Phase transition for loop representations of Quantum spin systems on trees

We consider a model of random loops on Galton-Watson trees with an offspring distribution with high expectation. We give the configurations a weighting of $\theta^{\#\text{loops}}$. For many $\theta>1$ these models are equivalent to certain quantum spin systems for various choices of the system parameters. We find conditions on the offspring distribution that guarantee the occurrence of a phase transition from finite to infinite loops for the Galton-Watson tree.Comment: 16 pages, 1 figur

Benchmarking of a software stack for autonomous racing against a professional human race driver

The way to full autonomy of public road vehicles requires the step-by-step replacement of the human driver, with the ultimate goal of replacing the driver completely. Eventually, the driving software has to be able to handle all situations that occur on its own, even emergency situations. These particular situations require extreme combined braking and steering actions at the limits of handling to avoid an accident or to diminish its consequences. An average human driver is not trained to handle such extreme and rarely occurring situations and therefore often fails to do so. However, professional race drivers are trained to drive a vehicle utilizing the maximum amount of possible tire forces. These abilities are of high interest for the development of autonomous driving software. Here, we compare a professional race driver and our software stack developed for autonomous racing with data analysis techniques established in motorsports. The goal of this research is to derive indications for further improvement of the performance of our software and to identify areas where it still fails to meet the performance level of the human race driver. Our results are used to extend our software's capabilities and also to incorporate our findings into the research and development of public road autonomous vehicles.Comment: Accepted at 2020 Fifteenth International Conference on Ecological Vehicles and Renewable Energies (EVER

Therapeutic Prospects of Metabolically Active Brown Adipose Tissue in Humans

The world-wide obesity epidemic constitutes a severe threat to human health and wellbeing and poses a major challenge to health-care systems. Current therapeutic approaches, relying mainly on reduced energy intake and/or increased exercise energy expenditure, are generally of limited effectiveness. Previously believed to be present only in children, the existence of metabolically active brown adipose tissue (BAT) was recently demonstrated also in healthy human adults. The physiological role of BAT is to dissipate chemical energy, mainly from fatty acids, as heat to maintain body temperature in cold environments. Recent studies indicate that the activity of BAT is negatively correlated with overweight and obesity, findings that raise the exciting possibility of new and effective weight reduction therapies based on increased BAT energy expenditure, a process likely to be amenable to pharmacological intervention

Multilayer Graph-Based Trajectory Planning for Race Vehicles in Dynamic Scenarios

Trajectory planning at high velocities and at the handling limits is a challenging task. In order to cope with the requirements of a race scenario, we propose a far-sighted two step, multi-layered graph-based trajectory planner, capable to run with speeds up to 212~km/h. The planner is designed to generate an action set of multiple drivable trajectories, allowing an adjacent behavior planner to pick the most appropriate action for the global state in the scene. This method serves objectives such as race line tracking, following, stopping, overtaking and a velocity profile which enables a handling of the vehicle at the limit of friction. Thereby, it provides a high update rate, a far planning horizon and solutions to non-convex scenarios. The capabilities of the proposed method are demonstrated in simulation and on a real race vehicle.Comment: Accepted at The 22nd IEEE International Conference on Intelligent Transportation Systems, October 27 - 30, 201

Minimum Race-Time Planning-Strategy for an Autonomous Electric Racecar

Increasing attention to autonomous passenger vehicles has also attracted interest in an autonomous racing series. Because of this, platforms such as Roborace and the Indy Autonomous Challenge are currently evolving. Electric racecars face the challenge of a limited amount of stored energy within their batteries. Furthermore, the thermodynamical influence of an all-electric powertrain on the race performance is crucial. Severe damage can occur to the powertrain components when thermally overstressed. In this work we present a race-time minimal control strategy deduced from an Optimal Control Problem (OCP) that is transcribed into a Nonlinear Problem (NLP). Its optimization variables stem from the driving dynamics as well as from a thermodynamical description of the electric powertrain. We deduce the necessary first-order Ordinary Differential Equations (ODE)s and form simplified loss models for the implementation within the numerical optimization. The significant influence of the powertrain behavior on the race strategy is shown.Comment: Accepted at The 23rd IEEE International Conference on Intelligent Transportation Systems, September 20 - 23, 202

A Stochastic Nonlinear Model Predictive Control with an Uncertainty Propagation Horizon for Autonomous Vehicle Motion Control

Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in high-dimensional systems with extended prediction horizons, such as autonomous vehicles. To enhance closed-loop performance in and feasibility in SNMPCs, we introduce the concept of the Uncertainty Propagation Horizon (UPH). The UPH limits the time for uncertainty propagation through system dynamics, preventing trajectory divergence, optimizing feedback loop advantages, and reducing computational overhead. Our SNMPC approach utilizes Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates nonlinear hard constraints on state expectations and nonlinear probabilistic constraints. We transform the probabilistic constraints into deterministic constraints by estimating the nonlinear constraints' expectation and variance. We then showcase our algorithm's effectiveness in real-time control of a high-dimensional, highly nonlinear system-the trajectory following of an autonomous passenger vehicle, modeled with a dynamic nonlinear single-track model. Experimental results demonstrate our approach's robust capability to follow an optimal racetrack trajectory at speeds of up to 37.5m/s while dealing with state estimation disturbances, achieving a minimum solving frequency of 97Hz. Additionally, our experiments illustrate that limiting the UPH renders previously infeasible SNMPC problems feasible, even when incorrect uncertainty assumptions or strong disturbances are present

R2^2NMPC: A Real-Time Reduced Robustified Nonlinear Model Predictive Control with Ellipsoidal Uncertainty Sets for Autonomous Vehicle Motion Control

In this paper, we present a novel Reduced Robustified NMPC (R$^2$NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5m/s, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144Hz