*Article* **Haptic Devices Based on Real-Time Dynamic Models of Multibody Systems**

**Nicolas Docquier \*, Sébastien Timmermans and Paul Fisette**

Mechatronic, Electrical Energy, and Dynamic Systems (MEED), Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium; sebastien.timmermans@uclouvain.be (S.T.); paul.fisette@uclouvain.be (P.F.)

**\*** Correspondence: nicolas.docquier@uclouvain.be

**Abstract:** Multibody modeling of mechanical systems can be applied to various applications. Humanin-the-loop interfaces represent a growing research field, for which increasingly more devices include a dynamic multibody model to emulate the system physics in real-time. In this scope, reliable and highly dynamic sensors, to both validate those models and to measure in real-time the physical system behavior, have become crucial. In this paper, a multibody modeling approach in relative coordinates is proposed, based on symbolic equations of the physical system. The model is running in a ROS environment, which interacts with sensors and actuators. Two real-time applications with haptic feedback are presented: a piano key and a car simulator. In the present work, several sensors are used to characterize and validate the multibody model, but also to measure the system kinematics and dynamics within the human-in-the-loop process, and to ultimately validate the haptic device behavior. Experimental results for both developed devices confirm the interest of an embedded multibody model to enhance the haptic feedback performances. Besides, model parameters variations during the experiments illustrate the infinite possibilities that such model-based configurable haptic devices can offer.

**Keywords:** multibody dynamics; symbolic generation; real-time computation; human-in-the-loop; haptic devices
