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In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $\Omega$ (the $S^{d-1}-$ sphere, in our…
We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is…
Biological and robotic systems often operate in confined environments where material must be gathered without centralized control. Inspired by the effective collection strategies of aquatic worms (Lumbriculus variegatus and Tubifex…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
This paper provides a bridge between the classical tiling theory and the complex neighborhood self-assembling situations that exist in practice. The neighborhood of a position in the plane is the set of coordinates which are considered…
Active colloidal particles typically exhibit a pronounced affinity for accumulating and being captured at boundaries. Here, we engineer long-range repulsive interactions between colloids that self-propel under an electric field and…
We prove that by successively combining subassemblies, we can achieve sublinear construction times for "staged" assembly of micro-scale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a $O(n\log^2{n})$-time algorithm for deciding if a…
We study the covering of the plane by non-overlapping rhombus tiles, a problem well-studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on…
We present an algorithm that produces a plan for relocating obstacles in order to grasp a target in clutter by a robotic manipulator without collisions. We consider configurations where objects are densely populated in a constrained and…
Collective guidance of out-of-equilibrium systems without using external fields is a challenge of paramount importance in active matter, ranging from bacterial colonies to swarms of self-propelled particles. Designing strategies to guide…
The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting…
This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner…
This paper investigates the use of a sampling-based approach, the RRT*, to reconfigure a 2D set of connected tiles in complex environments, where multiple obstacles might be present. Since the target application is automated building of…
We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…
We consider a swarm of mobile robots evolving in a bidimensional Euclidean space. We study a variant of the crash-tolerant gathering problem: if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in…
We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it. Repeated application of this algorithm results in the formation of unusual dynamical patterns: during the process…
We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the…