Robust tracking control of an Euler-Lagrange system subject to uncertain friction and impact

A robust tracking control problem is considered for an unknown Euler-Lagrange system to track a desired time-varying trajectory. Unknown dynamics including friction effects and impact forces from the environment are considered in the paper. It is challenging to model these two types of uncertain forces for Euler-Lagrange Systems such as robot manipulators and motors. A robust controller with adaptive control gain is designed to compensate the uncertain friction and impact force and control the system to track a desired trajectory. By using the adaptive control gain, the designed control law avoids the dependence of the control gains on the upper bounds of the uncertainties. Based on Lyapunov analysis, it is shown that the designed control law guarantees semi-globally asymptotic tracking result. Numerical simulation results are provided to illustrate the effectiveness of the designed controller.