This paper describes ongoing research into the design of a distributed robot control system targeted for a robotic system consisting of several manipulators equipped with a dextrous robot hand, specifically the Salisbury hand. The goal of this research is to produce a high-level control network which will allow the robotic system to be used in a task-oriented manner, i.e. where actions of the hand are specified in terms of their effects on objects. In this paper, we discuss the research issues involve in the design of a logical distributed model of computation specifically for the robot domain, and in the design of a dynamic mapping function to realize this model using a network of processors. We also sketch our preliminary ideas towards addressing these issues.