The underlying framework for controlling autonomous robots and complex automation applications are Operating Systems (OS) capable of scheduling perception-and-control tasks, as well as providing real-time data communication to other robotic peers and remote cloud computers. In this paper, we introduce CyberCortex AI, a robotics OS designed to enable heterogeneous AI-based robotics and complex automation applications. CyberCortex AI is a decentralized distributed OS which enables robots to talk to each other, as well as to High Performance Computers (HPC) in the cloud. Sensory and control data from the robots is streamed towards HPC systems with the purpose of training AI algorithms, which are afterwards deployed on the robots. Each functionality of a robot (e.g. sensory data acquisition, path planning, motion control, etc.) is executed within a so-called DataBlock of Filters shared through the internet, where each filter is computed either locally on the robot itself, or remotely on a different robotic system. The data is stored and accessed via a so-called Temporal Addressable Memory (TAM), which acts as a gateway between each filter's input and output. CyberCortex AI has two main components: i) the CyberCortex AI inference system, which is a real-time implementation of the DataBlock running on the robots' embedded hardware, and ii) the CyberCortex AI dojo, which runs on an HPC computer in the cloud, and it is used to design, train and deploy AI algorithms. We present a quantitative and qualitative performance analysis of the proposed approach using two collaborative robotics applications: i) a forest fires prevention system based on an Unitree A1 legged robot and an Anafi Parrot 4K drone, as well as ii) an autonomous driving system which uses CyberCortex AI for collaborative perception and motion control.