On controllability and observability of an n-link planar robot with a single actuator and a single encoder having different configurations

This paper concerns an n-link revolute planar robot with all the links moving in the same vertical plane and having a single actuator. An encoder attached to the actuator measures the joint angle where it is located. The linear controllability and observability of the robot around the upright equilibrium point (UEP), where all the links are in the upright position, are investigated. First, we present a simple test of the linear controllability and observability. Second, along with new properties of the mechanical parameters in the motion equation of the robot, we prove that the robot is linearly controllable and observable at the UEP, when the first or last joint is active (actuated) and the corresponding joint angle is measured, whatever the values of its mechanical parameters. The assumption of each link consisting of a massless rod with a point mass at its end in the previous studies is not needed in this paper. Moreover, the relationship between the controllability and strong structural controllability at the UEP of the robot with the last active joint is clarified.