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This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets. In the present paper, we introduce a notion of \emph{linear graph-directed IFS}…
The paper presents a strategy for robotic exploration problems using Space-Filling curves (SFC). The region of interest is first tessellated, and the tiles/cells are connected using some SFC. A robot follows the SFC to explore the entire…
Rigid-formation navigation of multiple robots is essential for applications such as cooperative transportation. This process involves a team of collaborative robots maintaining a predefined geometric configuration, such as a square, while…
For fully actuated rigid robots, kinematic inversion is a purely geometric problem, efficiently solved by closed-loop inverse kinematics (CLIK) schemes that compute joint configurations to position the robot body in space. For underactuated…
We study the \emph{{interval completion}} problem, which asks for the insertion of a set of at most $k$ edges to make a graph of $n$ vertices into an interval graph. We focus on chordal graphs with no small obstructions, where every…
In a context of autonomous robots, one of the most important task is to ensure the safety of the robot and its surrounding. Most of the time, the risk of navigation is simply said to be the probability of collision. This notion of risk is…
Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science,…
We study the Rendezvous problem for 2 autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible in a basic model when robots have no lights, even if the system is…
In this paper, we consider the problem of scattering a swarm of mobile oblivious robots in a continuous space. We consider the fully asynchronous setting where robots may base their computation on past observations, or may be observed by…
In this paper we consider the coverage control problem for a team of wire-traversing robots. The two-dimensional motion of robots moving in a planar environment has to be projected to one-dimensional manifolds representing the wires.…
In this work, we present solutions to the flocking and target interception problems of multiple nonholonomic unicycle-type robots using the distance-based framework. The control laws are designed at the kinematic level and are based on the…
The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…
Dispersion of mobile robots over the nodes of an anonymous graph is an important problem and turns out to be a crucial subroutine for designing efficient algorithms for many fundamental graph problems via mobile robots. In this problem,…
Human-robot interaction plays a crucial role to make robots closer to humans. Usually, robots are limited by their own capabilities. Therefore, they utilise Cloud Robotics to enhance their dexterity. Its ability includes the sharing of…
Formation control of multiple groups of agents finds application in large area navigation by generating different geometric patterns and shapes, and also in carrying large objects. In this paper, Centroid Based Transformation (CBT)…
Every rotationless outer automorphism of a finite rank free group is represented by a particularly useful relative train track map called a CT. The main result of this paper is that the constructions of CTs can be made algorithmic. A key…
Large demand for robotics and automation has been reflected in the sanding works, as current manual operations are labor-intensive, without consistent quality, and also subject to safety and health issues. While several machines have been…
Consider a surface $\Sigma$ with punctures that serve as marked points and at least one marked point on each boundary component. We build a filling surface $\Sigma_n$ by singling out one of the boundary components and denoting by $n$ the…
Autonomy for robots interacting with sand will enable a wide range of beneficial behaviors, from earth moving for construction and farming vehicles to navigating rough terrain for Mars rovers. The goal of this work is to shape sand into…
This paper introduces a distributed leaderless swarm formation control framework to address the problem of collectively driving a swarm of robots to track a time-varying formation. The swarm's formation is captured by the trajectory of an…