Related papers: Robots, computer algebra and eight connected compo…
A vertex set $U \subseteq V$ of an undirected graph $G=(V,E)$ is a $\textit{resolving set}$ for $G$, if for every two distinct vertices $u,v \in V$ there is a vertex $w \in U$ such that the distances between $u$ and $w$ and the distance…
Traversing environments with arbitrary obstacles poses significant challenges for bipedal robots. In some cases, whole body motions may be necessary to maneuver around an obstacle, but most existing footstep planners can only select from a…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of $k$ robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two…
Singularity in robot controls is an important problem. By identifying an appropriate trajectory for the robots, the singular situations can be avoided. In this paper an identification algorithm is proposed to control the robot such that it…
Aiming to generate easy-to-handle assembly sequences for robotic assembly, this study tackles assembly sequence generation by considering two tradeoff objectives: (1) insertion conditions and (2) degrees of constraints among assembled…
We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex…
A quantum robot is a mobile quantum system including an on bord quantum computer and ancillary systems, that interact with an environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements and…
We consider exploration of finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules. The number of possible shapes of a metamorphic robotic system grows as the number of modules increases. The shape of…
This paper aims to study a specific kind of parallel robot: Spherical Parallel Manipulators (SPM) that are capable of unlimited rolling. A focus is made on the kinematics of such mechanisms, especially taking into account uncertainties…
Sensor coverage is the critical multi-robot problem of maximizing the detection of events in an environment through the deployment of multiple robots. Large multi-robot systems are often composed of simple robots that are typically not…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric…
Motion planning has been studied for nearly four decades now. Complete, combinatorial motion planning approaches are theoretically well-rooted with completeness guarantees but they are hard to implement. Sampling-based and heuristic methods…
In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is non-positively curved. In particular, given such a complex we show how to define a boolean…
This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then…
We consider methods for connected reconfigurations by finite automate in the so-called \emph{hybrid} or \emph{Robot-on-Tiles} model of programmable matter, in which a number of simple robots move on and rearrange an arrangement of passive…
Parametric computer-aided design (CAD) is the dominant paradigm in mechanical engineering for physical design. Distinguished by relational geometry, parametric CAD models begin as two-dimensional sketches consisting of geometric primitives…
Inverse kinematics is a fundamental problem for articulated robots: fast and accurate algorithms are needed for translating task-related workspace constraints and goals into feasible joint configurations. In general, inverse kinematics for…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…