Building a modular robot control system using passivity and scattering theory

This paper analyses the problems and presents solutions for building a modular robot control system. The approach requires modeling the entire robot system using multi-dimensional passive networks, breaking the system into subnetwork "modules" and then discretizing the subnetworks, or n-ports, in a passivity preserving fashion. The main difficulty is the existence of "algebraic loops" in the discretized system. This problem is overcome by the use of scattering theory, whereby the inputs and outputs of the n-ports are mapped into wave variables before being discretized. By first segmenting the n-ports into nonlinear memoryless subnetworks and linear dynamic subnetworks and then discretizing using passivity preserving techniques such as Tustin's method, a complete modular robot control solution is obtained.