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Given the dynamic model of a UAV, a set of virtual geometric constraints is imposed on the system. Once these constraints are reached through a feedback control law, it is possible to show that the system exhibits a limit cycle that is the periodic trajectory to track. The work aims to keep the UAV on such a periodic trajectory. It is possible to stabilize the aerial vehicle on this oscillating motion through a modified LQR controller, designed based on a linear periodic system approximating the system dynamics around the desired orbit.

Proposed solutions: