arXiv subjects

Markus Herrmann-Wicklmayr

Publications and source records attributed to Markus Herrmann-Wicklmayr.

5 recordsLinked to original sources

arXiv2026

Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization

Multi-objective model predictive control (MOMPC) for fixed point stabilization requires an automated a priori decision-making (DM) mechanism to translate a high-level preference into a single solution. To this aim, we introduce an approach called individual minima-informed DM. This class of methods can be implemented through two sequential optimizations, regardless of the number of objectives, thereby improving the real-time capability of MOMPC. These methods operate on Pareto fronts (PFs) and leverage the individual minima (IM), which are characteristic Pareto-optimal points. By this, we aim to facilitate mapping a high-level preference to a point on the PF. Several approaches exist to guarantee the closed-loop stability of an MOMPC scheme. This work builds upon an approach known from the literature, which combines a quasi-infinite horizon scheme with an additional descent condition on the costs. Assuming that the terminal ingredients of the quasi-infinite horizon approach are fixed, then the size of a PF or the DM space is determined solely by the descent condition. This paper examines both the IM-informed DM methods and their integration into a stabilizing MOMPC scheme. The main contributions are twofold. First, we propose and systematically analyze six variants of IM-informed DM methods, including two novel methods, designed to facilitate the translation of a high-level preference to a point on the PF. Second, to retain the largest possible DM space for these methods, we show that they can be embedded into an MOMPC framework while preserving closed-loop stability under a descent condition that is less restrictive than in the literature. We further present a practical method for constructing the required terminal ingredients. A numerical case study confirms the closed-loop stability of the proposed framework and illustrates the potential benefit of adapting the preference online.

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arXiv2026

Non-Extreme Individual Minima for Improved Pareto Front Sampling Efficiency and Decision-Making

In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making, as the marginal rate of substitution is extreme: a marginal improvement in one objective necessitates a significant deterioration in at least one other objective. These unfavorable trade-offs frequently occur near the individual minima, where single objectives attain their minimum values without considering the remaining criteria. To address this, we propose the concept of \emph{non-extreme individual minima} that relies on the notion of $L$-practical proper efficiency. These points can serve as a less sensitive replacement for \emph{standard} individual minima in subsequent related methods. Specifically, they allow for a more practical restriction of the Pareto front sampling within a refined utopia-nadir hyperbox, provide a meaningful basis for image space normalization, and can enhance decision-making techniques, such as knee-point methods, by focusing on regions with acceptable trade-offs. We provide a computationally efficient algorithm to determine these non-extreme individual minima by solving at most $2n_J$ standard weighted-sum scalarizations, where $n_J$ is the number of objectives. To ensure robustness across varying objective scales, the method incorporates an integrated image space normalization strategy. Numerical examples, specifically a convex academic case and a non-convex real-world application, demonstrate that the method successfully excludes practically irrelevant regions in the image space.

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arXiv2025

Efficient Collision-Avoidance Constraints for Ellipsoidal Obstacles in Optimal Control: Application to Path-Following MPC and UAVs

This article proposes a modular optimal control framework for local three-dimensional ellipsoidal obstacle avoidance, exemplarily applied to model predictive path-following control. Static as well as moving obstacles are considered. Central to the approach is a computationally efficient and continuously differentiable condition for detecting collisions with ellipsoidal obstacles. A novel two-stage optimization approach mitigates numerical issues arising from the structure of the resulting optimal control problem. The effectiveness of the approach is demonstrated through simulations and real-world experiments with the Crazyflie quadrotor. This represents the first hardware demonstration of an MPC controller of this kind for UAVs in a three-dimensional task.

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arXiv2024

Efficient Avoidance of Ellipsoidal Obstacles with Model Predictive Control for Mobile Robots and Vehicles

In real-world applications of mobile robots, collision avoidance is of critical importance. Typically, global motion planning in constrained environments is addressed through high-level control schemes. However, additionally integrating local collision avoidance into robot motion control offers significant advantages. For instance, it reduces the reliance on heuristics and conservatism that can arise from a two-stage approach separating local collision avoidance and control. Moreover, using model predictive control (MPC), a robot's full potential can be harnessed by considering jointly local collision avoidance, the robot's dynamics, and actuation constraints. In this context, the present paper focuses on obstacle avoidance for wheeled mobile robots, where both the robot's and obstacles' occupied volumes are modeled as ellipsoids. To this end, a computationally efficient overlap test, that works for arbitrary ellipsoids, is conducted and novelly integrated into the MPC framework. We propose a particularly efficient implementation tailored to robots moving in the plane. The functionality of the proposed obstacle-avoiding MPC is demonstrated for two exemplary types of kinematics by means of simulations. A hardware experiment using a real-world wheeled mobile robot shows transferability to reality and real-time applicability. The general computational approach to ellipsoidal obstacle avoidance can also be applied to other robotic systems and vehicles as well as three-dimensional scenarios.

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arXiv2020

Robust Model Predictive Longitudinal Position Tracking Control for an Autonomous Vehicle Based on Multiple Models

The aim of this work is to control the longitudinal position of an autonomous vehicle with an internal combustion engine. The powertrain has an inherent dead-time characteristic and constraints on physical states apply since the vehicle is neither able to accelerate arbitrarily strong, nor to drive arbitrarily fast. A model predictive controller (MPC) is able to cope with both of the aforementioned system properties. MPC heavily relies on a model and therefore a strategy on how to obtain multiple linear state space prediction models of the nonlinear system via input/output data system identification from acceleration data is given. The models are identified in different regions of the vehicle dynamics in order to obtain more accurate predictions. The still remaining plant-model mismatch can be expressed as an additive disturbance which can be handled through robust control theory. Therefore modifications to the models for applying robust MPC tracking control theory are described. Then a controller which guarantees robust constraint satisfaction and recursive feasibility is designed. As a next step, modifications to apply the controller on multiple models are discussed. In this context, a model switching strategy is provided and theoretical and computational limitations are pointed out. Lastly, simulation results are presented and discussed, including computational load when switching between systems.

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