Force control of a two-linke planar manipulator with one flexible link

Force control of a two-link planar manipulator with one flexible link is considered in this study. The equations of motion are derived using the extended Hamilton's principle with only structural flexibility effects included in the dynamic model. The linear quadratic Gaussian/loop transfer recovery (LQG/LTR) design methodology is exploited to design a robust feedback control system that can handle modelling errors and sensor noise, and operate on Cartesian space trajectory errors. The LQG/LTR compensator together with a feedforward loop is used to simultaneously control the force exerted by the flexible manipulator normal to the environment and the position of the end-point in a direction tangent to the environment. Simulated results are presented for a numerical example.