Optimal Design of Haptic Interfaces

Haptic interfaces are computer-controlled motorized devices that physically interact with human operators to render presence of computationally mediated environments. Ideal haptic devices are desired to withstand human applied forces with very high stiffness and be capable of displaying a full range of impedances down to the minimum value humans can perceive. The performance of a haptic interface under closed loop control is measured by the transparency of the display, that is, by quantifying the correspondence between the desired and actually rendered impedance values. During haptic rendering, the haptic interface is coupled to the control system and its existence results in parasitic effects on the displayed impedances, deteriorating the perfect transparency. Therefore, independent of the control algorithm, both the kinematic and dynamic performance of the haptic device have an impact on the overall performance of the haptic display. Robotic manipulators with parallel kinematic chains are popular among haptic interfaces due to their inherent advantages in satisfying requirements of haptic applications with respect to their serial counterparts. Parallel mechanisms offer compact designs with high stiffness and have low effective inertia since their actuators can be grounded in many cases. In terms of dynamic performance, high position and force bandwidths are achievable with parallel mechanisms thanks to their light, but stiff structure. Besides, parallel mechanisms do not superimpose position errors at joints; hence, can achieve high precision. Despite these favorable characteristics of parallel mechanisms, optimal design of such mechanisms with closed kinematic chains is significantly more challenging. Parallel mechanisms have smaller workspace with possible singularities within the workspace and their kinematic, dynamic, and singularity analysis are considerably harder than that of serial manipulators. Due to the additional complexities involved, the dimensional synthesis of parallel mechanisms is still an active area of research. Optimum design of parallel mechanisms, even for a single objective function, is challenging due to the nonlinear, large scale nature of such mechanisms (Lee & Kim, 2006) and nonconvex properties of performance indices with respect to the design variables (Qi & Womersley, 1996). Many different optimization approaches applicable to nonlinear, non-convex optimization problems such as genetic algorithms (Lee et al., 2001; Lee & Kim, 2006; Stuckman & Easom, 1992; Zheng & Lewis, 1994), simulated annealing (Risoli et al., 1999), Bayesian techniques (Stuckman & Easom, 1992; Stuckman et al., 1991), Monte-Carlo simulations (Stuckman & Easom, 1992; Zheng & Lewis, 1994), controlled randomized searches (Lou et al., 2008), performance charts (Liu & Wang, 2007), workspace atlases (Liu et al., 2006), and branch and 12