This conceptual paper discusses how different aspects involving the autonomous operation of robots and vehicles will change when they have access to next-generation mobile networks. 5G and beyond connectivity is bringing together a myriad of technologies and industries under its umbrella. High-bandwidth, low-latency edge computing services through network slicing have the potential to support novel application scenarios in different domains including robotics, autonomous vehicles, and the Internet of Things. In particular, multi-tenant applications at the edge of the network will boost the development of autonomous robots and vehicles offering computational resources and intelligence through reliable offloading services. The integration of more distributed network architectures with distributed robotic systems can increase the degree of intelligence and level of autonomy of connected units. We argue that the last piece to put together a services framework with third-party integration will be next-generation low-latency blockchain networks. Blockchains will enable a transparent and secure way of providing services and managing resources at the Multi-Access Edge Computing (MEC) layer. We overview the state-of-the-art in MEC slicing, distributed robotic systems and blockchain technology to define a framework for services the MEC layer that will enhance the autonomous operations of connected robots and vehicles.