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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/