Verification of a linear dynamic model for flexible robotic manipulators

This paper describes a linear state-space model for a flexible single link manipulator arm. The resultant model is compared to an experimental four foot long direct drive manipulator. The method employed to generate the model utilizes a separable formulation of assumed modes to represent the tranverse displacement due to bending. Lagrangian dynamics are applied to determine the kinetic and potential energies for the system. The resultant dynamic equations are then organized into a state space model suitable for use in linear control system design procedures. The performance of the model is considered for different model orders and assumed modes. Several important aspects of candidate mode selection, and results for different model order are discussed. The final section of the paper provides a brief summary and describes ongoing and future work.