arXiv subjects

Dirk Wollherr

Publications and source records attributed to Dirk Wollherr.

27 records · Page 2Linked to original sources

arXiv2022

Stochastic Model Predictive Control with a Safety Guarantee for Automated Driving: Extended Version

Automated vehicles require efficient and safe planning to maneuver in uncertain environments. Largely this uncertainty is caused by other traffic participants, e.g., surrounding vehicles. Future motion of surrounding vehicles is often difficult to predict. Whereas robust control approaches achieve safe, yet conservative motion planning for automated vehicles, Stochastic Model Predictive Control (SMPC) provides efficient planning in the presence of uncertainty. Probabilistic constraints are applied to ensure that the maximal risk remains below a predefined level. However, safety cannot be ensured as probabilistic constraints may be violated, which is not acceptable for automated vehicles. Here, we propose an efficient trajectory planning framework with safety guarantees for automated vehicles. SMPC is applied to obtain efficient vehicle trajectories for a finite horizon. Based on the first optimized SMPC input, a guaranteed safe backup trajectory is planned using reachable sets. This backup is used to overwrite the SMPC input if necessary for safety. Recursive feasibility of the safe SMPC algorithm is proved. Highway simulations show the effectiveness of the proposed method regarding performance and safety.

eess.SY↗

arXiv2022

MS2MP: A Min-Sum Message Passing Algorithm for Motion Planning

Gaussian Process (GP) formulation of continuoustime trajectory offers a fast solution to the motion planning problem via probabilistic inference on factor graph. However, often the solution converges to in-feasible local minima and the planned trajectory is not collision-free. We propose a message passing algorithm that is more sensitive to obstacles with fast convergence time. We leverage the utility of min-sum message passing algorithm that performs local computations at each node to solve the inference problem on factor graph. We first introduce the notion of compound factor node to transform the factor graph to a linearly structured graph. We next develop an algorithm denoted as Min-sum Message Passing algorithm for Motion Planning (MS2MP) that combines numerical optimization with message passing to find collision-free trajectories. MS2MP performs numerical optimization to solve non-linear least square minimization problem at each compound factor node and then exploits the linear structure of factor graph to compute the maximum a posteriori (MAP) estimation of complete graph by passing messages among graph nodes. The decentralized optimization approach of each compound node increases sensitivity towards avoiding obstacles for harder planning problems. We evaluate our algorithm by performing extensive experiments for exemplary motion planning tasks for a robot manipulator. Our evaluation reveals that MS2MP improves existing work in convergence time and success rate.

cs.RO↗

arXiv2022

Constrained Visual-Inertial Localization With Application And Benchmark in Laparoscopic Surgery

We propose a novel method to tackle the visual-inertial localization problem for constrained camera movements. We use residuals from the different modalities to jointly optimize a global cost function. The residuals emerge from IMU measurements, stereoscopic feature points, and constraints on possible solutions in SE(3). In settings where dynamic disturbances are frequent, the residuals reduce the complexity of the problem and make localization feasible. We verify the advantages of our method in a suitable medical use case and produce a dataset capturing a minimally invasive surgery in the abdomen. Our novel clinical dataset MITI is comparable to state-of-the-art evaluation datasets, contains calibration and synchronization and is available at https://mediatum.ub.tum.de/1621941.

cs.CV↗

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.

eess.SY↗

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.

eess.SY↗

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.

eess.SY↗

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.

cs.RO↗

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.

eess.SY↗

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.

eess.SY↗