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Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are…

Social Robotics poses tough challenges to software designers who are required to take care of difficult architectural drivers like acceptability, trust of robots as well as to guarantee that robots establish a personalised interaction with…

In this report, we try to improve the performance of existing approaches for search operations in multi-robot context. We propose three novel algorithms that are using a triangular grid pattern, i.e., robots certainly go through the…

The similarity of graph structures, such as Meaning Representations (MRs), is often assessed via structural matching algorithms, such as Smatch (Cai and Knight, 2013). However, Smatch involves a combinatorial problem that suffers from…

A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many…

A basic task in the design of a robotic production cell is the relative placement of robot and workpiece. The fundamental requirement is that the robot can reach all process positions; only then one can think of further optimization.…

This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their…

Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…

We study the distance on the Bruhat-Tits building of the group $\mathrm{SL}_d(\mathbb{Q}_p)$ (and its other combinatorial properties). Coding its vertices by certain matrix representatives, we introduce a way how to build formulas with…

A locally-optimal structure is a combinatorial structure such as a maximal independent set that cannot be improved by certain (greedy) local moves, even though it may not be globally optimal. It is trivial to construct an independent set in…

To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…

In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many…

The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…

Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…

Cuspidal robots can move from one inverse or direct kinematic solution to another without ever passing through a singularity. These robots have remained unknown because almost all industrial robots do not have this feature. However, in…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

The use of neural networks in safety-critical systems requires safe and robust models, due to the existence of adversarial attacks. Knowing the minimal adversarial perturbation of any input x, or, equivalently, knowing the distance of x…

Homogeneity and heterogeneity represent a well-known trade-off in the design of modular robot systems. This work addresses the heterogeneity concept, its rationales, design choices and performance evaluation. We introduce challenges for…

We formulate an asymmetric (or non-commutative) distance between tasks based on Fisher Information Matrices, called Fisher task distance. This distance represents the complexity of transferring the knowledge from one task to another. We…