This paper describes a research project about robot control across a computing Grid, first step toward a Grid solution for generic process control. A computational Grid can significantly improve remote robot control. It can choose at any time the most suitable machine for each task, transparently run redundant computations for critical operations, adding fault tolerance, allowing robotic system sharing among remote partners. We built a Grid spanning France and Italy and successfully controlled a navigating robot and a robotic arm. Our Grid is based on the GridRPC paradigm, the DIET environment and an IPSEC-based VPN. We turned some modules of robotic applications into Grid services. Finally we developed a high-level API, specializing the GridRPC paradigm for our purposes, and a semantics for quickly adding new Grid services. 1 Motivations and Project Overview This paper introduces a Grid architecture for comfortable and fault tolerant robot control. It is part of a larger project aim...