Manipulator joint independent control and its structural stability

In spite of non-linearities and couplings existing in robot dynamics, local linear feedback schemes such as PD laws have been successfully used in motion control of non-direct drive robot manipulators with high gear ratios. This paper is motivated by finding out trajectory tracking stability conditions for this sort of joint independent control systems in terms of robot dynamic parameters such as motor shift inertia, arm inertia and gear ratios of the transmission. It shows that when the gear ratios of a robot manipulator with n joints are considerably high the overall non-linear system can be approximated by n decoupled subsystems dominated by servo motor dynamics and therefore be controlled by a independent local linear feedback controllers. The paper also shows the local stability condition and the boundedness of the trajectory tracking error if a system is stable