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line for the generated force input (first graph), retrievedvelocity (second graph) and position (third graph). Threedifferent perturbations of this force signal are then simulatedby distorting non-homogeneously in time the original forcesignal (shown in dashed, dotted, and dash-dotted line). Distortingthe signal in such a way simulates situations wherethe force applied by the user may appear with some temporalvariability across the different reproductions. We see that thesystem successfully adapts to these changes by changing themotion behaviors accordingly. For example, the force inputgenerated in dash-dotted line can represent the behavior ofa user first very slow at initiating the task (e.g. the user maynot be ready yet), which is reflected by a quasi constantforce of 4N sensed by the robot (first graph). Then the usersuddenly tries to lift the object, that is, after the simulatedsteady phase, a force signal similar to the demonstration butstretched in time is applied. We see in the second and thirdgraphs that the robot correctly handles this perturbation bystaying still first, and then helping the user lift the beam assoon as this one is ready (null velocity for the first one thirdof the motion). We then see that the the task is collaborativelyachieved.The last graph of Fig. 7 presents reproduction attempts(in black line) where the spatial generalization capabilitiesof the system are highlighted in the case of the robot actingas a leader. By starting from different initial positions, wesee that the system is able to retrieve an appropriate motionto lift the object.V. CONCLUSIONS AND FURTHER WORKIn this paper we proposed an approach to teach a robotcollaborative tasks through a probabilistic model based onHidden Markov Model and Gaussian Mixture Regression.We emphasized the role that teleoperation holds for transmittingboth dynamic and communicative information on thecollaborative task, which classical methods of Programmingby Demonstration have so far overlooked. We then showthrough an experiment consisting of lifting an object collaborativelywith a humanoid robot that the proposed modelcan efficiently encapsulate typical communication patternsbetween different dyads of users acting with stereotypicalcollaboration behaviors. Reproduction attempts in simulationhave finally been presented.We used here only stereotypical behaviors that were predefinedbefore the interaction between the two users to validatethe use of the haptic interface and proposed probabilisticmodel to record and encode physical collaborative skills.Further work will first concentrate on extending the frameworkto more natural interactions where the users are not toldexplicitly to behave with predetermined roles, thus extendingthe complexity of the haptic communication cues to transferto the robot. We are currently working on reproducing thelearned skill on the real robot, which will be used to evaluatethe performance of the proposed controller. 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