Nonlinear Position-Dependent Circuits: A Language for Describing Motions of Nonlinear Mechanical Systems

摘要: The analogy between the dynamics of a linear lumped-parameter electric circuit consisting resistor-inductor-capacitor (RLC) in series or parallel and that one degree-of-freedom mechanical system dashpotmass-spring is well known has been pointed out widely literature. This was extensively made use robotics by Mason (1981) Hogan (1985), who introduced new concepts “compliance control” “impedance respectively control physical interactions manipulator end-effector with objects robot task environments. However, this impedance compliance concept not yet generalized to cope nonlinearities objective system. On other side, generalization circuits towards nonlinear attempted Brayton Moser (1964), called “mixed potential function” demonstrated procedure construct Lyapunov-type functions from function prove stability under certain conditions. approach successive ones such as EL(Euler-Lagrange) formalism an Meisel (1966) are limited treatments only “electric circuits” do take into consideration large class related “mechanical” motion. In words, express motions systems, velocity vectors but also position key variables on which kinetic energy itself depends. That is, q always explicitly paired q, hence some elementary blocks must be considered position-dependent.