In this paper, the motion planning problem is studied for nonlinear differentially flat systems using B-splines parametrization of the flat output history. In order to satisfy the constraints continuously in time, the motion planning problem is transformed into a B-splines positivity problem. The latter problem is formulated as a convex semidefinite programming problem by means of a non-negative piecewise polynomial functions description based on sum of squares decomposition. The contribution of the paper is thus a one-step design procedure for motion planning that satisfies constraints continuously in time where usual Bspline and collocation techniques need post-analysis. Finally, an example of flexible link manipulator motion is presented to illustrate the overall approach.
In this paper, we present a feed-forward control approach for complex trajectory tracking by a tilting-rotor quadcopter during autonomous flight. Tilting-rotor quadcopter is a more agile version of conventional quadcopter as the propeller motors are actuated to tilt about the quadcopter arm. The tilt-rotor quad-copter is capable of following complex trajectories with ease. In this paper, we employ differential flatness based feed-forward position control by utilizing a combination of propeller rotational speeds along with rotor tilts. The rotational motion of propellers work simultaneously in sync with propeller tilts to control the position and orientation of the UAV during autonomous flight. The results for tracking complex trajectories have been presented by performing numerical simulations and a comparison is shown with respect to conventional quadcopter for similar flight conditions. It has been found that the tilt-rotor quadcopter is more efficient than the conventional quadcopter during complex trajectory following maneuvers.
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