Controllability and observability of n-link underactuated planar robot with multiple active intermediate links

Abstract

This paper concerns an n-link underactuated revolute planar robot in a vertical plane with two or more actuators and encoders. The linear controllability and observability of such a robot around the upright equilibrium point (UEP), where all the links are in the upright position, are investigated. This paper concerns the problem of the linear controllability and observability of an n-link planar robot around the UEP with only multiple intermediate links being active and the corresponding link angles being measured. When neither the first link nor the last link of the robot is active, and the robot has two or more active intermediate links and the corresponding link angles are measured, this paper proves via a new constructive example that, if there do not exist two active intermediate adjacent links, then there always exists a set of mechanical parameters that renders the robot linearly uncontrollable and unobservable around the UEP. When neither the first link nor the last link of the robot is active, together with an existing result, this paper shows that the robot is linearly controllable and observable, regardless of its mechanical parameters, if and only if there are at least two active adjacent links among the n-2 intermediate links and the corresponding link angles are measured.