Another language for describing motions of mechatronics systems: a nonlinear position-dependent circuit theory

Dynamics and control of nonlinear mechanical systems and advanced mechatronic systems can be investigated more vividly and efficiently by using corresponding nonlinear position-dependent circuits that describe Lagrange´s equations of motions and interactions with objects or/and task environments. Such expressions of Lagrange´s equations via nonlinear circuits are indebted to lumped-parameter discretization of mechanical systems as a set of rigid bodies through equations of motion due to Newton´s second law. This observation is quite analogous to validity of electric circuits that can be derived as lumped parameter versions of Maxwell´s equations of electromagnetic waves. Couplings of nonlinear mechanical circuits with electrical circuits through actuator dynamics are also discussed. In such electromechanical circuits the passivity should be a generalization of impedance concept in order to cope with general nonlinear position-dependent circuits and play a crucial role in their related motion control problems. In particular, it is shown that the passivity as an input-output property gives rise to a necessary and sufficient characterization of H_∞-tuning for disturbance attenuation of robotic systems, which can give another system theoretic interpretation of the energy conservation law.