Balance Control of a 4-DOF Underactuated Gymnastic Robot Based on LQR

The 4-DOF underactuated gymnastic robot is a complex control system which is multivariable, nonlinear and strong coupling. In this paper, according to the system of this kind of robot, the dynamic equation of rigid body is established firstly by using Lagrange method. Secondly, a linearization method for nonlinear robot mathematical model in the vicinity of vertical inverted equilibrium point is discussed. Then, a Linear Quadratic Regulator (LQR) is used to design the optimal controller of the handstand balance. Finally, some simulation results show the effectiveness of the proposed method.

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