Institut für Systemdynamik - ISD
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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.
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.
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.
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.
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.
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.
Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
(2021)
The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem together with the one-Mannheim error channel, where the error values are limited to Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extent the rate region where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.
Modular arithmetic over integers is required for many cryptography systems. Montgomeryreduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Mont-gomery reduction is used for rings of ordinary integers. In contrast, we investigate the modularreduction over rings of Gaussian integers. Gaussian integers are complex numbers where the real andimaginary parts are integers. Rings over Gaussian integers are isomorphic to ordinary integer rings.In this work, we show that Montgomery reduction can be applied to Gaussian integer rings. Twoalgorithms for the precision reduction are presented. We demonstrate that the proposed Montgomeryreduction enables an efficient Gaussian integer arithmetic that is suitable for elliptic curve cryptogra-phy. In particular, we consider the elliptic curve point multiplication according to the randomizedinitial point method which is protected against side-channel attacks. The implementation of thisprotected point multiplication is significantly faster than comparable algorithms over ordinary primefields.
The McEliece cryptosystem is a promising candidate for post-quantum public-key encryption. In this work, we propose q-ary codes over Gaussian integers for the McEliece system and a new channel model. With this one Mannheim error channel, errors are limited to weight one. We investigate the channel capacity of this channel and discuss its relation to the McEliece system. The proposed codes are based on a simple product code construction and have a low complexity decoding algorithm. For the one Mannheim error channel, these codes achieve a higher error correction capability than maximum distance separable codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding.