Orbital Stabilization of Hybrid Mechanical Systems—A Port‐Hamiltonian Approach

ABSTRACT In this article, we address the problem of stabilizing hybrid periodic orbits in mechanical systems characterized by both continuous and discrete dynamics. We introduce a total energy shaping controller, formulated in the port‐Hamiltonian framework, that guarantees asymptotic orbital stability of a prescribed hybrid periodic orbit. The approach ensures asymptotic stability by systematically regulating the system's energy, leveraging Lyapunov‐based analysis to guarantee boundedness across both flow and jump phases. The effectiveness of the proposed control law is demonstrated through numerical simulations, including its application to a 3‐DOF manipulator tasked with pushing an object.