On Stability and Passivity of Haptic Devices Characterized by a Series Elastic Actuation and Considerable End-Point Mass Jakob Oblak and Zlatko Matjačić University Rehabilitation Institute, Republic of Slovenia Linhartova 51, 1000 Ljubljana jakob.oblak@ir-rs.si Abstract—Series elastic actuators have considerable potential in rehabilitation robotics. However, the reflected mass of the motor and considerable robot’s end-point mass, both linked by an elastic element, result in a potentially unstable coupled mechanical oscillator. Since rehabilitation devices are in constant contact with patients, safety concerns and consequently the devices’ stability are very important. In this study, the conservative conditions that guarantee the stability of the haptic device (with a considerable end-point mass and driven by a series elastic actuator) were established. We have shown that sufficient damping should be presented in parallel to the spring in order to achieve the passivity of the haptic device. Theoretical results were confirmed in an experimental evaluation on previously developed rehabilitation device. Keywords; stability, passivity, haptics, series elastic actuation, end-point mass, rehabilitation robotics I. INTRODUCTION Introducing an elastic element in series with the motor provides us with many benefits including: more accurate and stable force control, attenuation of both backlash and friction nonlinear effects as well as the actuator’s own impedance, and providing greater shock tolerance (important due to the safety concerns). On the other hand, the principle known as the Series Elastic Actuator (SEA) [1, 2], results in the reduction of force bandwidth. Since relatively slow and gentle movements can be expected during the rehabilitation training, reduced force bandwidth does not present a significant problem. For that reason, the SEA principle has considerable potential in rehabilitation robotics. Using the SEA principle for the actuation of rehabilitation robots with a considerable end-point mass may present a challenge from the point of view of controlling the system. Considerable end-point mass in series with the SEA spring and motor mass, results in a coupled oscillator. One of the most important issues during the design of the rehabilitation device is safety since the rehabilitation robot is in constant contact with a patient. From the point of view of control that means that the device should be stable during its operation. However, the haptic device (the rehabilitation robot) and the patient are a coupled system as they are in direct contact. Even if each component of the coupled system is stable (both the patient and the robot), the coupled system as a whole can exhibit unstable behavior. On the other hand, it can be shown that passive systems coupled with feedback or in a parallel manner again yield a passive system. If we can make the haptic device passive, the haptic interface will also become passive and stable since a patient can be considered as a passive element. If the system is passive, it is also stable, yet the converse statement does not necessary hold. However, the passivity of the system provides us with conservative conditions regarding stability. The aim of this study is to establish through theoretical analysis the conservative conditions that guarantee the passivity of the haptic device driven by SEA actuators and having a considerable end-point mass. The validity of the established conditions is confirmed in an experimental evaluation on the Universal Haptic Device UHD [3-5], whereby a dissipative element, a mechanical damper, is placed in parallel with the SEA spring. II. METHODS A. Linearized model In Fig. 1, an open loop model of the system with considerable end-point mass driven by a SEA based actuation is illustrated. M and m denote the masses, X I and X o the positions, and F I and F O the forces on the motor and the end- point, respectively. The motor is connected to the end-point mass via the mechanical spring K and damper b. The equivalent for the viscous friction in the motor and planetary gearhead is labeled as B. The relation between the motor mass and end-point mass can be given by two differential equations: , (1) Study was financially supported by the Slovenian Research Agency. Figure 1. Linearized model. The motor (reflected mass M) is connected to the end-point (reflected mass m) via a spring (compliance K) and a viscous damper (damping b). 2011 IEEE International Conference on Rehabilitation Robotics Rehab Week Zurich, ETH Zurich Science City, Switzerland, June 29 - July 1, 2011 978-1-4244-9862-8/11/$26.00 ©2011 IEEE