“Robot Cloud” gradient climbing with point measurements

A scalar-field gradient climbing process for a large group of simple, low-capability mobile robotic agents using only point measurements is proposed and analyzed. The agents are assumed to be memoryless and to lack direct communication abilities. Their only implicit form of communication is by sensing the position of the members of the group. The proposed gradient following algorithm is based on a basic gathering algorithm. The gathering algorithm is augmented by controlling the agents' speed as follows: agents that sense a higher value of the field move slower toward the group center than those sensing lower values, thereby causing the swarm to drift in the direction of the underlying field gradient. Furthermore, a random motion component is added to each agent in order to prevent gathering and allow sampling of the scalar field. We prove that in the proposed algorithm, the group is cohesive and indeed follows the gradient of the scalar field. We also discuss an algorithm based on a more restrictive sensing capabilities for the agents.