Optimal Control for Acrobot with Two-link Manipulators

Abstract

Abstract This paper presents a unified treatment of the optimal control of under-actuated two-link manipulators. Firstly, a nonlinear invertible transfer is introduced to simplify design of controller, then several optimal control laws are established by maximum principle. Controller for swing-up area is based on performance index, while controller for attractive area is based on LQR (linear quadric regulator). It is proved that optimal control is not singular, invariant sets are obtained by theoretical analysis. The strategy for Acrobat is to use optimal control law to pump manipulators into linearizable area, then switch control law to LQR, which drives system to up-straight position. Local and global stability were analyzed in detail under control strategy using LaSalle’s invariance principle and WCLF (non-smooth control Lyapunov function). Simulation and comparison with previous results show that the proposed approach here is valid and of advantages.