On the PD+Luenberger controller/observer for the trajectory tracking of Robot Manipulators

This paper addresses the problem of the trajectory tracking of a Proportional Derivative controller with dynamics compensation where the joint velocity is not available to be measured. It is well known that when the robot joint position is given by an incremental optical encoder, the speed can be approximated by processing the joint positions. In the field of trajectory tracking for robot manipulators, one of the main problems is related to the design of control strategies where not all the state variables are available (in our particular case, the joint velocity). The reason is because the construction of the energy functions is based on fulfilling the Lyapunov main theorem, and for the robot manipulators case it depends on the availability of the velocity measurement. The goal of this paper is to design a controller that guarantees stability in the Lyapunov sense when the velocity is not available to be measured. To achieve this, we propose a controller scheme based on a PD+ compensator and a Luenberger-type observer. In order to demonstrate the effectiveness of the controller/observer presented here, a numerical simulation with trajectory tracking for a benchmark of 2-DoF linked-mechanical system is presented.