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In this paper we introduce a real-time steering controller ensuring the reach of a (possible mobile) target position and orientation, without requiring to build/update the full trajectory to that target. We name it the funnelling control. The final orientation is achieved through the continuous adjustment of the heading direction. This control mode is proactive in the sense that it anticipates the success/failure of the reach and adjusts the desired speed accordingly. Both features rely on an heterogeneously sampled table of radial-tangential seek angles obtained when the controller reaches a desired position target without prescribed orientation. By construction, the control update has a constant computing cost, even with variable target characteristics. Its low update cost makes it particularly suited for controlling a large number of mobile entities in real-time. The present exposition is made for an obstacle-free context.