Optimal Natural Frames
نویسندگان
چکیده
1. Intoduction. In this paper, we discuss a class of optimal control problems on Lie groups, focusing on the special Euclidean groups SE(n). The models we discuss arise in the dynamics and control of unmanned aerial vehicles (Justh & Krishnaprasad 2002, 2004, 2005), in continuum models in biophysics (Wiggins 2001) and in fluid mechanics (Newton 2001). In his Ph.D. thesis (Baillieul 1975, 1978), John Baillieul investigated optimal control problems on matrix Lie groups using the Maximum Principle of Pontryagin and methods from the calculus of variations, emphasizing in Chapter 3 of the thesis the details of the special case of SO(3). The present paper is somewhat in the spirit of that chapter, seeking explicit solutions while finding common patterns in a wider class of problems.
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