Uniform Scattering of Autonomous Mobile Robots in a Grid

Abstract

We consider the uniform scattering problem for a set of autonomous mobile robots deployed in a grid network: starting from an arbitrary placement in the grid, using purely localized computations, the robots must move so to reach in finite time a state of static equilibrium in which they cover uniformly the grid. The theoretical quest is on determining the minimal capabilities needed by the robots to solve the problem. We prove that uniform scattering is indeed possible even for very weak robots. The proof is constructive. We present a provably correct protocol for uniform self-deployment in a grid. The protocol is fully localized, collision-free, and it makes minimal assumptions; in particular: (1) it does not require any direct or explicit communication between robots; (2) it makes no assumption on robots synchronization or timing, hence the robots can be fully asynchronous in all their actions; (3) it requires only a limited visibility range; (4) it uses at each robot only a constant size memory, hence computationally the robots can be simple Finite-State Machines; (5) it does not need a global localization system but only orientation in the grid (e.g., a compass); (6) it does not require identifiers, hence the robots can be anonymous and totally identical.

The Power of Lights: Synchronizing Asynchronous Robots Using Visible Bits

“…Other important problems studied for these teams of robots include scattering (e.g., [3], [13]), where the robots are required to scatter on the plane where they operate; leader election, where the robots have to elect one of them as the leader of the team (e.g., [12]); and flocking, where the robots have to follow one of the robots while keeping a formation, like a flock of birds (e.g., [5], [18]). Also studied has been the problem of communicating the local coordinate systems (e.g., [4]).…”

Computing by Mobile Robotic Sensors

“…These investigations differ greatly from each other depending on the assumptions they make. Major differences exist depending on whether: the entities' actions are synchronized (e.g., [13,47,81,83]) or no timing assumptions exist (e.g., [31,35,53]); the sensors have persistent memory (e.g., [13,43,83]) or are oblivious (e.g., [35,46,79]); the sensors have the computational power of Turing machines (e.g., [81,83]) or are simple Finite State machines (e.g., [4,16,30,47]); the visibility/communication range is limited (e.g., [31,43,38,47,79]) or extends to the entire region (e.g., [1,10,12,35,83]). …”

“…One extreme is the unbounded memory case, where no information is ever erased; hence sensors can remember all past computations and actions (e.g., see [81,83]). The other extreme is when the size of the workspace is constant; in this case, the sensors are just FiniteState Machines (e.g., [4,16,47]) .…”

“…The uniform deployment algorithm scatter is a set of local rules for the robots designed by Barriére et al [4]. Each sensor has a state variable belonging to a set of states {−1, 0, 1, 2, 3, 4} (initialized to −1) which determines the set of rules to be followed, which solely depend on the robot's current state, its position, and the positions of the robots within its visibility radius.…”

“…polygonal with sides either parallel or perpendicular to one another (e.g., see Figure 8). The space can be completed to become a bicolored cellular rectangle 4 A, where each cell, called pixel is colored white if it is part of M, black otherwise (see Figure 8).…”