In the realm of pool maintenance, the advent of automatic pool cleaners represents an inflection point in the history of pool hygiene and upkeep. Commonly known as robots, these devices are designed to autonomously traverse the pool, removing debris and detritus that would otherwise accumulate on the floor and walls. The central question then becomes: how do these marvels of modern engineering accomplish their task? In order to fully appreciate the brilliance of automatic pool cleaners, we must delve into the dynamics of their operation and the factors that enable their efficient functioning.

Before we delve into the mechanics of these aquatic sanitization devices, it is imperative to note that automatic pool cleaners are divided into three primary categories: suction-side cleaners, pressure-side cleaners, and robotic pool cleaners. Each type represents a distinct approach to pool cleaning, leveraging different principles of fluid dynamics and automation technology.

• Suction-side cleaners, as the name implies, use the pool’s own suction, generated by the pump, to move around and vacuum the pool’s surfaces. These cleaners operate in a manner similar to a domestic vacuum cleaner, though the media being manipulated is water, rather than air. A hose connects the cleaner to the pool’s skimmer or dedicated suction line, and as water is sucked by the pump, the resulting flow propels the cleaner and draws in debris. The simplicity of suction-side cleaners makes them relatively affordable, though they do place additional strain on the pool's pump and filtration system.
• Pressure-side cleaners, on the other hand, are powered by the water pressure from a dedicated booster pump or the pool's return jets. These cleaners utilize a combination of jet propulsion and vortex suction to collect debris in a separate bag, thereby reducing strain on the pool’s filtration system. While pressure-side cleaners can cover more ground than their suction-side counterparts, they are a bit more complex, requiring additional plumbing for the booster pump, and hence are generally more expensive.
• The third category, robotic pool cleaners, represent the pinnacle of pool cleaning technology. Operating independently of the pool's circulation system, these cleaners use electric motors for propulsion and suction. Equipped with advanced features such as smart navigation, programmable timers, and powerful scrubbing brushes, these machines can methodically clean every inch of a pool, even scaling walls and stairs. The efficiency and effectiveness of robotic cleaners comes with a steeper price tag, but the trade-off is a hands-off, thorough cleaning and no additional strain on the pool's existing equipment.

By this point, the relevance of understanding the hydraulics of pool systems becomes clear. These cleaning systems, in their varied forms, leverage the principles of fluid dynamics to not just move about the pool, but also to create the suction needed to remove debris. Understanding these dynamics can guide the choice of cleaner, as each type comes with its own trade-offs in terms of cost, effectiveness, and strain on the pool's systems.

A masterstroke on the part of these devices' engineers is their use of randomness. Both suction-side and pressure-side cleaners lack sophisticated navigation systems, instead relying on random movement to cover the entire pool. This is based upon the statistical principle of ergodicity, which posits that, given enough time, these cleaners will cover every possible point within the pool. Robotic cleaners, however, incorporate intelligent algorithms and sensors to systematically cover the entire pool, reducing cleaning times and energy usage.

In conclusion, automatic pool cleaners represent a harmonious marriage of engineering, fluid dynamics, and statistics. By understanding their different operation modalities, pool owners can make an informed decision on which type best serves their needs. Whether one opts for a suction-side, pressure-side, or robotic cleaner, the result is the same: a cleaner pool with less effort. As technology continues to advance, one can only expect these devices to become even more efficient and effective, further transforming the task of pool cleaning from a tiresome chore to a spectacle of modern automation.