The paper present a model of the kinematics of a rotary, redundant manipulator, in the form of a Finite State Machine, this is in fact, an example of AI production systems. This model is able to supply us with succesive configurations, calculated immediately in Cartesian space and allowing at the same time to considerably simplify the computations engaged in the graph searching. For an automaton-type model of the manipulator kinematics, diverse strategies of searching for a collision-free trajectory, reduced to a search of an appropriate path in the state-transition graph of FSM, are analyzed.