In this paper, we exploit an integration between the mobility of robots and the collaboration between them to sample sensing areas that need to be observed. A collaborative and compressed mobile sensing algorithm is proposed for distributed robotic networks to build scalar field maps. In order to move in the sensing field and to avoid collision with obstacles and with each other, a control law is embedded into the robots. At a sampling time, each robot senses and adds data within its sensing range and collaborates to the others by exchanging data with its neighbors. A compressed sensing (CS) measurement created is a sum of scalar values collecting by a connected group of robots. A certain number of CS measurements is required at each robot to reconstruct all sensory readings from points of interest visited by the group of robots. The method reduces significantly data traffic among robots. We further analyze and formulate power consumption for the robots, and suggest some optimal cases for the robot to consume the least power.
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