Given a vehicle with irregular shape in 2d plane, and its start position and start orientation, like (sx, sy, sori), and also its goal position and goal orientation, like (gx, gy, gori). Between the start and goal, there're several irregular shaped obstacles which are also given. Question: is there an algorithm or some equations to compute whether the vehicle can travel from the start to the goal in polynomial time? Or what if the vehicle and obstacle's shapes are regular or convex?
I know that this can be solved by path planning algorithm like Hybrid A*, but the time complexity is high and I don't need the whole trajectory but only the accessibility. I wonder if it can be solved with less time cost.
Besides, I'd like to know if there's a formal terminology or definition of this problem. And I'll appreciate it if any papers or programming libraries can be provided.