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We prove a result which strongly hints at the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile…
We present a probabilistic approach for building, on the fly, 3-D models of unknown objects while being manipulated by a robot. We specifically consider manipulation tasks in piles of clutter that contain previously unseen objects. Most…
We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…
Prehensile object rearrangement in cluttered and confined spaces has broad applications but is also challenging. For instance, rearranging products in a grocery shelf means that the robot cannot directly access all objects and has limited…
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…
Polymer translocation in crowded environments is a ubiquitous phenomenon in biological systems. We studied polymer translocation through a pore in free, one-sided (asymmetric), and two-sided (symmetric) crowded environments. Extensive…
We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice…
Part assembly is a typical but challenging task in robotics, where robots assemble a set of individual parts into a complete shape. In this paper, we develop a robotic assembly simulation environment for furniture assembly. We formulate the…
We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the…
In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior…
We develop a unified scaling framework for the end-position distributions of tethered polymers confined in finite cylindrical geometries. Two observables are analysed: the longitudinal distribution P(x), along the confinement axis, and the…
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…
This paper presents planning algorithms for a robotic manipulator with a fixed base in order to grasp a target object in cluttered environments. We consider a configuration of objects in a confined space with a high density so no…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
Identifying ordered structures hidden in the packings of particles is a common scientific question in multiple fields. In this work, we investigate the dynamical organizations of a large number of initially randomly packed repulsive…
Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of…
A team of anonymous mobile agents represented by points freely moving in the plane have to gather at a single point and stop. Agents start at different points of the plane and at possibly different times chosen by the adversary. They are…