Dual pendula swing up and stabilization via smooth nonlinear trajectory planning and feedback control

The dual pendula swing up problem is considered and solved using Smooth Nonlinear Trajectory Planning (SNTP) and linear quadratic Gaussian (LQG) feedback control. A physical dual pendula system is designed and built to demonstrate the viability of the dual pendula swing up via SNTP and LQG control. The dual pendula swing up is successfully demonstrated on the physical dual pendula system. SNTP determines an appropriate forcing of the cart, which the dual pendula are mounted to, such that the dual pendula swing up to the inverted equilibrium; that is, SNTP determines an appropriate control trajectory that results in a desired state trajectory. The LQG control is implemented in two separate controllers: a state trajectory tracking controller to reject disturbances in following the planned optimal swing up state trajectory and a stabilizing controller to balance the inverted dual pendula.