Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems

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Mark B. Milam
PhD Dissertation, Control and Dynamical Systems

With the advent of powerful computing and efficient computational algorithms, real-time solutions to constrained optimal control problems are nearing a reality. In this thesis, we develop a computationally efficient Nonlinear Trajectory Generation (NTG) algorithm and describe its software implementation to solve, in real-time, nonlinear optimal trajectory generation problems for constrained systems. NTG is a nonlinear trajectory generation software package that combines nonlinear control theory, B-spline basis functions, and nonlinear programming. We compare NTG with other numerical optimal control problem solution techniques, such as direct collocation, shooting, adjoints, and differential inclusions. We demonstrate the performance of NTG on the Caltech Ducted Fan testbed. Aggressive, constrained optimal control problems are solved in real-time for hover- to-hover, forward flight, and terrain avoidance test cases. Real-time trajectory generation results are shown for both the two-degree of freedom and receding horizon control designs. Further experimental demonstration is provided with the station-keeping, reconfiguration, and deconfiguration of micro-satellite formation with complex nonlinear constraints. Successful application of NTG in these cases demonstrates reliable real-time trajectory generation, even for highly nonlinear and non-convex systems. The results are among the first to apply receding horizon control techniques for agile flight in an experimental setting, using representative dynamics and computation.