Browsing by Subject "Convexification"
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Item Lossless convexification of quadrotor motion planning with experiments(2014-08) Pehlivantürk, Can; Longoria, Raul G.; Açıkmeşe, BehçetThis thesis describes a motion planning method that is designed to guide an autonomous quadrotor. The proposed method is based on a novel lossless convexication, which was first introduced in (12), that allows convex representations of many non-convex control constraints, such as that of the quadrotors. The second contribution of this thesis is to include two separate methods to generate path constraints that capture non-convex position constraints. Using the convexied optimal trajectory generation problem with physical and path constraints, an algorithm is developed that generates fuel optimal trajectories given the initial state and desired final state. As a proof of concept, a quadrotor testbed is developed that utilize a state-of-the-art motion tracking system. The quadrotor is commanded via a ground station where the convexified optimal trajectory generation algorithm is successfully implemented together with a trajectory tracking feedback controller.Item Verification of successive convexification algorithm(2016-05) Berning, Andrew Walter, Jr.; Akella, Maruthi Ram, 1972-; Acikmese, BehcetIn this report, I describe a technique which allows a non-convex optimal control problem to be expressed and solved in a convex manner. I then verify the resulting solution to ensure its physical feasibility and its optimality. The original, non-convex problem is the fuel-optimal powered landing problem with aerodynamic drag. The non-convexities present in this problem include mass depletion dynamics, aerodynamic drag, and free final time. Through the use of lossless convexification and successive convexification, this problem can be formulated as a series of iteratively solved convex problems that requires only a guess of a final time of flight. The solution’s physical feasibility is verified through a nonlinear simulation built in Simulink, while its optimality is verified through the general nonlinear optimal control software GPOPS-II.