Abstract
AbstractIn this paper, we focus on the motion planning problem (MPP) of a generalized Dubins vehicle (GDV) with higher order dynamics, aiming at mitigating the drawbacks caused by the lack of smoothness of the Dubins curves. In the two‐dimensional case, the MPP is converted, by exploiting the Pontryagin maximum principle, into the problem of solving a set of algebraic equations (AEs). The solution of the set of AEs, which can also be applied to the MPP of chained‐form and flat systems, is found by systematically using the concept of elementary symmetric polynomial. Furthermore, in extending our results to the three‐dimensional case, the explicit expression of a new class of space curves is obtained using the Frenet frame. Simulation results show the superiority of the curves generated by the GDV over that generated by the conventional Dubins vehicle.
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