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Real‐time trajectory generation for differentially flat systems
Author(s) -
Van Nieuwstadt Michiel J.,
Murray Richard M.
Publication year - 1998
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199809)8:11<995::aid-rnc373>3.0.co;2-w
Subject(s) - trajectory , control theory (sociology) , trajectory optimization , nonlinear system , computer science , linearization , stability (learning theory) , convergence (economics) , feedback linearization , point (geometry) , mathematics , mathematical optimization , optimal control , control (management) , artificial intelligence , physics , geometry , quantum mechanics , astronomy , machine learning , economics , economic growth
This paper considers the problem of real‐time trajectory generation and tracking for nonlinear control systems. We employ a two‐degree‐of‐freedom approach that separates the nonlinear tracking problem into real‐time trajectory generation followed by local (gain‐scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real‐time trajectory generation problem for differentially flat systems with (possibly non‐minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included. © 1998 John Wiley & Sons, Ltd.