New approach for swinging up the Furuta pendulum: Theory and experiments

The problem of swinging up inverted pendulums has often been solved by stabilizing a particular class of homoclinic structures present in the dynamics of a physical pendulum. Here, new arguments are suggested to show how other homoclinic curves can be preplanned for dynamics of the passive-link of the robot. This is done by reparameterizing the motions according to geometrical relations among the generalized coordinates, which are known as virtual holonomic constraints. After that, conditions that guarantee the existence of periodic solutions surrounding the planned homoclinic orbits are derived. The corresponding trajectories, in contrast to homoclinic curves, admit efficient design of feedback control laws ensuring exponential orbital stabilization. The method is illustrated by simulations and supported by experimental studies on the Furuta pendulum. The implementation issues are discussed in detail.