Tham khảo tài liệu 'control problems in robotics and automation - b. siciliano and . valavanis (eds) part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 58 . Salcudean where Yd is a proper stable reference admittance model derived from the system in Fig. Y K is the teleoperation MCS system admittance matrix S K is the teleoperation MCS scattering matrix and PF is a weighting function. If such a problem had a solution the resulting system would perform within a known bound from the reference model and would be stable against any passive operator and environment dynamics. Even though this problem does not account for other plant uncertainties it cannot be solved by current techniques. A controller synthesis approach that optimizes a measure of transparency subject to a distance to passivity as defined in 45 is presented in 4 . The design is accomplished by using semi-infinite optimization see for example 37 to solve an optimization problem that is not necessarily convex. Another approach has been developed using the Youla parameterization of stabilizing controllers and convex optimization 22 . Since the variation in human impedance is relatively small by comparison to the change in environment impedance it was assumed that the hand impedance is known and fixed. High order controllers were designed by solving a convex optimization problem of the form min Wh Yh K - Y fd co such that inf Reyie K ja 0 stabilizing K w where Yh and Ytfd are admittance transfer functions designed and desired respectively and Yte is the MCS block admittance seen from the environment with a known operator impedance Zh- If the hand impedance is equal to that for which the system was designed the constraint on Yte ensures that the environment faces a passive system and hence it is stable for any strictly passive environment. Design examples showing performance tradeoffs or transparency robustness tradeoffs and experimental results have been presented. Nonlinear Transparent Control A nonlinear teleoperation scheme that is transparent at high gain was presented in 44 . The approach uses the nonlinear rigid body dynamics of the .
