Scaling laws for nonlinear controllers of dynamically equivalent rigid-link manipulators

Dimensional analysis is used to determine the nondimensional groups which define the dynamic equivalence conditions for rigid-link manipulators. Scaling laws for general actuators and nonlinear controllers are also presented. As an example, simulation results are presented which illustrate how a large two-link elbow manipulator operating on the Moon can be designed by constructing a dynamically equivalent prototype in Earth gravity, and also, how a sliding mode controller designed for the prototype Earth robot can be scaled for implementation on the Moon-based manipulator