engine power. For a discrete step transmission the gear shifting losses are essential for the optimal shift positions, but over all the solutions are close to continuous solutions.