Boris Lohmann

Georg Jank, Mattia Piccinini, Sebastian Wenk et al.

Feedforward steering control is a key component of hierarchical control architectures for autonomous racing. The goal is to reduce steering corrections from the feedback controllers by predicting the vehicle's inverse lateral dynamics. This paper presents a systematic benchmark of two learning-based and two empirical (analytical) feedforward steering controllers. We introduce a new \acf{ehd} formulation based on a polynomial surface fit that captures velocity-dependent nonlinear steering behavior with minimal parametrization. We test the feedforward controllers in a high-fidelity simulation framework based on the real-world Abu Dhabi Autonomous Racing League competition, using a high-fidelity double-track vehicle dynamics simulator. Open-loop evaluation shows that the learning-based controllers achieve the lowest prediction errors; however, closed-loop testing reveals that this improved accuracy does not translate into superior path tracking performance or lap times, even after iterative fine-tuning. In contrast, the proposed EHD approach achieves the best overall closed-loop robustness and lap time, highlighting the necessity of evaluating feedforward strategies within the complete trajectory planning and control software stack. Our code is available at https://github.com/TUMRT/steering_ff_control.

Maria Cruz Varona, Nico Schneucker, Boris Lohmann

This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of linear moment matching, we then extend this reduction concept to the nonlinear second-order case based on Astolfi [2010]. Then, similar simplifications as in Cruz Varona et al. [2019] are proposed to achieve a simulation-free nonlinear moment matching algorithm. A discussion on the simplifications and their limitations is presented, as well as a numerical example which illustrates the efficiency of the algorithm.

Maria Cruz Varona, Boris Lohmann

In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new degrees of freedom, which also come along with some challenges. This paper deals with both simple methods for the reduction of particular linear time-varying systems, as well as with a more advanced technique considering the emerging time derivatives.

Philipp Seiwald, Alessandro Castagnotto, Tatjana Stykel et al.

In this contribution, we extend the concept of $\mathcal{H}_2$ inner product and $\mathcal{H}_2$ pseudo-optimality to dynamical systems modeled by differential-algebraic equations (DAEs). To this end, we derive projected Sylvester equations that characterize the $\mathcal{H}_2$ inner product in terms of the matrices of the DAE realization. Using this result, we extend the $\mathcal{H}_2$ pseudo-optimal rational Krylov algorithm for ordinary differential equations to the DAE case. This algorithm computes the globally optimal reduced-order model for a given subspace of $\mathcal{H}_2$ defined by poles and input residual directions. Necessary and sufficient conditions for $\mathcal{H}_2$ pseudo-optimality are derived using the new formulation of the $\mathcal{H}_2$ inner product in terms of tangential interpolation conditions. Based on these conditions, the cumulative reduction procedure combined with the adaptive rational Krylov algorithm, known as CUREd SPARK, is extended to DAEs. Important properties of this procedure are that it guarantees stability preservation and adaptively selects interpolation frequencies and reduced order. Numerical examples are used to illustrate the theoretical discussion. Even though the results apply in theory to general DAEs, special structures will be exploited for numerically efficient implementations.

Georg Jank, Matthias Rowold, Boris Lohmann

This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous planning methods, our algorithm encourages global time optimality without being limited by coarse discretization. In the behavioral planning step, the fastest behavior is determined with a low-resolution spatio-temporal visibility graph. Based on the selected behavior, we calculate maneuver envelopes that are subsequently applied as constraints in a time-optimal control problem. The performance of our method is comparable to a parallel approach that selects the fastest trajectory from multiple optimizations with different behavior classes. However, our algorithm can be executed on a single core. This significantly reduces computational requirements, especially when multiple opponents are involved. Therefore, the proposed method is an efficient and practical solution for real-time multi-vehicle racing scenarios.

Joscha F. Bongard, Georg Jank, Simon Sagmeister et al.

We propose a robust nonlinear model predictive control (MPC) scheme for trajectory-tracking control of autonomous vehicles at the limits of handling on non-planar road surfaces. We derive the dynamics from first principles and selectively omit terms with negligible dynamic influence to maintain real-time capability. The resulting MPC with a three-dimensional (3D) dynamic single-track model integrates relevant dynamic effects directly into the prediction model and leverages them to improve prediction accuracy and therefore control performance. Even if the influence of terrain-induced vertical loads on the total acceleration potential is modeled, tire-road interactions are subject to uncertainty and disturbance. The uncertainty-aware constraint tightening scheme introduces a margin to constraint bounds to keep the vehicle controllable and stable in this environment. To validate our proposed approach, we perform high-fidelity dynamic double-track vehicle dynamics simulations on a model of a real circuit. We find that our algorithm can improve trajectory-tracking accuracy while maintaining low computation times.

Alexander Wischnewski, Maximilian Geisslinger, Johannes Betz et al.

Motorsport has always been an enabler for technological advancement, and the same applies to the autonomous driving industry. The team TUM Auton-omous Motorsports will participate in the Indy Autonomous Challenge in Octo-ber 2021 to benchmark its self-driving software-stack by racing one out of ten autonomous Dallara AV-21 racecars at the Indianapolis Motor Speedway. The first part of this paper explains the reasons for entering an autonomous vehicle race from an academic perspective: It allows focusing on several edge cases en-countered by autonomous vehicles, such as challenging evasion maneuvers and unstructured scenarios. At the same time, it is inherently safe due to the motor-sport related track safety precautions. It is therefore an ideal testing ground for the development of autonomous driving algorithms capable of mastering the most challenging and rare situations. In addition, we provide insight into our soft-ware development workflow and present our Hardware-in-the-Loop simulation setup. It is capable of running simulations of up to eight autonomous vehicles in real time. The second part of the paper gives a high-level overview of the soft-ware architecture and covers our development priorities in building a high-per-formance autonomous racing software: maximum sensor detection range, relia-ble handling of multi-vehicle situations, as well as reliable motion control under uncertainty.

Klaus Albert, Karmvir Singh Phogat, Felix Anhalt et al.

The Wheeled Inverted Pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discrete-time constrained optimal control problem. Further, we describe a nonlinear continuous-time model with parameters for designing a closed loop LQ-controller. A dual control architecture is implemented in which the designed optimal trajectory is then provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQ-controller in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

Alessandro Castagnotto, Heiko K. F. Panzer, Klaus-Dieter Reinsch et al.

Systems of differential-algebraic equations (DAEs) represent a widespread formalism in the modeling of constrained mechanical systems and electrical networks. Due to the automatic, object-oriented generation of the equations of motion and the resulting redundancies in the descriptor variables, DAE systems often reach a very high order. This motivates the use of model order reduction (MOR) techniques that capture the relevant input-output dynamics in a reduced model of much smaller order, while satisfying the constraints and preserving fundamental properties. Due to their particular structure, new MOR techniques designed to work directly on the DAE are required that reduce the dynamical part while preserving the algebraic. In this contribution, we exploit the specific structure of index-1 systems in semi-explicit form and present two different methods for stability-preserving MOR of DAEs. The first technique preserves strictly dissipativity of the underlying dynamics, the second takes advantage of H2-pseudo-optimal reduction and further allows for an adaptive selection of reduction parameters such as reduced order and Krylov shifts.