Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal specifications. Due to scaling issues with respect to the complexity of the specifications and the potential occurrence of non-differentiable terms, classical optimization methods often solve STL-based problems inefficiently. Smoothing and approximation techniques can alleviate these issues but require changing the optimization problem. This paper proposes a novel sampling-based method based on model predictive path integral control to solve optimal control problems with STL cost functions. We demonstrate the effectiveness of our method on benchmark motion planning problems and compare its performance with state-of-the-art methods. The results show that our method efficiently solves optimal control problems with STL costs.

In extended object tracking, basic parametric shapes such as ellipses and rectangles or non-parametric shape representations such as Fourier series or Gaussian processes can be utilized as shape priors. However, flexible non-parametric shape representations can be disproportionately detailed and computationally intensive for many applications. Therefore, we propose to adopt deformable superellipses for a low-dimensional and flexible representation of basic parametric shapes in this paper. We present a measurement model in 2D space that can cope with boundary and interior measurements simultaneously by recursively estimating an artificial noise variance for interior measurements. We investigate and compare the model in a simulated and real-world maritime scenario with the result that the combination of deformable superellipses and artificial measurement noise estimation performs better than state-of-the-art methods.

In extended object tracking, random matrices are commonly used to filter the mean and covariance matrix from measurement data. However, the relation from mean and covariance matrix to the extension parameters can become challenging when a lidar sensor is used. To address this, we propose virtual measurement models to estimate those parameters iteratively by adapting them, until the statistical moments of the measurements they would cause, match the random matrix result. While previous work has focused on 2D shapes, this paper extends the methodology to encompass 3D shapes such as cones, ellipsoids and rectangular cuboids. Additionally, we introduce a classification method based on Chamfer distances for identifying the best-fitting shape when the object’s shape is unknown. Our approach is evaluated through simulation studies and with real lidar data from maritime scenarios. The results indicate that a cone is the best representation for sailing boats, while ellipsoids are optimal for motorboats.

Interacting multiple model filters are most commonly used in the context of maneuvering targets, as they can represent the different dynamics of a real system by combining the estimates of multiple models. However, the interacting multiple model approach generally requires more computational effort than a single Kalman filter. In this work, down-sampling is used to reduce the computational effort. We propose an adaptive scheme to maintain the accuracy of the estimator to a defined level. To this end, the trace of the innovation covariance matrix is evaluated, and if it lies above a certain threshold, out-of-sequence measurements are iteratively used to improve the estimate until the uncertainty threshold is met. The approach is evaluated by Monte Carlo analysis. The results show that with this approach, the number of measurements to be processed, and thus the computational effort can be dynamically reduced, while the accuracy remains at a desired level.

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.

Random matrices are used to filter the center of gravity (CoG) and the covariance matrix of measurements. However, these quantities do not always correspond directly to the position and the extent of the object, e.g. when a lidar sensor is used.In this paper, we propose a Gaussian processes regression model (GPRM) to predict the position and extension of the object from the filtered CoG and covariance matrix of the measurements. Training data for the GPRM are generated by a sampling method and a virtual measurement model (VMM). The VMM is a function that generates artificial measurements using ray tracing and allows us to obtain the CoG and covariance matrix that any object would cause. This enables the GPRM to be trained without real data but still be applied to real data due to the precise modeling in the VMM. The results show an accurate extension estimation as long as the reality behaves like the modeling and e.g. lidar measurements only occur on the side facing the sensor.

Modeling a suitable birth density is a challenge when using Bernoulli filters such as the Labeled Multi-Bernoulli (LMB) filter. The birth density of newborn targets is unknown in most applications, but must be given as a prior to the filter. Usually the birth density stays unchanged or is designed based on the measurements from previous time steps. In this paper, we assume that the true initial state of new objects is normally distributed. The expected value and covariance of the underlying density are unknown parameters. Using the estimated multi-object state of the LMB and the Rauch-Tung-Striebel (RTS) recursion, these parameters are recursively estimated and adapted after a target is detected. The main contribution of this paper is an algorithm to estimate the parameters of the birth density and its integration into the LMB framework. Monte Carlo simulations are used to evaluate the detection driven adaptive birth density in two scenarios. The approach can also be applied to filters that are able to estimate trajectories.

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. The idea of this work is to validate these trajectories related to guaranteed motion safety, which means that it is not sufficient for a trajectory to be collision-free, but it must additionally ensure that an evasive manoeuvre is performable at any time. An approach using the distance and the evolution of the distance to the other vessels is proposed. The concept of Inevitable Collision States (ICS) is adopted to identify the states for which no evasive manoeuvre exist. Furthermore, it is implemented into a collision avoidance system for recreational crafts to demonstrate the performance.

The aim of the paper is to make a contribution to the mobile robot self-localization problem, when the initial position is unknown. It is assumed that a simple map of the environment, consisting of a list of 2D-edge coordinates is available. These are regarded as natural or artificial landmarks. It is further assumed that the position of edges can be detected by a sensor in the local coordinate frame of the robot. From every pair of feature measures and map-landmarks, hypotheses of the robot-pose are constructed. These are regarded as measurement inputs into the probabilistic data association using Bayesian formulation (PDAB) approach. The presented first results demonstrates that the suggested method in combination with low level features is a promising approach for self-localization in unstructured and sparse modeled environments.

We consider the problem of generating smooth trajectories for a fast moving mobile robot in a cluttered environment, when online path updating is performed. The well-known smoothing methods using clothoids, cubic spirals or polynominal curves are extended by taking into account the conditions for a continuously differentiable path update. We use the Hamilton-Jacobi framework to create a continuously differentiable interpolation of an existing path of straight lines and arcs of circles. The smoothing approach is combined with the generation of an appropriate velocity profile along the path. The results are compared to those obtained by more classical smoothing methods and to the polynominal approach implemented on the car-like robot MoViLaR of our institute. Finally an embedding of this method into the robot's hierarchical control structure is presented.