Modeling and observer-based augmented adaptive control of flexible-joint free-floating space manipulators

• The Lagrange dynamic model of a flexible-joint space manipulator was derived.
• To use singular perturbation approach, a flexibility compensator was proposed.
• A singularly perturbed model was formulated.
• An augmented composite controller with good tracking performance was proposed.
• The controller need not measure the derivatives of the generalized coordinate.

The velocity observer based adaptive control of flexible-joint free-floating space manipulators with parametric uncertainties and modeling errors is addressed. First, the dynamical model of a free-floating space manipulator with two flexible revolute joints is established by the Lagrange equations. Second, a flexibility compensator was proposed, which could make the equivalent joint stiffness large enough to use traditional singular perturbation approach. Based on singular perturbation theory, the system is decomposed into two subsystems, a slow subsystem and a flexible-joint fast subsystem. Then a composite controller which consisted of a slow control component and a flexible-joint fast control component was proposed. A sliding velocity observer based augmented adaptive control algorithm was applied to control the slow subsystem. The flexible-joint fast controller was designed with the estimated velocity by linear observer to stabilize the fast subsystem around the equilibrium trajectory set up by the slow subsystem under the effect of the slow controller. Finally, numerical simulations were carried out, which showed that elastic joint vibrations had been stabilized effectively with good tracking performance.