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Institute
- Institut für Systemdynamik - ISD (103) (remove)
This paper presents a modeling approach of an industrial heating process where a stripe-shaped workpiece is heated up to a specific temperature by applying hot air through a nozzle. The workpiece is moving through the heating zone and is considered to be of infinite length. The speed of the substrate is varying over time. The derived model is supposed to be computationally cheap to enable its use in a model-based control setting. We start by formulating the governing PDE and the corresponding boundary conditions. The PDE is then discretized on a spatial grid using finite differences and two different integration schemes, explicit and implicit, are derived. The two models are evaluated in terms of computational effort and accuracy. It turns out that the implicit approach is favorable for the regarded process. We optimize the grid of the model to achieve a low number of grid nodes while maintaining a sufficient amount of accuracy. Finally, the thermodynamical parameters are optimized in order to fit the model's output to real-world data that was obtained by experiments.
Code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-ary codes lead to high error correction capabilities. Hence, these codes achieve high work factors for information set decoding attacks. In this work, we adapt this concept to codes for the weight-one error channel, i.e., a binary channel model where at most one bit-error occurs in each block of m bits. We also propose a low complexity decoding algorithm for the proposed codes. Compared to codes over Gaussian and Eisenstein integers, these codes achieve higher minimum Hamming distances for the dual codes of the inner component codes. This property increases the work factor for a structural attack on concatenated codes leading to higher overall security. For comparable security, the key size for the proposed code construction is significantly smaller than for the classic McEliece scheme based on Goppa codes.
Nowadays, most digital modulation schemes are based on conventional signal constellations that have no algebraic group, ring, or field properties, e.g. square quadrature-amplitude modulation constellations. Signal constellations with algebraic structure can enhance the system performance. For instance, multidimensional signal constellations based on dense lattices can achieve performance gains due to the dense packing. The algebraic structure enables low-complexity decoding and detection schemes. In this work, signal constellations with algebraic properties and their application in spatial modulation transmission schemes are investigated. Several design approaches of two- and four-dimensional signal constellations based on Gaussian, Eisenstein, and Hurwitz integers are shown. Detection algorithms with reduced complexity are proposed. It is shown, that the proposed Eisenstein and Hurwitz constellations combined with the proposed suboptimal detection can outperform conventional two-dimensional constellations with ML detection.
Virtual measurement models (VMM) can be used to generate artificial measurements and emulate complex sensor models such as Lidar. The input of the VMM is an estimation and the output is the set of measurements this estimation would cause. A Kalman filter with extension estimation based on random matrices is used to filter mean and covariance of the real measurements. If these match the mean and covariance of the artificial measurements, then the given estimation is appropriate. The optimal input of the VMM is found using an adaptation algorithm. In this paper, the VMM approach is expanded for multi-extended object tracking where objects can be occluded and are only partially visible. The occlusion can be compensated if the extension estimation is performed for all objects together. The VMM now receives as input an estimation for the multi-object state and the output are the measurements that this multi-object state would cause.
With the high resolution of modern sensors such as multilayer LiDARs, estimating the 3D shape in an extended object tracking procedure is possible. In recent years, 3D shapes have been estimated in spherical coordinates using Gaussian processes, spherical double Fourier series or spherical harmonics. However, observations have shown that in many scenarios only a few measurements are obtained from top or bottom surfaces, leading to error-prone estimates in spherical coordinates. Therefore, in this paper we propose to estimate the shape in cylindrical coordinates instead, applying harmonic functions. Specifically, we derive an expansion for 3D shapes in cylindrical coordinates by solving a boundary value problem for the Laplace equation. This shape representation is then integrated in a plain greedy association model and compared to shape estimation procedures in spherical coordinates. Since the shape representation is only integrated in a basic estimator, the results are preliminary and a detailed discussion for future work is presented at the end of the paper.
Feature-Based Proposal Density Optimization for Nonlinear Model Predictive Path Integral Control
(2022)
This paper presents a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control. In MPPI control, the optimal control is calculated by solving a stochastic optimal control problem online using the weighted inference of stochastic trajectories. While the algorithm can be excellently parallelized the closed- loop performance is dependent on the information quality of the drawn samples. Because these samples are drawn using a proposal density, its quality is crucial for the solver and thus the controller performance. In classical MPPI control, the explored state-space is strongly constrained by assumptions that refer to the control value variance, which are necessary for transforming the Hamilton-Jacobi-Bellman (HJB) equation into a linear second-order partial differential equation. To achieve excellent performance even with discontinuous cost-functions, in this novel approach, knowledge-based features are used to determine the proposal density and thus, the region of state- space for exploration. This paper addresses the question of how the performance of the MPPI algorithm can be improved using a feature-based mixture of base densities. Further, the developed algorithm is applied on an autonomous vessel that follows a track and concurrently avoids collisions using an emergency braking feature.
This paper presents a systematic comparison of different advanced approaches for motion prediction of vessels for docking scenarios. Therefore, a conventional nonlinear gray-box-model, its extension to a hybrid model using an additional regression neural network (RNN) and a black-box-model only based on a RNN are compared. The optimal hyperparameters are found by grid search. The training and validation data for the different models is collected in full-scale experiments using the solar research vessel Solgenia. The performances of the different prediction models are compared in full-scale scenarios. %To use the investigated approaches for controller design, a general optimal control problem containing the advanced models is described. These can improve advanced control strategies e.g., nonlinear model predictive control (NMPC) or reinforcement learning (RL). This paper explores the question of what the advantages and disadvantages of the different presented prediction approaches are and how they can be used to improve the docking behavior of a vessel.
The growing error rates of triple-level cell (TLC) and quadruple-level cell (QLC) NAND flash memories have led to the application of error correction coding with soft-input decoding techniques in flash-based storage systems. Typically, flash memory is organized in pages where the individual bits per cell are assigned to different pages and different codewords of the error-correcting code. This page-wise encoding minimizes the read latency with hard-input decoding. To increase the decoding capability, soft-input decoding is used eventually due to the aging of the cells. This soft-decoding requires multiple read operations. Hence, the soft-read operations reduce the achievable throughput, and increase the read latency and power consumption. In this work, we investigate a different encoding and decoding approach that improves the error correction performance without increasing the number of reference voltages. We consider TLC and QLC flashes where all bits are jointly encoded using a Gray labeling. This cell-wise encoding improves the achievable channel capacity compared with independent page-wise encoding. Errors with cell-wise read operations typically result in a single erroneous bit per cell. We present a coding approach based on generalized concatenated codes that utilizes this property.
In this paper, a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control is presented. Using the MPPI approach, the optimal feedback control is calculated by solving a stochastic optimal control (OCP) problem online by evaluating the weighted inference of sampled stochastic trajectories. While the MPPI algorithm can be excellently parallelized, the closed-loop performance strongly depends on the information quality of the sampled trajectories. To draw samples, a proposal density is used. The solver’s and thus, the controller’s performance is of high quality if the sampled trajectories drawn from this proposal density are located in low-cost regions of state-space. In classical MPPI control, the explored state-space is strongly constrained by assumptions that refer to the control value’s covariance matrix, which are necessary for transforming the stochastic Hamilton–Jacobi–Bellman (HJB) equation into a linear second-order partial differential equation. To achieve excellent performance even with discontinuous cost functions, in this novel approach, knowledge-based features are introduced to constitute the proposal density and thus the low-cost region of state-space for exploration. This paper addresses the question of how the performance of the MPPI algorithm can be improved using a feature-based mixture of base densities. Furthermore, the developed algorithm is applied to an autonomous vessel that follows a track and concurrently avoids collisions using an emergency braking feature. Therefore, the presented feature-based MPPI algorithm is applied and analyzed in both simulation and full-scale experiments.
Docking Control of a Fully-Actuated Autonomous Vessel using Model Predictive Path Integral Control
(2022)
This paper presents the docking control of an autonomous vessel using the nonlinear Model Predictive Path Integral (MPPI) approach. This algorithm is based on a path integral over stochastic trajectories and can be parallelized easily. The controller parameters are tuned offline using knowledge of the system and simulations, including nonlinear state and disturbance observer. The cost function implicitly contains information regarding the surrounding of the docking position. This approach allows continuous optimization of the trajectory with respect to the system state, disturbance state and actuator dynamics. The control strategy has been tested in full-scale experiments using the solar research vessel Solgenia. The investigated MPPI controller has demonstrated excellent performance in both, simulation and real-world experiments. This paper addresses the question of how the MPPI algorithm can be applied to dock a fully-actuated vessel and what benefits its application achieves.
This paper presents the swinging up and stabilization control of a Furuta pendulum using the recently published nonlinear Model Predictive Path Integral (MPPI) approach. This algorithm is based on a path integral over stochastic trajectories and can be parallelized easily. The controller parameters are tuned offline regarding the nonlinear system dynamics and simulations. Constraints in terms of state and input are taken into account in the cost function. The presented approach sequentially computes an optimal control sequence that minimizes this optimal control problem online. The control strategy has been tested in full-scale experiments using a pendulum prototype. The investigated MPPI controller has demonstrated excellent performance in simulation for the swinging up and stabilizing task. In order to also achieve outstanding performance in a real-world experiment using a controller with limited computing power, a linear quadratic controller (LQR) is designed for the stabilization task. In this paper, the determination of the controller parameters for the MPPI algorithm is described in detail. Further, a discussion treats the advantages of the nonlinear MPPI control.
In this paper, approximating the shape of a sailing boat using elliptic cones is investigated. Measurements are assumed to be gathered from the target's surface recorded by 3D scanning devices such as multilayer LiDAR sensors. Therefore, different models for estimating the sailing boat's extent are presented and evaluated in simulated and real-world scenarios. In particular, the measurement source association problem is addressed in the models. Simulated investigations are conducted with a static and a moving elliptic cone. The real-world scenario was recorded with a Velodyne Alpha Prime (VLP-128) mounted on a ferry of Lake Constance. Final results of this paper constitute the extent estimation of a single sailing boat using LiDAR data applying various measurement models.
Reliability Assessment of an Unscented Kalman Filter by Using Ellipsoidal Enclosure Techniques
(2022)
The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable for nonlinear processes than the linearization-based Extended Kalman Filter (EKF) due to the enhanced approximation capabilities of its underlying probability distribution, it is not a priori obvious whether its strategy for selecting sigma points is sufficiently accurate to handle nonlinearities in the system dynamics and output equations. Such inaccuracies may arise for sufficiently strong nonlinearities in combination with large state, disturbance, and parameter covariances. Then, computationally more demanding approaches such as particle filters or the representation of (multi-modal) probability densities with the help of (Gaussian) mixture representations are possible ways to resolve this issue. To detect cases in a systematic manner that are not reliably handled by a standard EKF or UKF, this paper proposes the computation of outer bounds for state domains that are compatible with a certain percentage of confidence under the assumption of normally distributed states with the help of a set-based ellipsoidal calculus. The practical applicability of this approach is demonstrated for the estimation of state variables and parameters for the nonlinear dynamics of an unmanned surface vessel (USV).
Experimental Validation of Ellipsoidal Techniques for State Estimation in Marine Applications
(2022)
A reliable quantification of the worst-case influence of model uncertainty and external disturbances is crucial for the localization of vessels in marine applications. This is especially true if uncertain GPS-based position measurements are used to update predicted vessel locations that are obtained from the evaluation of a ship’s state equation. To reflect real-life working conditions, these state equations need to account for uncertainty in the system model, such as imperfect actuation and external disturbances due to effects such as wind and currents. As an application scenario, the GPS-based localization of autonomous DDboat robots is considered in this paper. Using experimental data, the efficiency of an ellipsoidal approach, which exploits a bounded-error representation of disturbances and uncertainties, is demonstrated.
Multi-object tracking filters require a birth density to detect new objects from measurement data. If the initial positions of new objects are unknown, it may be useful to choose an adaptive birth density. In this paper, a circular birth density is proposed, which is placed like a band around the surveillance area. This allows for 360° coverage. The birth density is described in polar coordinates and considers all point-symmetric quantities such as radius, radial velocity and tangential velocity of objects entering the surveillance area. Since it is assumed that these quantities are unknown and may vary between different targets, detected trajectories, and in particular their initial states, are used to estimate the distribution of initial states. The adapted birth density is approximated as a Gaussian mixture, so that it can be used for filters operating on Cartesian coordinates.
Extended Target Tracking With a Lidar Sensor Using Random Matrices and a Virtual Measurement Model
(2022)
Random matrices are widely used to estimate the extent of an elliptically contoured object. Usually, it is assumed that the measurements follow a normal distribution, with its standard deviation being proportional to the object’s extent. However, the random matrix approach can filter the center of gravity and the covariance matrix of measurements independently of the measurement model. This work considers the whole chain from data acquisition to the linear Kalman Filter with extension estimation as a reference plant. The input is the (unknown) ground truth (position and extent). The output is the filtered center of gravity and the filtered covariance matrix of the measurement distribution. A virtual measurement model emulates the behavior of the reference plant. The input of the virtual measurement model is adapted using the proposed algorithm until the output parameters of the virtual measurement model match the result of the reference plant. After the adaptation, the input to the virtual measurement model is considered an estimation for position and extent. The main contribution of this paper is the reference model concept and an adaptation algorithm to optimize the input of the virtual measurement model.
Kapitel 2 der vorliegenden Arbeit beschreibt die theoretischen Grundlagen optimaler Regelung und die unterschiedlichen Methoden des Pfadintegral Frameworks zur Reglersynthese. Zudem wird ein Ansatz zur Erweiterung des stochastischen NMPC dargestellt, sodass eine Adaption an eine real vorliegende Systemdynamik erfolgt. Weiter wird eine Methode entwickelt und beschrieben, welche die Effizienz des Algorithmus stark erhöht.
In Kapitel 3 wird aufgezeigt, wie die Pfadintegral Regelung dazu genutzt wird ein Furuta Pendel aufzuschwingen.
In Kapitel 4 werden die Algorithmen zur Lösung unterschiedlicher Problemstellungen im Kontext eines Forschungsboot appliziert. So wird unter anderem gezeigt, wie ein Pfadintegral Regelungsalgorithmus genutzt werden kann, um autonom mit dem Forschungsboot Solgenia am Steg der HTWG Konstanz anzulegen.
Abschließend wird in Kapitel 5 ein Fazit aus den Ergebnissen gezogen, diese eingeordnet und ein Ausblick auf weitere mögliche Arbeiten gegeben.
This paper describes the development of a control system for an industrial heating application. In this process a moving substrate is passing through a heating zone with variable speed. Heat is applied by hot air to the substrate with the air flow rate being the manipulated variable. The aim is to control the substrate’s temperature at a specific location after passing the heating zone. First, a model is derived for a point attached to the moving substrate. This is modified to reflect the temperature of the moving substrate at the specified location. In order to regulate the temperature a nonlinear model predictive control approach is applied using an implicit Euler scheme to integrate the model and an augmented gradient based optimization approach. The performance of the controller has been validated both by simulations and experiments on the physical plant. The respective results are presented in this paper.
Trajectory Tracking of a Fully-actuated Surface Vessel using Nonlinear Model Predictive Control
(2021)
The trajectory tracking problem for a fully-actuated real-scaled surface vessel is addressed in this paper. The unknown hydrodynamic and propulsion parameters of the vessel’s dynamic model were identified using an experimental maneuver-based identification process. Then, a nonlinear model predictive control (NMPC) scheme is designed and the controller’s performance is assessed through the variation of NMPC parameters and constraints tightening for tracking a curved trajectory.
In this paper, a systematic comparison of three different advanced control strategies for automated docking of a vessel is presented. The controllers are automatically tuned offline by applying an optimization process using simulations of the whole system including trajectory planner and state and disturbance observer. Then investigations are conducted subject to performance and robustness using Monte Carlos simulation with varying model parameters and disturbances. The control strategies have also been tested in full scale experiments using the solar research vessel Solgenia. The investigated control strategies all have demonstrated very good performance in both, simulation and real world experiments. Videos are available under https://www.htwg-konstanz.de/forschung-und-transfer/institute-und-labore/isd/regelungstechnik/videos/