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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.
In 3D extended object tracking (EOT), well-established models exist for tracking the object extent using various shape priors. A single update, however, has to be performed for every measurement using these models leading to a high computational runtime for high-resolution sensors. In this paper, we address this problem by using various model-independent downsampling schemes based on distance heuristics and random sampling as pre-processing before the update. We investigate the methods in a simulated and real-world tracking scenario using two different measurement models with measurements gathered from a LiDAR sensor. We found that there is a huge potential for speeding up 3D EOT by dropping up to 95\% of the measurements in our investigated scenarios when using random sampling. Since random sampling, however, can also result in a subset that does not represent the total set very well, leading to a poor tracking performance, there is still a high demand for further research.
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.
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.
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.
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.
Ein Beitrag zum Beobachterentwurf und zur sensorlosen Folgeregelung translatorischer Magnetaktoren
(2020)
A constructive method for the design of nonlinear observers is discussed. To formulate conditions for the construction of the observer gains, stability results for nonlinear singularly perturbed systems are utilised. The nonlinear observer is designed directly in the given coordinates, where the error dynamics between the plant and the observer becomes singularly perturbed by a high-gain part of the observer injection, and the information of the slow manifold is exploited to construct the observer gains of the reduced-order dynamics. This is in contrast to typical high-gain observer approaches, where the observer gains are chosen such that the nonlinearities are dominated by a linear system. It will be demonstrated that the considered approach is particularly suited for self-sensing electromechanical systems. Two variants of the proposed observer design are illustrated for a nonlinear electromagnetic actuator, where the mechanical quantities, i.e. the position and the velocity, are not measured
A constructive nonlinear observer design for self-sensing of digital (ON/OFF) single coil electromagnetic actuators is studied. Self-sensing in this context means that solely the available energizing signals, i.e., coil current and driving voltage are used to estimate the position and velocity trajectories of the moving plunger. A nonlinear sliding mode observer is considered, where the stability of the reduced error dynamics is analyzed by the equivalent control method. No simplifications are made regarding magnetic saturation and eddy currents in the underlying dynamical model. The observer gains are constructed by taking into account some generic properties of the systems nonlinearities. Two possible choices of the observer gains are discussed. Furthermore, an observer-based tracking control scheme to achieve sensorless soft landing is considered and its closed-loop stability is studied. Experimental results for observer-based soft landing of a fast-switching solenoid valve under dry conditions are presented to demonstrate the usefulness of the approach.
Flatness-based feed-forward control of solenoid actuators is considered. For precise motion planning and accurate steering of conventional solenoids, eddy currents cannot be neglected. The system of ordinary differential equations including eddy currents, that describes the nonlinear dynamics of such actuators, is not differentially flat. Thus, a distributed parameter approach based on a diffusion equation is considered, that enables the parametrization of the eddy current by the armature position and its time derivatives. In order to design the feedforward control, the distributed parameter model of the eddy current subsystem is combined with a typical nonlinear lumped parameter model for the electrical and mechanical subsystems of the solenoid. The control design and its application are illustrated by numerical and practical results for an industrial solenoid actuator.