Comprehensive modeling for simultaneous position and force control of deformable manipulators

The authors present comprehensive dynamic modeling of a deformable manipulator by using the Hamiltonian principle. The model is formulated by considering the deformable arm as a Timoshenko beam model. Hence, the shear, bending, and rotational inertia effect of the manipulator are all taken into account in the dynamic formulation. To obtain a comprehensive dynamic model, the gravitational effect, which is missing in most deformable manipulator dynamic models, is also included in the formulation. Then, an efficient motion and force controller design method utilizing root contour analysis is proposed. With the proposed method the multi-controller gains of the position/force controller for the deformable manipulator can be chosen analytically, as opposed to the method of trial and error used conventionally for selecting manipulator controller gains. The tuning process of these controllers´ gains proves the simplicity of gain selection. The motion/force simulation results verify the effectiveness of the controllers. The simulation results also show that the derived control scheme, which is based on a linear control system analysis, can drive the highly nonlinear deformable arm to achieve the desired position and force satisfactorily