tailieunhanh - Advanced Robotics - Control of Interactive Robotic Interfaces Volume 29 Part 7

Tham khảo tài liệu 'advanced robotics - control of interactive robotic interfaces volume 29 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 106 3 A Port-Hamiltonian Approach to the Control of Interaction interacts with the rest of the world and if s s is its corresponding scattering representation we have that a system is passive if and only if there exists a finite positive constant p such that I i I p 3-29 JO - JO - Loosely speaking a system is passive if and only if the outgoing energy is bounded by the incoming energy namely if and only if there is no internal production of energy. One could think to deal with delayed virtual environment by simply discretizing a port-Hamiltonian system with power variables as input output and then to treat the delay in the same way as in telemanipulation see next chapter for many more details . In Fig. we can see how the problem can be tackled in telemanipulation. The power variables of the port of the port-Hamiltonian system are coded into scattering variables and then sent through the communication channel. The port-Hamiltonian system is passive and it has a passive behavior at the power port. By using the scattering representation of the power port and by transmitting scattering waves this passive behavior is simply conserved during the communication independently of any delay. Unfortunately when dealing with delayed virtual environments the power variables at the power port are not consistent in the sense that they refer to different instants of time and this causes as shown in Eq. a non passive behavior of the system at the port. If we used the scheme in Fig. the scattering waves would simply replicate the non passive behavior of the systems leaving the problem unsolved. The delay has to be treated therefore in a different way in case of delayed virtual environment. The reason of this discrepancy is that while in telemanipulation the problem concerning delay is in the transmission of power variables and therefore something external to the system in case of delayed port-Hamiltonian systems the delay is intrinsic into the dynamics of the system .