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For physical human-robot interaction, safety and dependability are of utmost importance due to the potential risk a relatively powerful robot poses for human beings. From the control standpoint, it is possible to increase this level of safety by guaranteeing that the robot will never exhibit any unstable behaviour. However, stability is not the only concern in the design of a controller for such a robot. During human-robot interaction, the resulting cooperative motion should be truly intuitive and should not restrict in any way the human performance. For this purpose, we have designed a new variable admittance control law that guarantees the stability of the robot during constrained motion and also provides a very intuitive human interaction. The first characteristic is provided by the design of a stability observer while the other is based on a variable admittance control scheme that uses the force derivative as a way to predict human intention. The stability observer is based on a previous stability investigation of cooperative motion which implies the knowledge of the interaction stiffness. A method to accurately estimate this stiffness online using the data coming from the encoder and from a multi-axis force sensor at the end effector is also provided. The stability and intuitivity of the control law were verified in a user study during a cooperative drawing task with a 3 degree-of-freedom (dof) parallel robot.