Orbital stabilization of point-to-point maneuvers in underactuated mechanical systems

The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered this paper. main motivation comes from the problem ensuring convergence to so-called point-to-point maneuver underactuated mechanical system. Namely, smooth curve its state--control space, which consistent with dynamics and connects two (linearly) stabilizable equilibrium points. proposed method uses particular parameterization, together state projection onto as combine linearization techniques for purpose: Jacobian at equilibria on boundaries transverse along orbit. This allows computation stabilizing gains offline by solving semidefinite programming problem. resulting controller, simultaneously stabilizes both final equilibrium, time-invariant, locally Lipschitz continuous, requires no switching, has familiar feedforward plus feedback--like structure. also complemented synchronization function--based arguments planning such maneuvers systems one degree underactuation. Numerical simulations non-prehensile manipulation ball rolling between points upon "butterfly" robot demonstrates efficacy synthesis.