Grid-Based Search
Grid-based approaches overlay a grid on configuration space, and assume each configuration is identified with a grid point. At each grid point, the robot is allowed to move to adjacent grid points as long as the line between them is completely contained within Cfree (this is tested with collision detection). This discretizes the set of actions, and search algorithms (like A*) are used to find a path from the start to the goal.
These approaches require setting a grid resolution. Search is faster with coarser grids, but the algorithm will fail to find paths through narrow portions of Cfree. Furthermore, the number of points on the grid grows exponentially in the configuration space dimension, which make them inappropriate for high-dimensional problems.
Traditional grid-based approaches produce paths whose heading changes are constrained to multiples of a given base angle, often resulting in suboptimal paths. Any-angle path planning approaches find shorter paths by propagating information along grid edges (to search fast) without constraining their paths to grid edges (to find short paths).
Grid-based approaches often need to search repeatedly, for example, when the knowledge of the robot about the configuration space changes or the configuration space itself changes during path following. Incremental heuristic search algorithms replan fast by using experience with the previous similar path-planning problems to speed up their search for the current one.
Read more about this topic: Motion Planning, Algorithms
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