Stability considerations for a two-link force-controlled flexible manipulator

The effect of link flexibility on the dynamic stability of a two-link force-controlled robot manipulator is investigated. Assuming that the contact point is locked, the nonlinear open-loop equations for the compliant motion are derived. By using the hybrid force-position control law, the closed-loop dynamic equations are explicitly derived and linearized about some equilibrium configuration. Stability analyses are carried out by computing the eigenvalues of the linearized system equations. Results are verified by numerical simulations using the complete nonlinear dynamic equations. The effect of the wrist force sensor stiffness on the dynamic stability is also investigated. Results show that the link flexibility is an important source of dynamic instability in the motion of force-controlled manipulators. Moreover, the system stability is dominated by the effect of the distributed flexibility of the first link