Perception-centric Force Scaling function for Stable Bilateral Interaction D. Botturi, S. Galvan, M. Vicentini and C. Secchi Abstract— In this paper a force scaling function for an haptic system is the output of the psychophysics experiments that have been carried out with the aim of better understanding the hu- man perception capabilities. The experimental work consists in measuring the differential thresholds of force perception applied to the hand-arm system. These findings support our claim that the human perception of forces and torques depends on force intensity and works differently along different directions, thus suggesting that perception can be enhanced by suitable scaling. We have identified a scaling function for each direction and we have shown that this variable scalings can be safely embedded in a passivity based teleoperation system in order to improve the feeling perceived by the user during the interaction with remote environments. I. INTRODUCTION The force feedback provided by a haptic device is usually defined as the sensation of weight or resistance felt by a human operator [1]. It requires a device that produces a force to the operator such as the one of the interaction with a real object, allowing a person to feel the weight of virtual objects, or the resistance to motion they create. Several works are relevant to the quantitative measures of hu- man biomechanical, sensorimotor, and cognitive abilities that affect the design of force-reflecting haptic interfaces. One of the most common measures is related to the Just Noticeable Difference (JND), which is the minimal difference between two stimuli (F vs. F +ΔI ) that leads to a change in the human perceptual experience and is detectable by a human being. The JND percentage value for pinching motions between finger and thumb was found to be around 7% of the reference force [2]; in a force matching experiment about the elbow flexor muscles, a JND ranging between 5% and 9% was observed [3]. The JND was found to be relatively constant over a range of different base force values between 2.5 and 10 N, and essentially independent from reference force and displacement [4]. In previous work, such as [5], [6], are presented results in human force perception for the design of haptic device but they are focused on finger capabilities or the described ex- periments do not primarily investigate haptic environments. The authors, in previous work [7], proposed a perception This work was partially founded by the AccuRobAs project under EU’s 6th Framework Programme (contract IST-045201) D. Botturi, S. Galvan and M. Vicentini are with Computer Science Dept, University of Verona, Strada le Grazie 15, 37134 Verona, Italy {botturi,galvan,vicentini} @metropolis.sci.univr.it C. Secchi is with DISMI, University of Modena and Reggio Emilia Viale Allegri 13, 42100 Reggio Emilia, Italy secchi.cristian@unimore.it experiment aimed to explore differences in ability of a person to discriminate a wide range of force intensities applied to a hand-grip along the axis of a reference frame positioned at the hand. In particular, differences in terms of force perception relatively to the stimulus intensity and among directions and orientations were observed and identified. This finding could let distinguish the most sensible directions for the arm, allowing to determine a suitable scaling matrix for force-feedback in haptic environments. In this paper we Fig. 1. The experimental setup with the FRHC haptic device. The translational and rotational axes are depicted accompanied by their names. describe how it is possible to use this variable scaling matrix to improve performance in bilateral teleoperation. This is a new approach to force augmentation in teleoperation, since the acquainted concept of scaling in this field concerns mainly constant amplification. Furthermore, the use of ad hoc scaling functions for each axis direction is also a novelty and its motivation comes from the human perception capabilities. A main theoretical problem arises at this point. In fact, it is not clear whether using a variable scaling factor in the interconnection between master and slave sides leaves the overall telemanipulation system stable. Passivity theory has been widely used for the control of bilateral telemanipulators since it allows to guarantee a stable behavior of the system thanks to impedance control techniques [8]. Port-Hamiltonian systems can be used for the design of passivity based bilateral teleoperators. They are passive systems and they allow to model all physical systems and, furthermore, to represent very clearly the energetic structures and the power flows [9]. Thus, we will address the problem of the variable scaling for the class of port- Hamiltonian based teleoperators in order to clearly model the energetic flows within the teleoperator and to represent a wide class of real systems.