arXiv subjects

Lukas Taus

Publications and source records attributed to Lukas Taus.

5 recordsLinked to original sources

arXiv2026

Optimal Transmitter Placement in Realistic Urban Environments

In a wireless network, transmitter locations strongly impact achievable rates. Cellular deployment is a difficult non-convex problem, typically addressed using simplified models and heuristics. We propose a mathematically rigorous framework incorporating detailed site-specific maps, material properties, and realistic attenuation. We introduce an aggregated network-quality functional scoring receiver-weighted signal quality, impose deployment costs via cardinality and budget constraints, and establish submodularity under practical conditions. To solve the optimization problem, we propose the Interference-Aware Submodular Placement Algorithm (IA-SPA) with a theoretical approximation guarantee relative to the optimum. IA-SPA incorporates existing base stations and prohibited areas, making it applicable to clean-slate and incremental deployments. We evaluate our approach using ray-tracing simulations on 3D maps of San Francisco and Florence, comparing against known deployments by AT and T, T-Mobile, and Iliad. Our strategy achieves significant increases in mean data rate (about 2x) and edge rate (2-8x) using the same number of transmitters. These gains persist under simultaneous exclusionary zones, small-scale fading, material/geometric perturbations, and incremental densification of existing networks. The pipeline has linear computational dependence on candidate sites, and wall-clock measurements demonstrate practical runtime at city scale.

cs.IT↗

arXiv2026

Rendezvous Planning from Sparse Observations of Optimally Controlled Targets

We develop a probabilistic framework for \emph{rendezvous planning}: given sparse, noisy observations of a fast-moving target, plan rendezvous spatiotemporal coordinates for a set of significantly slower seeking agents. The unknown target trajectory is estimated under uncertain dynamics using a filtering approach that combines a kernel-based maximum a posteriori estimation with Gaussian process correction, producing a mixture over trajectory hypotheses. This estimate is used to select spatiotemporal rendezvous points that maximize the probability of successful rendezvous. Points are chosen sequentially by greedily minimizing failure probability in the current belief space, which is updated after each step by conditioning on unsuccessful rendezvous attempts. We show that the failure-conditioned update correctly captures the posterior belief for subsequent decisions, ensuring that each step in the greedy sequence is informed by a statistically consistent representation of the remaining search space, and derive the corresponding Bayesian updates incorporating temporal correlations intrinsic to the trajectory model. This result provides a systematic framework for planning under uncertainty in applications of autonomous rendezvous such as unmanned aerial vehicle refueling, spacecraft servicing, autonomous surface vessel operations, search and rescue missions, and missile defense. In each, the motion of the target entity can be modeled using a system of differential equations undergoing optimal control for a chosen objective, in our example case Hamilton--Jacobi--Bellman solutions for minimum arrival time of a Dubins car with uncertain turning radius and destination.

math.OC↗

arXiv2024

Fast End-to-End Generation of Belief Space Paths for Minimum Sensing Navigation

We revisit the problem of motion planning in the Gaussian belief space. Motivated by the fact that most existing sampling-based planners suffer from high computational costs due to the high-dimensional nature of the problem, we propose an approach that leverages a deep learning model to predict optimal path candidates directly from the problem description. Our proposed approach consists of three steps. First, we prepare a training dataset comprising a large number of input-output pairs: the input image encodes the problem to be solved (e.g., start states, goal states, and obstacle locations), whereas the output image encodes the solution (i.e., the ground truth of the shortest path). Any existing planner can be used to generate this training dataset. Next, we leverage the U-Net architecture to learn the dependencies between the input and output data. Finally, a trained U-Net model is applied to a new problem encoded as an input image. From the U-Net's output image, which is interpreted as a distribution of paths,an optimal path candidate is reconstructed. The proposed method significantly reduces computation time compared to the sampling-based baseline algorithm.

cs.RO↗

arXiv2024

Optimizing Sensor Network Design for Multiple Coverage

Sensor placement optimization methods have been studied extensively. They can be applied to a wide range of applications, including surveillance of known environments, optimal locations for 5G towers, and placement of missile defense systems. However, few works explore the robustness and efficiency of the resulting sensor network concerning sensor failure or adversarial attacks. This paper addresses this issue by optimizing for the least number of sensors to achieve multiple coverage of non-simply connected domains by a prescribed number of sensors. We introduce a new objective function for the greedy (next-best-view) algorithm to design efficient and robust sensor networks and derive theoretical bounds on the network's optimality. We further introduce a Deep Learning model to accelerate the algorithm for near real-time computations. The Deep Learning model requires the generation of training examples. Correspondingly, we show that understanding the geometric properties of the training data set provides important insights into the performance and training process of deep learning techniques. Finally, we demonstrate that a simple parallel version of the greedy approach using a simpler objective can be highly competitive.

cs.LG↗

arXiv2023

Efficient and robust Sensor Placement in Complex Environments

We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to consider solutions that are robust against sensor failure or adversarial attacks. This paper addresses these challenges of designing minimal sensor sets that achieve multi-coverage constraints -- every point in the environment is covered by a prescribed number of sensors. We propose a greedy algorithm to achieve the objective. Further, we explore deep learning techniques to accelerate the evaluation of the objective function formulated in the greedy algorithm. The training of the neural network reveals that the geometric properties of the data significantly impact the network's performance, particularly at the end stage. By taking into account these properties, we discuss the differences in using greedy and $ε$-greedy algorithms to generate data and their impact on the robustness of the network.

cs.LG↗