This paper presents a rigorous, analytical framework for interactive control methods such as sti ness and impedance control. This paper does not present a novel synthesis method for robot control design. Rather, it presents a proper framework to analyse controllers for robots whose purpose is to interact energetically with the environment.First geometrical tools are introduced that are used in kinematic and dynamic analysis of the spatio-mechanical systems common in robotics.`Port behaviour' and`behavioural deviation' are then de®ned both intuitively and rigorously. The utility of this framework is demonstrated by a non-trivial example. Concepts of the behavioural approach are used. NomenclatureQ con®guration space X work space A actuator con®guration space U actuator signal input space M measurable variable space E euclidian Space T¤ X tangent bundle of X T ¤ X cotangent bundle of X T r;s X tensor bundle of type … r; s † T¤ X p tangent space of X at p 2 X T ¤ X p cotangent space of X at p 2 X T r;s X p tensor space of type … r; s † at p 2 X C a ne connection on X k C parallel w.r.t. connection C F free¯ow space E free e ort space pr … n † nth prolongatioñ W W port outcome space W extended port outcome space U universe of port outcomes B port behaviour T £W W