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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, 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.
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 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.