arXiv subjects

Matthias K. Hoffmann

Publications and source records attributed to Matthias K. Hoffmann.

4 recordsLinked to original sources

arXiv2026

Reconstruction of continuum robots by marker-free shape registration of image data using a kinematic model

Continuum robots are slender, flexible manipulators that navigate confined, curved workspaces and are gaining traction in aerospace, inspection, automation, and minimally invasive medical applications. Predicting their shape from physics-based models alone remains challenging, making accurate measurement of the deformed backbone essential for model validation and reference-data acquisition. We present an optimization-based shape-registration algorithm that fits a parametric three-dimensional curve directly to image observations within a photogrammetric pipeline, targeting marker-free measurement rather than sensing under occlusion. By matching reconstruction points to robot pixels, the method requires no prior knowledge of the robot's location in each image. Across most configurations, the estimated backbone deviates from ground truth by less than 1 mm (0.67% of the robot's length). On real concentric-tube continuum robots, the reconstruction agrees with ten discrete manual photogrammetric measurements over 18 configurations, while replacing the manual procedure with an automated pipeline that runs in roughly 0.5 s per configuration.

cs.RO↗

arXiv2025

Optimality-Informed Neural Networks for Solving Parametric Optimization Problems

Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. This is computationally demanding, particularly, if solutions have to be computed across strongly varying parameter values, e.g., in real-time control or for model-based design. Thus, we propose to learn the mapping from parameters to the primal optimal solutions and to their corresponding duals using neural networks, giving a dense estimation in contrast to gridded approaches. Our approach, Optimality-informed Neural Networks (OptINNs), combines (i) a KKT-residual loss that penalizes violations of the first-order optimality conditions under standard constraint qualifications assumptions, and (ii) problem-specific output activations that enforce simple inequality constraints (e.g., box-type/positivity) by construction. This design reduces data requirements, allows the prediction of dual variables, and improves feasibility and closeness to optimality compared to penalty-only training. Taking quadratic penalties as a baseline, since this approach has been previously proposed for the considered problem class in literature, our method simplifies hyperparameter tuning and attains tighter adherence to optimality conditions. We evaluate OptINNs on different nonlinear optimization problems ranging from low to high dimensions. On small problems, OptINNs match a quadratic-penalty baseline in primal accuracy while additionally predicting dual variables with low error. On larger problems, OptINNs achieve lower constraint violations and lower primal error compared to neural networks based on the quadratic-penalty method. These results suggest that embedding feasibility and optimality into the network architecture and loss can make learning-based surrogates more accurate, feasible, and data-efficient for parametric optimization.

math.OC↗

arXiv2022

Multi-Objective Model-Predictive Control for Dielectric Elastomer Wave Harvesters

This contribution deals with multi-objective model-predictive control (MPC) of a wave energy converter (WEC) device concept, which can harvest energy from sea waves using a dielectric elastomer generator (DEG) power take-off system. We aim to maximise the extracted energy through control while minimising the accumulated damage to the DEG. With reference to system operation in stochastic waves, we first generate ground truth solutions by solving an optimal control problem, and we analyse the MPC performance to determine a prediction horizon that trades off accuracy and efficiency for computation. Fixed weights in the MPC scheme can produce unpredictable costs for variable sea condition, meaning the average rate of cost accumulation can vary vastly. To steer this cost growth, we propose a heuristic to adapt the algorithm by changing the weighting of the cost functions using for fulfilling the long-time goal of accumulating a small enough damage in a fixed time. A simulated case-study is presented in order to evaluate the performance of the proposed MPC framework and the weight-adaptation algorithm. The proposed heuristic proves to be able to limit the amount of accumulated damage while remaining close to (or even improving) the energy yield obtained with a comparable fixed-weight MPC.

eess.SY↗

arXiv2022

Path Planning for Concentric Tube Robots: a Toolchain with Application to Stereotactic Neurosurgery

We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neurosurgery with real-world data obtained from labelled MPRI scans.

math.OC↗