Stability case study of the ACROBOTER underactuated service robot

The dynamics of classical robotic systems are usually described by ordinary differential equations via selecting a minimum set of independent generalized coordinates. However, different parameterizations and the use of a nonminimum set of (dependent) generalized coordinates can be advantageous in such cases when the modeled device contains closed kinematic loops and/or it has a complex structure. On one hand, the use of dependent coordinates, like natural coordinates, leads to a different mathematical representation where the equations of motion are given in the form of differential algebraic equations. On the other hand, the control design of underactuated robots usually relies on partial feedback linearization based techniques which are exclusively developed for systems modeled by independent coordinates. In this paper, we propose a different control algorithm formulated by using dependent coordinates. The applied computed torque controller is realized via introducing actuator constraints that complement the kinematic constraints which are used to describe the dynamics of the investigated service robotic system in relatively simple and compact form. The proposed controller is applied to the computed torque control of the planar model of the ACROBOTER service robot. The stability analysis of the digitally controlled underactuated service robot is provided as a real parameter case study for selecting the optimal control gains.