A Parallel Distributed Strategy for Arraying a Scattered Robot Swarm

We consider the problem of organizing a scattered group of $n$ robots in two-dimensional space, with geometric maximum distance $D$ between robots. The communication graph of the swarm is connected, but there is no central authority for organizing it. We want to arrange them into a sorted and equally-spaced array between the robots with lowest and highest label, while maintaining a connected communication network. In this paper, we describe a distributed method to accomplish these goals, without using central control, while also keeping time, travel distance and communication cost at a minimum. We proceed in a number of stages (leader election, initial path construction, subtree contraction, geometric straightening, and distributed sorting), none of which requires a central authority, but still accomplishes best possible parallelization. The overall arraying is performed in $O(n)$ time, $O(n^2)$ individual messages, and $O(nD)$ travel distance. Implementation of the sorting and navigation use communication messages of fixed size, and are a practical solution for large populations of low-cost robots

On the hardness of unlabeled multi-robot motion planning

In unlabeled multi-robot motion planning several interchangeable robots operate in a common workspace. The goal is to move the robots to a set of target positions such that each position will be occupied by some robot. In this paper, we study this problem for the specific case of unit-square robots moving amidst polygonal obstacles and show that it is PSPACE-hard. We also consider three additional variants of this problem and show that they are all PSPACE-hard as well. To the best of our knowledge, this is the first hardness proof for the unlabeled case. Furthermore, our proofs can be used to show that the labeled variant (where each robot is assigned with a specific target position), again, for unit-square robots, is PSPACE-hard as well, which sets another precedence, as previous hardness results require the robots to be of different shapes

Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape

Mobile Robot Path Planning in Static Environment

The success of Particle Swarm Optimization (PSO) and Genetic algorithm (GA) as single objective optimizer has motivated researchers to extend the use of this bio- inspired techniques to other areas. One of them is multi-objective optimization. As a part of this review we present a classification of the approaches and identify the main approaches here. We describe useful performance measures and simulation results of conventional Genetic algorithm and PSO. We extend this to multi-objective genetic algorithm and PSO. This means that GA and PSO optimizes path based on two criteria: length and difficult. Another method that has new to this field of research is the Artificial Potential field method. In this method the entire space is supposed to contain a potential field and we calculate the net force that is acted upon the robot to reach its goal

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

Symbiotic Navigation in Multi-Robot Systems with Remote Obstacle Knowledge Sharing

Large scale operational areas often require multiple service robots for coverage and task parallelism. In such scenarios, each robot keeps its individual map of the environment and serves specific areas of the map at different times. We propose a knowledge sharing mechanism for multiple robots in which one robot can inform other robots about the changes in map, like path blockage, or new static obstacles, encountered at specific areas of the map. This symbiotic information sharing allows the robots to update remote areas of the map without having to explicitly navigate those areas, and plan efficient paths. A node representation of paths is presented for seamless sharing of blocked path information. The transience of obstacles is modeled to track obstacles which might have been removed. A lazy information update scheme is presented in which only relevant information affecting the current task is updated for efficiency. The advantages of the proposed method for path planning are discussed against traditional method with experimental results in both simulation and real environments