A Lagrange‐Euler‐assumed modes approach to modeling flexible robotic manipulators

Abstract

Abstract This paper presents a general Lagrange‐Euler‐assumed modes dynamics formulation for lightweight flexible manipulators. The proposed explicit form formulation, not yet available in the existing literature, can be viewed as an extended version of the Lagrange‐Euler formulation for rigid manipulators. The deformation of a link from its rigid body position is modeled by a homogeneous 4×4 transformation matrix composed of summations of assumed link modes. The number of modes can be arbitrarily selected. The joint flexibility is modeled by a linear torsionai spring with known characteristics. The methodology presented can be easily used to derive the full nonlinear dynamic equations of flexible manipulators by computing only the dynamic coefficients using computer algebra such as MACSYMA. The resulting nonlinear dynamic equations are in a closed form and are especially suitable for advanced nonlinear control strategy synthesis. Taken as an illustrative example, a two‐link flexible manipulator is studied to demonstrate the effectiveness of the formulation.