Outlines

Robots have become increasingly popular due to their ability to perform complex tasks and operate in unknown and hazardous environments. Many robotic systems are underactuated i.e., they have fewer control inputs than their degrees-of-freedom. Common examples of underactuated robotic systems are legged robots such as bipeds, flying robots such as quadrotors, and swimming robots. Due to limited control authority, underactuated systems are prone to instability and are difficult to control. This work demonstrates the feasibility of impulsive inputs to address the challenging control problem of orbital stabilization. A repetitive motion is described by closed orbits and therefore, orbital stabilization, i.e., stabilization of closed orbits is important for many applications such as bipedal walking and steady swimming. We first present the problem of energy-based orbital stabilization using continuous inputs and intermittent impulsive braking. The orbit is a manifold where the active generalized coordinates are fixed, and the total mechanical energy of the system is equal to some desired value. The problem of orbital stabilization using virtual holonomic constraints (VHC) is presented next. VHCs are enforced using a continuous controller which guarantees existence of closed orbits. A Poincaré section is constructed on the desired orbit and the orbit is stabilized using impulsive inputs which are applied intermittently when the system trajectory crosses the Poincaré section. The effectiveness of the two orbital stabilization control methods is demonstrated using simulations and hardware experiment.

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