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In multi-extended object tracking, parameters (e.g., extent) and trajectory are often determined independently. In this paper, we propose a joint parameter and trajectory (JPT) state and its integration into the Bayesian framework. This allows processing measurements that contain information about parameters and states. Examples of such measurements are bounding boxes given from an image processing algorithm. It is shown that this approach can consider correlations between states and parameters. In this paper, we present the JPT Bernoulli filter. Since parameters and state elements are considered in the weighting of the measurement data assignment hypotheses, the performance is higher than with the conventional Bernoulli filter. The JPT approach can be also used for other Bayes filters.
The random matrix approach is a robust algorithm to filter the mean and covariance matrix of noisy observations of a dynamic object. Afterward, virtual measurement models can be used to find iteratively the extent parameters of an object that would cause the same statistical moments within their measurements. In previous work, this was limited to elliptical targets and only contour measurements.In this paper, we introduce the parallel use of an elliptical, triangular and rectangular-shaped virtual measurement model and a shape classification that selects the model that fits best to the measurements. The measurement likelihood is modeled either via ray tracing, a uniformly or normally spatial distribution over the object’s extent or as a combination of those.The results show that the extent estimation works precisely and that the classification accuracy highly depends on the measurement noise.
Feature-Based Proposal Density Optimization for Nonlinear Model Predictive Path Integral Control
(2022)
This paper presents a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control. In MPPI control, the optimal control is calculated by solving a stochastic optimal control problem online using the weighted inference of stochastic trajectories. While the algorithm can be excellently parallelized the closed- loop performance is dependent on the information quality of the drawn samples. Because these samples are drawn using a proposal density, its quality is crucial for the solver and thus the controller performance. In classical MPPI control, the explored state-space is strongly constrained by assumptions that refer to the control value variance, which are necessary for transforming the 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 used to determine the proposal density and thus, the 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. Further, the developed algorithm is applied on an autonomous vessel that follows a track and concurrently avoids collisions using an emergency braking feature.
This paper presents a systematic comparison of different advanced approaches for motion prediction of vessels for docking scenarios. Therefore, a conventional nonlinear gray-box-model, its extension to a hybrid model using an additional regression neural network (RNN) and a black-box-model only based on a RNN are compared. The optimal hyperparameters are found by grid search. The training and validation data for the different models is collected in full-scale experiments using the solar research vessel Solgenia. The performances of the different prediction models are compared in full-scale scenarios. %To use the investigated approaches for controller design, a general optimal control problem containing the advanced models is described. These can improve advanced control strategies e.g., nonlinear model predictive control (NMPC) or reinforcement learning (RL). This paper explores the question of what the advantages and disadvantages of the different presented prediction approaches are and how they can be used to improve the docking behavior of a vessel.
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/
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.
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.
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.
Docking Control of a Fully-Actuated Autonomous Vessel using Model Predictive Path Integral Control
(2022)
This paper presents the docking control of an autonomous vessel using the 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 using knowledge of the system and simulations, including nonlinear state and disturbance observer. The cost function implicitly contains information regarding the surrounding of the docking position. This approach allows continuous optimization of the trajectory with respect to the system state, disturbance state and actuator dynamics. The control strategy has been tested in full-scale experiments using the solar research vessel Solgenia. The investigated MPPI controller has demonstrated excellent performance in both, simulation and real-world experiments. This paper addresses the question of how the MPPI algorithm can be applied to dock a fully-actuated vessel and what benefits its application achieves.
Comparison of Data-Driven Modeling and Identification Approaches for a Self-Balancing Vehicle
(2023)
This paper gives a systematic comparison of different state–of–the–art modeling approaches and the corresponding parameter identification processes for a self–balancing vehicle. In detail, a nonlinear grey box model, its extension to consider friction effects, a parametric black box model based on regression neural networks, and a hybrid approach are presented. The parameters of the models are identified by solving a nonlinear least squares problem. The training, validation, and test datasets are collected in full–scale experiments using a self–balancing vehicle. The performance of the different models used for ego–motion prediction are compared in full–scale scenarios, as well. The investigated model architectures can be used to improve both, simulation environments and model–based controller design. This paper shows the upsides and downsides arising from using the different modeling approaches. Videos showing the self–balancing vehicle in action are available at: https://tinyurl.com/mvn8j7vf22nd
This paper compares novel methods to efficiently include input constraints using the nonlinear Model Predictive Path Integral (MPPI) approach. The MPPI algorithm solves stochastic optimal control problems and is based on sampled trajectories. MPPI results from the physical path integral framework. Sample-based algorithms are characterized by the fact that they can be computed in parallel and offer the possibility to handle discontinuous dynamics and cost functions. However, using standard MPPI the input costs in the Lagrange term have to be chosen quadratic. This fact is unfavorable for various real applications. Further, in standard nonlinear model predictive control (NMPC) approaches hard box constraints on the control input trajectory can be treated directly. In this contribution, novel architectures based on integrator action are compared. The investigated input constraint MPPI controllers were tested on an autonomous self-balancing vehicle. Therefore both, simulation and real-world experiments are presented. This paper addresses the question of how the MPPI algorithm can be further developed to consider input box constraints. Videos of the self-balancing vehicle are available at: https: https://tinyurl.com/mvn8j7vf
Analysing observability is an important step in the
process of designing state feedback controllers. While for linear
systems observability has been widely studied and easy-to-check
necessary and sufficient conditions are available, for nonlinear
systems, such a general recipe does not exist and different classes
of systems require different techniques. In this paper, we analyse
observability for an industrial heating process where a stripe-
shaped plastic workpiece is moving through a heating zone where
it is heated up to a specific temperature by applying hot air to its
surface through a nozzle. A modeling approach for this process
is briefly presented, yielding a nonlinear Ordinary Differential
Equation model. Sensitivity-based observability analysis is used
to identify unobservable states and make suggestions for addi-
tional sensor locations. In practice, however, it is not possible
to place additional sensors, so the available measurements are
used to implement a simple open-loop state estimator with
offset compensation and numerical and experimental results are
presented.
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.
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.
Recently published nonlinear model-based control
approaches achieve impressive performances in complex real-
world applications. However, due to model-plant mismatches
and unforeseen disturbances, the model-based controller’s per-
formance is limited in full-scale applications. In most applica-
tions, low-level control loops mitigate the model-plant mismatch
and the sensitivity to disturbances. But what is the influence
of these low-level control loops? In this paper, we present
the model predictive path integral (MPPI) control of a self-
balancing vehicle and investigate the influence of subordinate
control loops on closed-loop performance. Therefore, simulation
and full-scale experiments are performed and analyzed. Subor-
dinate control loops empower the MPPI controller because they
dampen the influence of disturbances, and thus improve the
model’s accuracy. This is the basis for the successful application
of model-based control approaches in real-world systems. All
in all, a model is used to design a low-level controller, then
its closed-loop behavior is determined, and this model is used
within the superimposed MPPI control loop – modeling for
control and vice versa.