Initial study of autonomous trajectory generation for unmanned aerial vehicles

Many approaches to trajectory generation for nonlinear systems approximate the feasible set using polytopes. This approximation can be very poor even for simple differentially flat systems. For a large class of flat systems arising in aerospace applications, the feasible flat output set is defined in terms of rational function inequalities. We use this observation and a well-known result from robust control to derive a linear fractional representation (LFR) of the feasible set. It is possible to obtain good convex sufficient conditions for trajectory generation from the LFR as similar problems have been tackled in p-analysis related work. In this paper, we develop a sufficient bilinear problem from the LFR. The global optimization algorithm of Floudas and Visweswaran (1990) can be used to check feasibility though not in polynomial time. We present an example to illustrate the difficulties with polytopic approximations and the advantages of the proposed LFR approach.