An efficient inverse kinematics solver is a key element in applications targeting the on-line or off-line postural control of complex articulated figures. In the present paper we progressively describe the strategic components of a very general and robust inverse kinematics architecture. We then present an efficient recursive algorithm enforcing an arbitrary number of strict priorities to arbitrate the fulfillment of conflicting constraints. Due to its local nature, the moderate cost of the solution allows this architecture to run within an interactive environment. The algorithm is illustrated on the postural control of complex articulated figures