Barrier Lyapunov Function Based Controller Design for Euler-Lagrange Systems with Reduced Control Effort

Abstract

In this paper, a novel nonlinear controller is designed for Euler- Lagrange (EL) systems while satisfying user-defined safety-constraints in position variables. The EL systems, which are highly popular for modeling a variety of non-linear mechanical plants like aircraft, spacecraft, quad-rotors, robotic manipulators, etc., critically demand safety-constraint satisfaction during trajectory tracking applications. Barrier Lyapunov Function (BLF) is widely used for systematically designing the controller to prevent safety-constraint violation during trajectory tracking. By proving the boundedness of BLF in a closed loop, safety-constraint satisfaction is analytically guaranteed. The fundamental principle of BLF is that if the states are reaching close to the boundary of a safe region, the high control input is applied to the system to push states far inside the boundary. In practical scenarios, such a high control effort requirement may lead to the critical problem of actuator saturation. This work alleviates the issue of high control effort requirements in the BLF framework. The proposed BLF-based controller is capable of guaranteeing safety-constraint satisfaction with less control effort, making the design practically viable. Simulation results validate significant improvement in terms of reduction in control input magnitude of the proposed algorithm in contrast to conventional BLF-based control algorithms.