Geometric control using the state-dependent Riccati equation: application to aerial-acrobatic maneuvers

Acrobatic flip is one of the most challenging representatives of aggressive maneuvers to test the performance of an aerial system’s capability or a controller. A variable-pitch rotor quadcopter generates thrust in both vertical directions for the special design of the rotor’s actuation mechanism. This research proposes two possible solutions for the flip: a regulation solution based on the geometric control approach; and tracking a predefined optimal smooth trajectory covering a turnover. The first solution uses a geometric control approach that is immune to singular points since the rotation matrix is integrated on the manifold on SO(3). The second solution proposes an optimal trajectory generation for flip maneuver using open-loop optimal control, two-point boundary value problem (TPBVP) approach. Since generated open-loop state information is not applicable without a controller, the state-dependent differential Riccati equation (SDDRE) is chosen for trajectory tracking.