Stability Boundary and Transparency for Haptic Rendering

Over the past years haptic interfaces have been successfully integrated into a wide range of fields such as engineering (Borro et al., 2004) or surgery (Basdogan et al., 2004). Haptic devices allow users to interact with a certain environment, either remote or virtual, by the sense of touch. In these applications—unlike in conventional robotic systems—the user shares workspace with the device. Therefore, an unstable behaviour can damage the device, or even worse, harm the operator. Thus, stability must be guaranteed to ensure user safety and achieve high haptic performance. Unfortunately, preserving haptic stability usually implies reducing the range of dynamic impedances achievable by the system. Hence, rigid virtual objects cannot be perceived as stiff as real ones, and the overall haptic performance and transparency perception are considerably degraded. Developing stable controllers able to exhibit a wide dynamic range of impedances is a persistent challenge in the field of haptics. This chapter describes main research carried out by the authors on stability issues for haptic rendering, as well as on the development of transparent haptic controllers. In a haptic system, the stability boundary for haptic rendering depends on many factors, such as inherent interface dynamics, motor saturation, sensor resolution or time delay. Section 2 introduces the state-of-the-art on stability studies showing the influence of many of these phenomena. Beyond related work, Section 3 analyses the influence of viscous damping and delay on the stability boundary for haptic rendering. Although the shape of the stability boundaries found is quite complex, a linear condition which summarises the relation between virtual stiffness, viscous damping and delay is proposed. Section 4 analyses the influence of the first vibration mode of the system on the stability boundary. The majority of haptic models used to analyse stability do not consider the existence of internal vibration modes. However, it will be shown that for certain interfaces vibration modes must be taken into account to correctly obtain the range of impedances achievable by the system. 5