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The trajectory tracking problem for a real-scaled fully-actuated surface vessel is addressed in this paper. A nonlinear model predictive control (NMPC) scheme was designed to track a reference trajectory, considering state and input constraints, and environmental disturbances, which were assumed to be constant over the prediction horizon. The controller was tested by performing docking maneuvers using the real-scaled research vessel from the University of Applied Sciences Konstanz at the Rhine river in Germany. A comparison between the experimental results and the simulated ones was analyzed to validate the NMPC controller.
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.
The problem of vessel collisions or near-collision situations on sea, often caused by human error due to incomplete or overwhelming information, is becoming more and more important with rising maritime traffic. Approaches to supply navigators and Vessel Traffic Services with expert knowledge and suggest trajectories for all vessels to avoid collisions, are often aimed at situations where a single planner guides all vessels with perfect information. In contrast, we suggest a two-part procedure which plans trajectories using a specialised A* and negotiates trajectories until a solution is found, which is acceptable for all vessels. The solution obeys collision avoidance rules, includes a dynamic model of all vessels and negotiates trajectories to optimise globally without a global planner and extensive information disclosure. The procedure combines all components necessary to solve a multi-vessel encounter and is tested currently in simulation and on several test beds. The first results show a fast converging optimisation process which after a few negotiation rounds already produce feasible, collision free trajectories.
This paper presents the integration of a spline based extension model into a probability hypothesis density (PHD) filter for extended targets. Using this filter the position and extension of each object as well as the number of present objects can jointly be estimated. Therefore, the spline extension model and the PHD filter are addressed and merged in a Gaussian mixture (GM) implementation. Simulation results using artificial laser measurements are used to evaluate the performance of the presented filter. Finally, the results are illustrated and discussed.
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.
Small vessels or unmanned surface vehicles only have a limited amount of space and energy available. If these vessels require an active sensing collision avoidance system it is often not possible to mount large sensor systems like X-Band radars. Thus, in this paper an energy efficient automotive radar and a laser range sensor are evaluated for tracking surrounding vessels. For these targets, those type of sensors typically generate more than one detection per scan. Therefore, an extended target tracking problem has to be solved to estimate state end extension of the vessels. In this paper, an extended version of the probabilistic data association filter that uses random matrices is applied. The performance of the tracking system using either radar or laser range data is demonstrated in real 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.
This paper presents a new likelihood-based partitioning method of the measurement set for the extended object probability hypothesis density (PHD) filter framework. Recent work has mostly relied on heuristic partitioning methods that cluster the measurement data based on a distance measure between the single measurements. This can lead to poor filter performance if the tracked extended objects are closely spaced. The proposed method called Stochastic Partitioning (StP) is based on sampling methods and was inspired by a former work of Granström et. al. In this work, the StP method is applied to a Gaussian inverse Wishart (GIW) PHD filter and compared to a second filter implementation that uses the heuristic Distance Partitioning (DP) method. The performance is evaluated in Monte Carlo simulations in a scenario where two objects approach each other. It is shown that the sampling based StP method leads to an improved filter performance compared to DP.
Knowing the position of the spool in a solenoid valve, without using costly position sensors, is of considerable interest in a lot of industrial applications. In this paper, the problem of position estimation based on state observers for fast-switching solenoids, with sole use of simple voltage and current measurements, is investigated. Due to the short spool traveling time in fast-switching valves, convergence of the observer errors has to be achieved very fast. Moreover, the observer has to be robust against modeling uncertainties and parameter variations. Therefore, different state observer approaches are investigated, and compared to each other regarding possible uncertainties. The investigation covers a High-Gain-Observer approach, a combined High-Gain Sliding-Mode-Observer approach, both based on extended linearization, and a nonlinear Sliding-Mode-Observer based on equivalent output injection. The results are discussed by means of numerical simulations for all approaches, and finally physical experiments on a valve-mock-up are thoroughly discussed for the nonlinear Sliding-Mode-Observer.
Sliding-mode observation with iterative parameter adaption for fast-switching solenoid valves
(2016)
Control of the armature motion of fast-switching solenoid valves is highly desired to reduce noise emission and wear of material. For feedback control, information of the current position and velocity of the armature are necessary. In mass production applications, however, position sensors are unavailable due to cost and fabrication reasons. Thus, position estimation by measuring merely electrical quantities is a key enabler for advanced control, and, hence, for efficient and robust operation of digital valves in advanced hydraulic applications. The work presented here addresses the problem of state estimation, i.e., position and velocity of the armature, by sole use of electrical measurements. The considered devices typically exhibit nonlinear and very fast dynamics, which makes observer design a challenging task. In view of the presence of parameter uncertainty and possible modeling inaccuracy, the robustness properties of sliding mode observation techniques are deployed here. The focus is on error convergence in the presence of several sources for modeling uncertainty and inaccuracy. Furthermore, the cyclic operation of switching solenoids is exploited to iteratively correct a critical parameter by taking into account the norm of the observation error of past switching cycles of the process. A thorough discussion on real-world experimental results highlights the usefulness of the proposed state observation approach.
In the past years, algorithms for 3D shape tracking using radial functions in spherical coordinates represented with different methods have been proposed. However, we have seen that mainly measurements from the lateral surface of the target can be expected in a lot of dynamic scenarios and only few measurements from the top and bottom parts leading to an error-prone shape estimate in the top and bottom regions when using a representation in spherical coordinates. We, therefore, propose to represent the shape of the target using a radial function in cylindrical coordinates, as these only represent regions of the lateral surface, and no information from the top or bottom parts is needed. In this paper, we use a Fourier-Chebyshev double series for 3D shape representation since a mixture of Fourier and Chebyshev series is a suitable basis for expanding a radial function in cylindrical coordinates. We investigate the method in a simulated and real-world maritime scenario with a CAD model of the target boat as a reference. We have found that shape representation in cylindrical coordinates has decisive advantages compared to a shape representation in spherical coordinates and should preferably be used if no prior knowledge of the measurement distribution on the surface of the target is available.
In this paper, a novel measurement model based on spherical double Fourier series (DFS) for estimating the 3D shape of a target concurrently with its kinematic state is introduced. Here, the shape is represented as a star-convex radial function, decomposed as spherical DFS. In comparison to ordinary DFS, spherical DFS do not suffer from ambiguities at the poles. Details will be given in the paper. The shape representation is integrated into a Bayesian state estimator framework via a measurement equation. As range sensors only generate measurements from the target side facing the sensor, the shape representation is modified to enable application of shape symmetries during the estimation process. The model is analyzed in simulations and compared to a shape estimation procedure using spherical harmonics. Finally, shape estimation using spherical and ordinary DFS is compared to analyze the effect of the pole problem in extended object tracking (EOT) scenarios.
Sensorlose Positionsregelung eines hydraulischen Proportional-Wegeventils mittels Signalinjektion
(2017)
Es wird eine Methode zur sensorlosen Positionsbestimmung bei elektromagnetisch betätigten Aktoren vorgestellt. Dabei werden basierend auf einer Signalinjektion die positionsabhängigen Parameter bei der injizierten Frequenz bestimmt und daraus über ein geeignetes Modell die Position des Magnetankers ermittelt. Die Eignung des Verfahrens zur sensorlosen Positionsregelung wird an einem bidirektionalen Proportionalventil anhand praktischer Versuche demonstriert.
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).
Probabilistic data association for tracking extended targets under clutter using random matrices
(2015)
The use of random matrices for tracking extended objects has received high attention in recent years. It is an efficient approach for tracking objects that give rise to more than one measurement per time step. In this paper, the concept of random matrices is used to track surface vessels using highresolution automotive radar sensors. Since the radar also receives a large number of clutter measurements from the water, for the data association problem, a generalized probabilistic data association filter is applied. Additionally, a modification of the filter update step is proposed to incorporate the Doppler velocity measurements. The presented tracking algorithm is validated using Monte Carlo Simulation, and some performance results with real radar data are shown as well.
The improvement of collision avoidance for vessels in close range encounter situations is an important topic for maritime traffic safety. Typical approaches generate evasive trajectories or optimise the trajectories of all involved vessels. Such a collision avoidance system has to produce evasive manoeuvres that do not confuse other navigators. To achieve this behaviour, a probabilistic obstacle handling based on information from a radar sensor with target tracking, that considers measurement and tracking uncertainties is proposed. A grid based path search algorithm, that takes the information from the probabilistic obstacle handling into account, is then used to generate evasive trajectories. The proposed algorithms have been tested and verified in a simulated environment for inland waters.
The method of signal injection is investigated for position estimation of proportional solenoid valves. A simple observer is proposed to estimate a position-dependent parameter, i.e. the eddy current resistance, from which the position is calculated analytically. Therefore, the relationship of position and impedance in the case of sinusoidal excitation is accurately described by consideration of classical electrodynamics. The observer approach is compared with a standard identification method, and evaluated by practical experiments on an off-the-shelf proportional solenoid valve.