Yep! It can be solved for some specific cases though — e.g. I stumbled upon a few papers that calculate the optimal path for parallel parking using systems of differential equations [1][2]

[1] https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7463491

[2] http://www.tsi.lv/sites/default/files/editor/science/Researc...