Path planning in the presence of dynamic obstacles is a challenging problem due to the added time dimension in search space. In approaches that ignore the time dimension and treat dynamic obstacles as static, frequent re-planning is unavoidable as the obstacles move, and their solutions are generally sub-optimal and can be incomplete. To achieve both optimality and completeness, it is necessary to consider the time dimension during planning. The notion of adaptive dimensionality has been successfully used in high-dimensional motion planning such as manipulation of robot arms, but has not been used in the context of path planning in dynamic environments. In this paper, we apply the idea of adaptive dimensionality to speed up path planning in dynamic environments for a robot with no assumptions on its dynamic model. Specifically, our approach considers the time dimension only in those regions of the environment where a potential collision may occur, and plans in a low-dimensional state-space elsewhere. We show that our approach is complete and is guaranteed to find a solution, if one exists, within a cost sub-optimality bound. We experimentally validate our method on the problem of 3D vehicle navigation (x, y, heading) in dynamic environments. Our results show that the presented approach achieves substantial speedups in planning time over 4D heuristic-based A*, especially when the resulting plan deviates significantly from the one suggested by the heuristic.
@cite_4 , highly accurate heuristic values are computed by solving a low-dimensional problem and are then used to direct high-dimensional planning. However, this approach does not explicitly decrease the dimensionality of the state-space and can lead to long planning times when the heuristic is incorrect.
@cite_4
2066852548
This paper presents a solution to the problem of finding an effective yet admissible heuristic function for A* by precomputing a look-up table of solutions. This is necessary because traditional heuristic functions such as Euclidean distance often produce poor performance for certain problems. In this case, the technique is applied to the state lattice, which is used for full state space motion planning. However, the approach is applicable to many applications of heuristic search algorithms. The look-up table is demonstrated to be feasible to generate and store. A principled technique is presented for selecting which queries belong in the table. Finally, the results are validated through testing on a variety of path planning problems. Index Terms – motion planning, state lattice, heuristic, nonholonomic, mobile robot