Abstract This paper proposes an end-to-end learning from demonstration framework for teaching force-based manipulation tasks to robots. The strengths of this work are manyfold. First, we deal with the problem of learning through force perceptions exclusively. Second, we propose to exploit haptic feedback both as a means for improving teacher demonstrations and as a human-robot interaction tool, establishing a bidirectional communication channel between the teacher and the robot, in contrast to the works using kinesthetic teaching. Third, we address the well-known what to imitate? problem from a different point of view, based on the mutual information between perceptions and actions. Lastly, the teacher's demonstrations are encoded using a Hidden Markov Model, and the robot execution phase is developed by implementing a modified version of Gaussian Mixture Regression that uses implicit temporal information from the probabilistic model, needed when tackling tasks with ambiguous perceptions. Experimental results show that the robot is able to learn and reproduce two different manipulation tasks, with a performance comparable to the teacher's one.  Keywords Programming by demonstration One of the main challenges in Robotics is to develop robots that can interact with humans in a natural way, sharing the same dynamic and unstructured environments. Learning from demonstration (LfD) 1 is a type of human-robot interaction (HRI) whose purpose is to transfer knowledge or skills to the robot. Here, a human user carries out examples of a given task while a robot observes these executions and extracts relevant information for learning, representing and reproducing the taught task under unknown conditions [1, 2] . HRI requires suitable communication channels for conveying information between a human and a robot [3, 4] . In LfD, most existing works rely on vision or on motion sensors as input channels to the robotic system. As for vision-based input, positional information about the objects in the scene is captured with a set of cameras, which are also used to locate and follow markers placed on the teacher's body [5, 6] . Most state-of-the-art approaches consider vision as the best choice for extracting information from teacher examples, as human beings do in everyday tasks [7, 8] . However, vision-based systems must deal with the typical problems such as occlusion, appearance changes and complex human-robot kinematics mapping, which can be partly solved using motion sensors instead. Such type of sensors allows to track the teacher's motion more precisely and to establish a simpler mapping, which make them appropriate to teach tasks to humanoid robots [5, [9] [10] [11] . In contrast to these works, we are concerned with learning from force-based perceptions. Force conveys relevant information for several tasks where vision or motion sensors can not provide sufficient data to learn a motion or a set of primitives. In many daily tasks, people use 1 Also known as programming by demonstration or imitation learning. 123
An interesting approach to teaching force-based manipulation is presented in REF .
A robot learning from demonstration framework to perform force-based manipulation tasks
Intelligent Service Robotics
Computer Science