Although many algorithms exist for robotic complete, coverage path planning (CPP), most algorithms are not practical for real-world use because they rely on perfect, prior knowledge of a static target environment, hardwired path planning or substantial human interaction, among other things. Moreover, many algorithms do not consider the real-world constraints of limited on-board power, computing, memory or communications, especially for low cost, multi-agent swarms. For aerospace applications, power-constrained CPP algorithms are critical because they can impact the effectiveness of future applications, such as the development of autonomous multi-robot teams for lunar site-preparation, mining and construction, or the development of terrestrial multi-robot teams to conduct visual or x-ray inspections of aircraft bodies. In this paper, we apply the Artificial Neural Tissue (ANT) control algorithm   to solve simulated CPP tasks, where multiple agents cooperate and completely or almost completely, cover 2-dimensional, basic geometric, open grid areas in linear or quasilinear time, where time complexity is measured by the number of robot time steps and the open grid cells to cover. In these ANT simulations, there is no central controller and the agents are constrained by limited time steps, a priori knowledge of the target environment, on-board memory and sensors. Also, the agents do not communicate among themselves. However, the ANT agents do rely on pheromones/markers to track whether a grid cell has been visited, and receive information from a central station concerning total area coverage, time and global reference directions. In these CPP tasks, the performance of ANT is comparable to the best-known, grid-based, heuristic coverage algorithm with a quasilinear upper bound cover time  .