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Autonomous racing has increasingly become a research subject as it provides insights into dynamic, high-speed situations. One crucial aspect of handling these situations, especially in the presence of dynamic obstacles, is the generation of a collision-free trajectory that represents a safe behavior and is also competitive in the case of racing. We propose a local planning approach that generates such trajectories for a racing car on an oval race track by searching a spatiotemporal graph. A considerable challenge of search-based methods in a spatiotemporal domain is the curse of dimensionality. Therefore, we propose how a previously presented graph structure that is based on intervals instead of discrete values can be searched more efficiently without losing optimality by using a uniform-cost search strategy. We extend the search method to make it anytime-capable so that it can provide a suboptimal trajectory even if the search has to be terminated early. The graph-based planning approach allows us to apply a flexible cost function so that our approach can operate fully autonomously on an oval race track, including the pit lane. We present a cost function for oval racing and explain how the terms contribute to the desired behaviors. This is supported by results with a full-scale prototype.

In motion planning for autonomous racing, the challenge arises in planning smooth trajectories close to the handling limits of the vehicle with a sufficient planning horizon. Graph-based trajectory planning methods can find the global discrete-optimal solution, but they suffer from the curse of dimensionality. Therefore, to achieve low computation times despite a long planning horizon, coarse discretization and simple edges that are efficient to generate must be used. However, the resulting rough trajectories cannot reach the handling limits of the vehicle and are also difficult to track by the controller, which can lead to unstable driving behavior. In this paper, we show that the initial edges connecting the vehicle’s estimated state with the actual graph are crucial for vehicle stability and race performance. We therefore propose a sampling-based approach that relies on jerk-optimal curves to generate these initial edges. The concept is introduced using a layer-based graph, but it can be applied to other graph structures as well. We describe the integration of the curves within the graph and the required adaptation to racing scenarios. Our approach enables stable driving at the handling limits and fully autonomous operation on the race track. While simulations show the comparison of our concept with an alternative approach based on uniform acceleration, we also present experimental results of a dynamic overtake with speeds up to 74 m/s on a full-size vehicle.

A new Proactive Nonlinear Disturbance Compensator (PNDC) for vibration damping in a quarter car is presented. A Flatness Based Disturbance Compensator (FBDC) for a nonlinear quarter car model is derived that decouples the chassis acceleration completely from the known road disturbance. This leads to a high level of driving comfort but to a loss in driving safety. Therefore a Proactive Linear Disturbance Compensator (PLDC) is added. This controller uses knowledge of the future road disturbance to reach a compromise between driving safety and driving comfort. The sensitivity of the nonlinear, proactive disturbance compensator to varying parameters or measurement noise is examined in simulations, and the tuning of the design parameters is shown. Furthermore, results from experiments on the institute's quarter car test stand are discussed. These have shown that the performance of the proposed method exceeds a linear quadratic regulator in simulations and experiments and that the driving comfort can be increased by more than fifty percent without a decrease in driving safety.

In this contribution, we develop a feedback controller in the form of a parametric function for a mobile inverted pendulum. The control both stabilizes the system and drives it to target positions with target orientations. A design of the controller based only on a cost function is difficult for this task, which is why we choose to train the controller using imitation learning on optimized trajectories. In contrast to popular approaches like policy gradient methods, this approach allows us to shape the behavior of the system by including equality constraints. When transferring the parametric controller from simulation to the real mobile inverted pendulum, the control performance is degraded due to the reality gap. A robust control design can reduce the degradation. However, for the framework of imitation learning on optimized trajectories, methods that explicitly consider robustness do not yet exist to the knowledge of the authors. We tackle this research gap by presenting a method to design a robust controller in the form of a recurrent neural network, to improve the transferability of the trained controller to the real system. As a last step, we make the behavior of the parametric controller adjustable to allow for the fine tuning of the behavior of the real system. We design the controller for our system and show in the application that the recurrent neural network has increased performance compared to a static neural network without robustness considerations.

Humanoid service robots in domestic environments have to interact with humans and their surroundings in a safe and reliable way. One way to manage that is to equip the robotic systems with force-torque sensors to realize a physically compliant whole-body behavior via impedance control. To provide mobility, such robots often have wheeled platforms. The main advantage is that no balancing effort has to be made compared to legged humanoids. However, the nonholonomy of most wheeled systems prohibits the direct implementation of impedance control due to kinematic rolling constraints that must be taken into account in modeling and control. In this paper we design a whole-body impedance controller for such a robot, which employs an admittance interface to the kinematically controlled mobile platform. The upper body impedance control law, the platform admittance interface, and the compensation of dynamic couplings between both subsystems yield a passive closed loop. The convergence of the state to an invariant set is shown. To prove asymptotic stability in the case of redundancy, priority-based approaches can be employed. In principle, the presented approach is the extension of the well-known and established impedance controller to mobile robots. Experimental validations are performed on the humanoid robot Rollin’ Justin. The method is suitable for compliant manipulation tasks with low-dimensional planning in the task space.

The primary goal of this study is the formulation of a soft sensor that predicts industrially relevant mechanical properties for freeform bending. This serves as the foundation of a closed-loop property control. It is hypothesized that by inline measurement of hardness, predictions regarding residual hoop stresses, local strength and strain level can be achieved. A novel hardness-based correlation scheme is introduced, which is implemented into an extended Kalman filter (EKF) and allows an inline prediction of local strength, residual hoop stresses and plasticity. Furthermore, the ultrasonic contact impedance (UCI) method is validated as a suitable inline measuring solution.

In this paper, a new structure-preserving scheme for the reduction of linear port-Hamiltonian systems with dissipation using Krylov subspaces is presented. It is shown how to choose the projection matrices in order to guarantee the moment matching property and to obtain a passive and thus stable reduced-order model in port-Hamiltonian form. The method is suitable for the reduction of largescale systems as it employs only the well-known Arnoldi algorithm and matrix-vector multiplications to compute the reduced-order model. Afinite element model is reduced to illustrate the new method.

In this paper, a new framework to address the stability preservation problem in projection-based model order reduction is presented. Sufficient conditions for obtaining stable reduced models are established and proven by using the notions of contractivity and matrix measure. Based on these results, we present two model reduction algorithms that preserve stability using any orthogonal projection. In addition, we show that for some system classes, stability preservation can be guaranteed just by choosing a suitable state space representation, which is applicable to the large class of models obtained by the Finite Element Method (FEM).

Given a Control Lyapunov Function (CLF), Sontag's famous Formula provides a nonlinear state-feedback guaranteeing asymptotic stability of the setpoint. At the same time, a cost function that depends on the CLF is minimized. While there exist methods to construct CLFs for certain classes of systems, the impact on the resulting performance is unclear. This article aims to make two contributions to this problem: (1) We show that using the value function of an LQR design as CLF, the resulting Sontag-type controller minimizes a classical quadratic cost around the setpoint and a CLF-dependent cost within the domain where the CLF condition holds. We also show that the closed-loop system is stable within a local region at least as large as that generated by the LQR. (2) We show a related CLF design for feedback-linearizable systems resulting in a global CLF in a straight-forward manner; The Sontag design then guarantees global asymptotic stability while minimizing a quadratic cost at the setpoint and a CLF-dependent cost in the whole state-space. Both designs are constructive and easily applicable to nonlinear multi-input systems under mild assumptions.