Visual servoing of an under-actuated dynamic rigid-body system: an image based approach

Abstract—A new image-based control strategy for visual ser-voing of a class of under-actuated rigid body systems is presented. The proposed control design applies to “eye-in-hand ” systems where the camera is fixed to a rigid body with actuated dynamics. The control design is motivated by a theoretical analysis of the dynamic equations of motion of a rigid body and exploits passivity-like properties of these dynamics to derive a Lyapunov control algorithm using robust backstepping techniques. The proposed control is novel in considering the full dynamic system incorporating all degrees of freedom (albeit for a restricted class of dynamics) and in not requiring measurement of the relative depths of the observed image points. A motivating application is the stabilization of a scale model autonomous helicopter over a marked landing pad. Index Terms—Image-based visual servo (IBVS), nonlinear con-trol, rigid-body dynamics, under-actuated systems. I