This paper presents modified hybrid A.sup.* algorithms to facilitate more efficient path finding around narrow passages under the shape and kinematic constraints of a car-like vehicle. First, we ...propose spline- and bidirectional-search-based hybrid A.sup.* using G.sup.2 continuous motion primitives with multiple turning radii depending on cubic Bezier curves. In addition, we present a heuristic applying the vector field histogram to find a path around narrow passages with efficiency rather than optimization. We demonstrate the benefits of our method through simulations and experimental results using an autonomous ground vehicle in environments with narrow passages. Keywords Bidirectional-search-based hybrid A.sup.* * G.sup.2 continuous path planning * Car-like vehicle * Narrow passage
We establish several necessary and sufficient conditions for the existence and uniqueness of Hermitian positive definite (HPD) solutions to the general matrix equationwhere p, m are positive ...integers, Mi (i = 1, 2, …, m) are n × n nonsingular complex matrices, A and B are HPD matrices, and then give three algorithms to get the unique solution. Moreover, we give two numerical examples to illustrate the effectiveness of the theoretical results and the behavior of the considered methods.
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