arXiv subjects

Marion Leibold

Publications and source records attributed to Marion Leibold.

27 records · Page 2Linked to original sources

arXiv2021

Multistage Stochastic Model Predictive Control for Urban Automated Driving

Trajectory planning in urban automated driving is challenging because of the high uncertainty resulting from the unknown future motion of other traffic participants. Robust approaches guarantee safety, but tend to result in overly conservative motion planning. Hence, we propose to use Stochastic Model Predictive Control for vehicle control in urban driving, allowing to efficiently plan the vehicle trajectory, while maintaining the risk probability sufficiently low. For motion optimization, we propose to use a two-stage hierarchical structure that plans the trajectory and the maneuver separately. A high-level layer takes advantage of a long prediction horizon and of an abstract model to plan the optimal maneuver, and a lower level is in charge of executing the selected maneuver by properly planning the vehicle's trajectory. Numerical simulations are included, showing the potential of our proposal.

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arXiv2021

Data Generation Method for Learning a Low-dimensional Safe Region in Safe Reinforcement Learning

Safe reinforcement learning aims to learn a control policy while ensuring that neither the system nor the environment gets damaged during the learning process. For implementing safe reinforcement learning on highly nonlinear and high-dimensional dynamical systems, one possible approach is to find a low-dimensional safe region via data-driven feature extraction methods, which provides safety estimates to the learning algorithm. As the reliability of the learned safety estimates is data-dependent, we investigate in this work how different training data will affect the safe reinforcement learning approach. By balancing between the learning performance and the risk of being unsafe, a data generation method that combines two sampling methods is proposed to generate representative training data. The performance of the method is demonstrated with a three-link inverted pendulum example.

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arXiv2021

Learning a Low-dimensional Representation of a Safe Region for Safe Reinforcement Learning on Dynamical Systems

For safely applying reinforcement learning algorithms on high-dimensional nonlinear dynamical systems, a simplified system model is used to formulate a safe reinforcement learning framework. Based on the simplified system model, a low-dimensional representation of the safe region is identified and is used to provide safety estimates for learning algorithms. However, finding a satisfying simplified system model for complex dynamical systems usually requires a considerable amount of effort. To overcome this limitation, we propose in this work a general data-driven approach that is able to efficiently learn a low-dimensional representation of the safe region. Through an online adaptation method, the low-dimensional representation is updated by using the feedback data such that more accurate safety estimates are obtained. The performance of the proposed approach for identifying the low-dimensional representation of the safe region is demonstrated with a quadcopter example. The results show that, compared to previous work, a more reliable and representative low-dimensional representation of the safe region is derived, which then extends the applicability of the safe reinforcement learning framework.

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arXiv2021

Model Predictive Control with Models of Different Granularity and a Non-uniformly Spaced Prediction Horizon

Horizon length and model accuracy are defining factors when designing a Model Predictive Controller. While long horizons and detailed models have a positive effect on control performance, computational complexity increases. As predictions become less precise over the horizon length, it is worth investigating a combination of different models and varying time step size. Here, we propose a Model Predictive Control scheme that splits the prediction horizon into two segments. A detailed model is used for the short-term prediction horizon and a simplified model with an increased sampling time is employed for the long-term horizon. This approach combines the advantage of a long prediction horizon with a reduction of computational effort due to a simplified model and less decision variables. The presented Model Predictive Control is recursively feasible. A simulation study demonstrates the effectiveness of the proposed method: employing a long prediction horizon with advantages regarding computational complexity.

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arXiv2021

Collision Avoidance with Stochastic Model Predictive Control for Systems with a Twofold Uncertainty Structure

Model Predictive Control (MPC) has shown to be a successful method for many applications that require control. Especially in the presence of prediction uncertainty, various types of MPC offer robust or efficient control system behavior. For modeling, uncertainty is most often approximated in such a way that established MPC approaches are applicable for specific uncertainty types. However, for a number of applications, especially automated vehicles, uncertainty in predicting the future behavior of other agents is more suitably modeled by a twofold description: a high-level task uncertainty and a low-level execution uncertainty of individual tasks. In this work, we present an MPC framework that is capable of dealing with this twofold uncertainty. A scenario MPC approach considers the possibility of other agents performing one of multiple tasks, with an arbitrary probability distribution, while an analytic stochastic MPC method handles execution uncertainty within a specific task, based on a Gaussian distribution. Combining both approaches allows to efficiently handle the twofold uncertainty structure of many applications. Application of the proposed MPC method is demonstrated in an automated vehicle simulation study.

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arXiv2021

Minimization of Constraint Violation Probability in Model Predictive Control

While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability depending on a predefined risk parameter. However, for safety-critical systems it is not only important to bound the constraint violation probability but to reduce this probability as much as possible. Therefore, an approach is necessary that minimizes the constraint violation probability while ensuring that the Model Predictive Control optimization problem remains feasible. We propose a novel Model Predictive Control scheme that yields a solution with minimal constraint violation probability for a norm constraint in an environment with uncertainty. After minimal constraint violation is guaranteed the solution is then also optimized with respect to other control objectives. Further, it is possible to account for changes over time of the support of the uncertainty. We first present a general method and then provide an approach for uncertainties with symmetric, unimodal probability density function. Recursive feasibility and convergence of the method are proved. A simulation example demonstrates the effectiveness of the proposed method.

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arXiv2021

Gaussian Process-based Stochastic Model Predictive Control for Overtaking in Autonomous Racing

A fundamental aspect of racing is overtaking other race cars. Whereas previous research on autonomous racing has majorly focused on lap-time optimization, here, we propose a method to plan overtaking maneuvers in autonomous racing. A Gaussian process is used to learn the behavior of the leading vehicle. Based on the outputs of the Gaussian process, a stochastic Model Predictive Control algorithm plans optimistic trajectories, such that the controlled autonomous race car is able to overtake the leading vehicle. The proposed method is tested in a simple simulation scenario.

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arXiv2021

Combined Robust and Stochastic Model Predictive Control for Models of Different Granularity

Long prediction horizons in Model Predictive Control (MPC) often prove to be efficient, however, this comes with increased computational cost. Recently, a Robust Model Predictive Control (RMPC) method has been proposed which exploits models of different granularity. The prediction over the control horizon is split into short-term predictions with a detailed model using MPC and long-term predictions with a coarse model using RMPC. In many applications robustness is required for the short-term future, but in the long-term future, subject to major uncertainty and potential modeling difficulties, robust planning can lead to highly conservative solutions. We therefore propose combining RMPC on a detailed model for short-term predictions and Stochastic MPC (SMPC), with chance constraints, on a simplified model for long-term predictions. This yields decreased computational effort due to a simple model for long-term predictions, and less conservative solutions, as robustness is only required for short-term predictions. The effectiveness of the method is shown in a mobile robot collision avoidance simulation.

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arXiv2021

Grid-Based Stochastic Model Predictive Control for Trajectory Planning in Uncertain Environments

Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined risk parameter. However, considering chance constraints in an optimization problem can be challenging and computationally demanding. In this paper, we present a grid-based Stochastic Model Predictive Control approach. This approach allows to determine a simple deterministic reformulation of the chance constraints and reduces the computational effort, while considering the stochastic nature of the environment. Within the proposed method, we first divide the environment into a grid and, for each predicted step, assign each cell a probability value, which represents the probability that this cell will be occupied by surrounding vehicles. Then, the probabilistic grid is transformed into a binary grid of admissible and inadmissible cells by applying a threshold, representing a risk parameter. Only cells with an occupancy probability lower than the threshold are admissible for the controlled vehicle. Given the admissible cells, a convex hull is generated, which can then be used for trajectory planning. Simulations of an autonomous driving highway scenario show the benefits of the proposed grid-based Stochastic Model Predictive Control method.

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