Subhash Bhagat

Fault-tolerant gathering of asynchronous oblivious mobile robots under one-axis agreement

This paper addresses gathering, a fundamental coordination problem for multi-robot systems, for n ? 2 asynchronous, oblivious mobile robots in the presence of f faulty robots. Earlier work has reported that the asynchronous robots cannot gather at a point without having some assumptions on multiplicity detection or total agreement in coordinate axis or constant amount of persistent memory bits. This paper shows that gathering is possible by agreeing only on one axis. Traditionally the robots have been assumed to be transparent. This work proves that gathering is achievable under one axis agreement even if the robots have obstructed visibility. In both the cases, deterministic fault-tolerant algorithms have been presented, for any initial static configuration of the robots. This paper is the first attempt at studying the gathering problem under the combination of three realistic model specifications (i) agreement in one axis (ii) obstructed visibility (iii) arbitrary number of faulty robots.

Formation of General Position by Asynchronous Mobile Robots Under One-Axis Agreement

The traditional distributed model of autonomous, homogeneous, mobile point robots usually assumes that the robots do not create any visual obstruction for the other robots, i.e., the robots are see through. In this paper, we consider a slightly more realistic model, by incorporating the notion of obstructed visibility (i.e., robots are not see through) for other robots. Under the new model of visibility, a robot may not have the full view of its surroundings. Many of the existing algorithms demand that each robot should have the complete knowledge of the positions of other robots. Since, vision is the only mean of their communication, it is required that the robots are in general position (i.e., no three robots are collinear). We consider asynchronous robots. They also do not have common chirality (or any agreement on a global coordinate system). In this paper, we present a distributed algorithm for obtaining a general position for the robots in finite time from any arbitrary configuration. The algorithm also assures collision free motion for each robot. This algorithm may also be used as a preprocessing module for many other subsequent tasks performed by the robots.

Fault-Tolerant Gathering of Asynchronous Oblivious Mobile Robots under One-Axis Agreement

In this paper, we have studied one of the fundamental coordination problems for multi robot system, namely gathering, for n ≥ 2 asynchronous, oblivious mobile robots in the presence of f < n faulty robots. Earlier works have reported that, in general, to solve gathering problem for asynchronous robots, many assumptions are required, like multiplicity detection or total agreement in coordinate axis or constant amount of memory bits. However, in this paper we have proved that gathering of asynchronous robots is possible with less number of such assumptions and even in the presence of any number of faulty robots. In our case, the robots only agree on the direction and orientation of any one axis.

Fault-tolerant Gathering of Semi-synchronous Robots

This paper addresses the Gathering problem which asks robots to gather at a single point which is not fixed in advance, for a set of small, autonomous, mobile robots. The problem is studied for a set of semi-synchronous robots under SSY NC model when the robots may become faulty (crash fault). Depending upon the capabilities of the robots, the algorithms are designed to tolerate maximum number of faults. This work assumes weak multiplicity detection capability of the robots. The contribution of this work is in two folds. First, a distributed algorithm is presented which can tolerate at most (⌊n/2 - 1⌋) crash faults for n ≥ 7 robots with weak multiplicity detection only. For the second algorithm, it is also assumed that robots know the mobility capacity of all the robots. The algorithm presented here can tolerate at most (n - 6) crash faults for n ≥ 7 robots.

Optimum Gathering of Asynchronous Robots

This paper considers the problem of gathering a set of asynchronous robots on the two dimensional plane under the additional requirement that the maximum distance traversed by the robots should be minimized. One of the implications of this optimization criteria is the energy efficiency for the robots. The results of this paper are two folds. First, it is proved that multiplicity detection capability is not sufficient to solve the constrained gathering problem for a set of oblivious robots even when the robots are fully synchronous. The problem is then studied for the robots having O(1) bits persistent memory and a distributed algorithm is proposed for the problem in this model for a set of \(n\ge 5\) robots. The proposed algorithm uses only two bits of persistent memory.

Gathering of Opaque Robots in 3D Space

Gathering is a fundamental coordination problem for multi-robot systems. This paper presents a study of the gathering problem for a set of oblivious, autonomous mobile robots in the three dimensional Euclidean space, under obstructed visibility model. In this model, robots are considered to be opaque. Robots may not have the complete view of the configuration. This paper assumes only an agreement on the direction and orientation of one coordinate axis. A distributed algorithm is proposed to solve the gathering problem for a set of asynchronous robots, when the system does not contain any faulty robot. Another distributed algorithm is presented to solve the problem for a set of semi-synchronous robots under crash fault model. The proposed algorithm can tolerate an arbitrary number of crash faults. Both algorithms work for an arbitrary initial robot configuration.

Optimum Circle Formation by Autonomous Robots

This paper considers a constrained version of the circle formation problem for a set of asynchronous, autonomous robots on the Euclidean plane. The circle formation problem asks a set of autonomous, mobile robots, initially having distinct locations, to place themselves, within finite time, at distinct locations on the circumference of a circle (not defined a priori), without colliding with each other. The constrained circle formation problem demands that in addition the maximum distance moved by any robot to solve the problem should be minimized. A basic objective of the optimization constrain is that it implies energy savings of the robots. This paper presents results in two parts. First, it is shown that the constrained circle formation problem is not solvable for oblivious asynchronous robots under ASYNC model even if the robots have rigid movements. Then the problem is studied for robots which have O(1) bits of persistent memory. The initial robot configurations, for which the problem is not solvable in this model, are characterized. For other configurations, a distributed algorithm is presented to solve the problem for asynchronous robots. Only one bit of persistent memory is needed in the proposed algorithm.

Gathering Asynchronous Robots in the Presence of Obstacles

This work addresses the problem of Gathering a swarm of point robots when the plane of deployment has non-intersecting transparent convex polygonal obstacles. While multiplicity detection is enough for gathering three or more asynchronous robots without obstacles, it is shown that in the presence of obstacles, gathering may not be possible even in the FSYNC model with all of multiplicity detection, memory, chirality and direction-only axis agreement. Initial configurations for which gathering is impossible are characterized. For other configurations, a distributed algorithm for the gathering problem is proposed without any extra assumption on the capabilities of the robots. The algorithm works even if the configuration contains points of multiplicities.

Optimum Algorithm for Mutual Visibility Among Asynchronous Robots with Lights

This paper addresses the constrained version of the mutual visibility problem for a set of asynchronous, opaque robots in the Euclidean plane. The mutual visibility problem asks the robots to form a configuration, within finite time and without collision, in which no three robots are collinear. The constrained mutual visibility problem in addition aims to minimize the maximum number of movements by a single robot. One of the implications of this constrained version of mutual visibility problem is that it also addresses issue of energy efficiency. The robots have a constant amount of persistent memory and they are equipped with externally visible lights which can assume a constant number of predefined colors. The colors represent different states of the robots and are used both for internal memory and communication. The colors of the lights do not change automatically. A distributed algorithm is proposed to solve the constrained mutual visibility problem for a set of asynchronous robots using only seven colors. The proposed algorithm does not impose any other restriction on the capability of the robots and guarantees collision-free movements for the robots.