Programming frameworks  are application generators with the following components: library of software modules (building blocks out of which the system is constructed), a method for designing new modules that can be appended to the above mentioned library, a pattern according to which ready modules can be assembled into a complete system jointly exerting control over it and realizing the task at hand. The presented transition function based formalism can be applied to specifying programming frameworks for robot controllers executing very diverse tasks. The paper deals with systems consisting of multiple embodied agents, influencing the environment through e#27;ectors, gathering information from the environment through sensors and communicating with other agents through communication channels. The presented code patterns pertain to behavioural agents. The formalism was instrumental in the design of MRROC++ robot programming framework, which has been used for producing controllers of single and two manipulator systems performing diverse tasks. The formalism introduces rigor into the discussion of the structure of embodied agent controllers. It is used as the means for the specification of the functions of the components of the control system and the structure of the communication links between them. This structures the implementation of a programming framework, and that in turn makes the coding of specific controllers much easier, both from the point of view of dealing with the hardware configuration of the system and the specific task that has to be executed.