tailieunhanh - Advanced Robotics - Control of Interactive Robotic Interfaces Volume 29 Part 10

Tham khảo tài liệu 'advanced robotics - control of interactive robotic interfaces volume 29 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 168 5 Transparency in Port-Hamiltonian Based Telemanipulation with respect k and b it is possible to estimate the elastic and the damping coefficients by means of the least squares method 138 . For a recent efficient contact impedance estimation algorithm see 69 70 . A Behavioral Framework for Evaluating Transparency In Chap. 1 we have seen that the behavioral approach introduced in 330 243 is a very powerful tool for modeling and it has been shown that port-Hamiltonian framework fits very well into this modeling philosophy. Furthermore the behavioral approach has been very useful also from a control point of view as illustrated in Chap. 2 where the control as interconnection paradigm allowed to have many more insights in the energy shaping problem. In Chap. 3 it has been shown that interaction between physical systems takes place through localized power ports through which the systems exchange energy. Thus in order to understand the way in which the human operator perceives the remote environment it is necessary to describe the behavior of the system at these ports. The aim of this section is to exploit the behavioral paradigm to describe the behavior at the interaction power port and hence to develop a general framework for the study of transparency in bilateral telemanipulation systems both linear and nonlinear. Analysis of the Port Behavior For a spatial manipulator with n links interacting with the environment the configuration manifold X can be represented with the Cartesian product of the six-dimensional Lie group SE ffy each Lie group represents the space of homogeneous matrices expressing the spatial configuration of each interacting link. Thus X SE 3 X---X SE X -- n times In case there is only one end effector interacting with the environment X SE 3 . The set of interaction flows for a robotic system interacting with n links is the following vector space F se 3 X X se 3 5-3 - - n times where se 3 is the Lie algebra associated to SE 3 and .