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The Complete Coverage Path Planning (CCPP) problem is a subfield of industrial motion planning that has applications in various domains, ranging from mobile robotics to treatment applications. Especially in precision agriculture with a high level of automation, the use of CCPP techniques is essential for efficient resource utilization, reduced soil compaction, and increased yields. This paper reviews...
A series of technical and social aspects have led the pressure to increase energy efficiency and reduce the level of environmental impact in agricultural production. Crop producers and equipment manufacturers have identified computerized assistance in operation management as an indispensable tool to optimize agricultural processes. A central place is occupied in this regard by the so called digital...
Light detection and ranging (LiDAR) sensors have proven to be a valuable tool to gather spatial information about the environment and are a crucial component in perception of autonomous systems. In the agricultural domain, state‐of‐the‐art algorithms for detection, classification, and tracking often utilize a combination of LiDAR and camera by fusing both semantic and spatial information. This is...
Accurate models are crucial for simulating, optimizing, and controlling real‐world processes. Parameter identification—the task of estimating the unknown parameters of a dynamical system based on measurements—is challenging and there exist various methods to approach it. Integration‐based methods, such as shooting methods and full discretization, approximate the model output by numerically solving...
In the transition away from fossil energy, the use of renewable energy is gaining more importance. Agricultural businesses have a high energy demand as well as space for the installation of renewable energies, such as photovoltaic systems (PV). However, with the growing difference between electricity prices and feed‐in tariffs, the profitability of photovoltaic systems increasingly depends on the...
With the transition towards renewable energy underway, demand‐side management together with the local generation of renewable energy is receiving growing attention. Optimizing the self‐consumption of locally produced renewable energy can not only have financial benefits for the respective household or business (and improve their autarky from increasingly unstable energy markets), but also help improve...
Nonlinear optimization problems arise in the context of many engineering processes and other real‐world applications. Depending on the complexity of modeled phenomena and constraints, such problems can feature multiple local solutions of different nature. Primarily, the quality of a solution is measured by the value of an objective function, and hence, one aims to find a global optimum. In many cases,...
In many application areas that involve solving parametric optimization problems, it is desirable that solutions of perturbed problems do not deviate too much from the original ones. In this work, we develop a criterion which characterizes the stability of a local solution of an unconstrained parametric nonlinear program with respect to parameter perturbations. It is defined as the solution of an optimization...
Due to their inherently complex structure, bilevel optimization problems are often transformed into single‐level problems in order to make them numerically solvable. In this work, we present a novel reformulation strategy, in which we introduce sets of variables and constraints that represent the process of numerically solving the lower‐level problem based on a full step exact Hessian sequential quadratic...
In this contribution we consider linear quadratic regulator problems subject to parameter perturbations within the system dynamics. Due to the perturbations, optimality of the regulator would be lost. Iteratively recomputing the optimal feedback matrix is likely to be too costly for real‐time applications, but approximated updates using parametric sensitivities can be efficiently derived. Online parameter...
The digital revolution, especially in the field of manufacturing, has great potential to change the economy sustainably. In this work, the development of methods for predictive maintenance and condition monitoring is a central focus. Data‐based models for drive technology in automotive production are investigated in order to generate adequate models, to make statements about the life cycle of the...
In this work, we formulate and solve the problem of finding the ball of maximum radius around a local minimum of a nonlinear optimization problem, which is invariant with respect to the gradient descent method. This problem arises in the context of solving sequences of nonlinear optimization problems, in which one usually strives to converge to qualitatively similar solutions. We illustrate our idea...
When applying the single shooting approach to solve nonlinear dynamic parameter identification problems, difficulties like undesired minima can occur. To circumvent this, we apply a homotopy continuation to find global minima. In contrast to the literature, we reduce the resulting series of optimization problems to a single one which leads us to the opportunity to compute homotopy paths in a more...
Numerical methods for parameter identification of dynamical systems are based on matching model outputs to measurements. Computing the model output requires numerical integration techniques, though. In this contribution, we study the role of integration methods for mechanical systems. Since mechanical systems have characteristic properties, using structure‐preserving integration methods suggests itself...
To achieve true autonomy during critical mission phases in deep space, it is imperative to know which states are attainable from a given starting point using only admissible control inputs. These attainable states form the reachable set. If the latter is computed in real time, this can provide a system for Guidance, Navigation and Control on‐board of an autonomous spacecraft with knowledge of all...
In this work, we apply transcription methods known from optimal control to nonlinear dynamic parameter identification problems. We analyze and compare the methods with the help of an application example from robotics. More specifically, we investigate their robustness against varying initial parameters and show numerically, that an increasing number of variables leads to a more robust optimization...
This paper shows how a discrete approximation of a Pareto front can be refined with polynomial interpolation. For this we exploit the information given by the discrete samples of the Pareto front and in addition we use parametric sensitivity information from these samples. The pararmetric sensitivities are afterwards used to ensure feasibility of the obtained interpolated solutions by applying an...
Nowadays Parameter Identification Problems (PIP) are one of the main tasks in many engineering applications. For example, a model for the dynamic behavior of a robotic system has to be found. Before we can work with a system, e.g. solve an optimal control problem (OCP) to optimally perform an assigned task, we have to identify unknown parameters within the system model. In general, system identification...
Solving an engineering problem starts with the description of the problem in mathematical formulas and the identification of parameters. The generated model is then used to simulate the behavior of the underlying system. However, most systems are not static. They change over time. Thus, the model needs to be adapted to these activities otherwise the predictions are wrong.
A data driven modeling method...
This paper shows how an electrical distribution network can be modeled as constraints of a continuous nonlinear optimization problem. The objective is to minimize the deviation from a given nominal voltage. We explain how this setup can be used to optimize wire diameters within the network. Thus we find the optimal expansion of the network by identifying wires which should be enforced. The results...
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