| 1. |
- Bergman, Kristoffer, 1990-
(författare)
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Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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. The objective in optimal motion planning problems is to find feasible motion plans that also optimize a performance measure. From a control perspective, the problem is an instance of an optimal control problem. This thesis addresses optimal motion planning problems for complex dynamical systems that operate in unstructured environments, where no prior reference such as road-lane information is available. Some example scenarios are autonomous docking of vessels in harbors and autonomous parking of self-driving tractor-trailer vehicles at loading sites. The focus is to develop optimal motion planning algorithms that can reliably be applied to these types of problems. This is achieved by combining recent ideas from automatic control, numerical optimization and robotics.The first contribution is a systematic approach for computing local solutions to motion planning problems in challenging unstructured environments. The solutions are computed by combining homotopy methods and direct 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 a state-of-the-art asymptotically optimal motion planner based on random sampling.The second contribution is an optimization-based framework for automatic generation of motion primitives for lattice-based motion planners. 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 framework computes a library of motion primitives by simultaneously optimizing the motions and the terminal states.The final contribution of this thesis is a motion planning framework that combines the strengths of sampling-based planners with direct optimal control in a novel way. The sampling-based planner is applied to the problem in a first step using a discretized search space, where the system dynamics and objective function are chosen to coincide with those used in a second step based on optimal control. This combination ensures that the sampling-based motion planner provides a feasible motion plan which is highly suitable as warm-start to the optimal control step. Furthermore, the second step is modified such that it also can be applied in a receding-horizon fashion, where the proposed combination of methods is used to provide theoretical guarantees in terms of recursive feasibility, worst-case objective function value and convergence to the terminal state. The proposed motion planning framework is successfully applied to several problems in challenging unstructured environments for tractor-trailer vehicles. The framework is also applied and tailored for maritime navigation for vessels in archipelagos and harbors, where it is able to compute energy-efficient trajectories which complies with the international regulations for preventing collisions at sea.
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| 2. |
- Bergman, Kristoffer, 1990-
(författare)
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On Motion Planning Using Numerical Optimal Control
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 3. |
- Fliess, Michel, et al.
(författare)
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An Algebraic Approach to Linear and Nonlinear Control
- 1994
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The analysis and design of control systems has been greatly influenced by the mathematical tools being used. Maxwell introduced linear differential equations in the 1860’s. Nyquist, Bode and others started the systematic use of tranfer functions, utilizing complex analysis in the 1930’s. Kalman brought forward state space analysis around 1960. For nonlinear systems, differential geometric concepts have been of great value recently. We will argue here that algebraic methods can be very useful for both linear and nonlinear systems. To give some motivation we will begin by looking at a few examples.
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| 4. |
- Forsman, Krister, et al.
(författare)
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Constructive Algebra and Control Theory
- 1993
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Ingår i: Proceedings of the 1993 International Symposium on The Mathematical Theory of Networks and Systems. - Linköping : Linköping University. - 9783055016615 ; , s. 149-152
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Rapport (övrigt vetenskapligt/konstnärligt)
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| 5. |
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| 6. |
- Gerdin, Markus, et al.
(författare)
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Global Identifiability of Complex Models, Constructed from Simple Submodels
- 2007
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Ingår i: Modeling, Estimation and Control. - Linköping : Linköping University Electronic Press. - 9783540735694 ; , s. 123-133
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- It is a typical situation in modern modeling that a total model is built up from simpler submodels, or modules, for example residing in a model library. The total model could be quite complex, while the modules are well understood and analysed. A procedure to decide global parameter identifiability for such a collection of model equations of differential-algebraic nature is suggested. It is shown how to make use of the natural modularization of the model structure. Basically, global identifiability is obtained if and only if each module is identifiable, and the connecting signals can be retrieved from the external signals, without knowledge of the values of the parameters.
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| 7. |
- Gerdin, Markus, et al.
(författare)
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On Identifiability of Object-Oriented Models
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- When estimating unknown parameters, it is important that the model is identifiable so that the parameters can be estimated uniquely. For nonlinear differential-algebraic equation models with polynomial equations, a differential algebra approach to examine identifiability is available. This approach can be slow, so the present paper describes how this method can be modularized for object-oriented models. A characteristic set of equations is computed for components in model libraries, and stored together with the components. When an object-oriented model is built using such models, identifiability can be examined using the stored equations.
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| 8. |
- Germundsson, Roger, et al.
(författare)
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A Unified Constructive Study of Linear, Nonlinear and Discrete Event Systems
- 1995
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Starting from the behavioral point of view a system is defined by its set of behaviors. In discrete time this is a relation over D N and hence a very infinite object. A model is a relation over D N for some finite N that can be extended to a behavior. Furthermore properties of a system is defined in terms of its behavior. Starting from a constructive point of view we need to be able to represent and manipulate systems. A natural choice is to use some a constructive model, i.e. one that can be finitely represented and manipulated. We will consider four such classes of models: polynomial and linear relations over finite and infinite fields. There are a number of restrictions on the geometric (or behavioral) operations that are possible for each of these classes and still remain within the class. If we want to interpret our models as systems and analyze system properties, then several properties become impossible to compute. Some examples: The set of reachable states for a polynomial model over an infinite field is in general impossible to compute. It may converge to be fractal. The set of reacable states ik steps or less in a linear model cannot be represented as a linear set in general.
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| 9. |
- Glad, Torkel, 1947-, et al.
(författare)
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Aircraft Pitch Attitude Control using Backstepping
- 2000
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Ingår i: Proceedings of Reglermöte 2000. - Linköping : Linköping University Electronic Press. ; , s. 143-148
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- A nonlinear approach to the automatic pitch attitude control problem for a generic fighter aircraft is presented. A nonlinear model describing the longitudinal equations of motion in strict feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free design parameters. Two tuning schemes are proposed based on the desired locally linear controller properties. The controller is evaluated using the HIRM fighter aircraft model.
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| 10. |
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