20 research outputs found
A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints
A computationally efficient method to solve non-convex programming problems
with linear equality constraints is presented. The proposed method is based on
a recursively feasible and descending sequential convex programming procedure
proven to converge to a locally optimal solution. Assuming that the first
convex problem in the sequence is feasible, these properties are obtained by
convexifying the non-convex cost and inequality constraints with inner-convex
approximations. Additionally, a computationally efficient method is introduced
to obtain inner-convex approximations based on Taylor series expansions. These
Taylor-based inner-convex approximations provide the overall algorithm with a
quadratic rate of convergence. The proposed method is capable of solving
problems of practical interest in real-time. This is illustrated with a
numerical simulation of an aerial vehicle trajectory optimization problem on
commercial-of-the-shelf embedded computers
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Lossless convexification of quadrotor motion planning with experiments
textThis 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.Mechanical Engineerin