Brief Announcement: Model Checking Rendezvous Algorithms for Robots with Lights in Euclidean Space

This announces the first successful attempt at using model-checking techniques to verify the correctness of self-stabilizing distributed algorithms for robots evolving in a continuous environment. The study focuses on the problem of rendezvous of two robots with lights and presents a generic verification model for the SPIN model checker. It will be presented in full at an upcoming venue

Correlation Clustering Based Coalition Formation For Multi-Robot Task Allocation

In this paper, we study the multi-robot task allocation problem where a group of robots needs to be allocated to a set of tasks so that the tasks can be finished optimally. One task may need more than one robot to finish it. Therefore the robots need to form coalitions to complete these tasks. Multi-robot coalition formation for task allocation is a well-known NP-hard problem. To solve this problem, we use a linear-programming based graph partitioning approach along with a region growing strategy which allocates (near) optimal robot coalitions to tasks in a negligible amount of time. Our proposed algorithm is fast (only taking 230 secs. for 100 robots and 10 tasks) and it also finds a near-optimal solution (up to 97.66% of the optimal). We have empirically demonstrated that the proposed approach in this paper always finds a solution which is closer (up to 9.1 times) to the optimal solution than a theoretical worst-case bound proved in an earlier work

Gathering Anonymous, Oblivious Robots on a Grid

We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved