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Passivity of a Two-Link Planar Flexible Manipulator Using an Exact Model Derived from a Recursive Dynamic Formulation

Abstract This paper provides a proof of passivity of a two-link planar flexible manipulator whose dynamics is described by a set of nonlinear ordinary and partial differential equations. We first propose a recursive dynamic formulation for multi-link planar flexible manipulators so that we have an exact model having simple structure of equation, which can simplify the proof of passivity in comparison with an exact model having complex structure derived by such as Hamilton's principle. We then perform passivity analysis of a two-link planar flexible manipulator by differentiating an energy-based storage function along with the exact model under the assumption that no external force or moment acts on the end-effector of the manipulator. The analysis results in that the flexible manipulator defines a passive map from the joint torques to the joint angles with respect to the energy-based storage function.