New results for controllability and observability of an n-link underactuated planar robot with different actuator-sensor configurations

摘要

This paper concerns an n-link underactuated revolute planar robot with all the links moving in the same vertical plane and having two or more actuators and encoders. An encoder attached to each of the actuator measures the link angle. The linear controllability and observability of the robot around the upright equilibrium point, where all the links are in the upright position, are investigated. It is shown in an existing result that the robot with an actuator and an encoder is linearly controllable and observable regardless of the mechanical parameters if the first link or the last link of the robot is active (actuated) and the corresponding link angle is measured. When neither the first link nor the last link of the robot is active, this paper proves that the robot is linearly controllable and observable regardless of the mechanical parameters if there are two active adjacent links of (n - 2) intermediate links and the corresponding link angles are measured. This paper provides further insights into the linear controllability and observability of an n-link underactuated planar robot with different actuator-sensor configurations.