Inversion Based End-Effector Trajectory Tracking of Passive-Joint Manipulators

End-effector trajectory tracking of manipulators with passive joints is a challenging task since classical approaches known from fully actuated systems cannot be applied. The paper presents the inversion based control design for manipulators with passive joints, whereby the complexity of the inverse model highly depends on the stability properties of the internal dynamics. For the inverse model the control problem is included here by servo-constraints. For minimum phase systems the internal dynamics can be solved by forward time integration. For non-minimum phase systems a bounded solution is found by solving the internal dynamics as a boundary value problem. The example of a three-arm manipulator with one passive joint is used as application, whereby minimum phase and non-minimum phase designs are considered. The obtained inverse models are used in experiments to control the real system.