Passivity-based 3D Dynamic Visual Feedback Control with a Fixed Camera
Hiroyuki KAWAI, Toshiyuki MURAO, Takehito AZUMA, Masayuki FUJITA
In this paper, we investigate the control and the estimation of dynamic visual feedback systems with a fixed camera. Firstly the fundamental representation of the visual feedback system with four coordinate frames is established by using the homogeneous representation and adjoint transformation. Secondly we consider the observer which is reproduced from the fundamental representation of relative rigid body motion just as Luenberger observer for linear systems. Then, the relationship between the estimation error in the 3D workspace and in the image plane is established. Next, we derive the passivity of the dynamic visual feedback system by combining the passivity of both the visual feedback system and the manipulator dynamics. The stability via Lyapunov method for the full 3D dynamic visual feedback system is discussed based on the passivity. The L2-gain performance analysis for the disturbance attenuation problem is considered via the dissipative systems theory. Finally simulation results are shown to verify the stability and L2-gain performance of the dynamic visual feedback system.