(206) Combinatorial methods are complete (will return a path or say one doesn’t exist, correctly)

The exact structure of the problem is important in combinatorial methods. In particular cases, efficient algorithms are applicable.

(207) Roadmaps provide a discrete representation of the continuous planing problem

(208) A number of planning algorithms that work in 2D don’t generalize to higher dimensions

(213) Many path planning algos are based on computational geometry methods, which is generally interested in sorting in multiple dimensions

(215) Costs for many 2d algos are O(nlgn)

(224) Algorithms that work in higher-d spaces take dimensional slices at vertices until they are back to the 2d case

(226) In many real problems, obstacles aren’t polys but rather have smooth surfaces.

This can be broken down into a discrete set of configurations for a position by encoding good poses in a stack

“important aspect” of this is detecting critical changes when a area in the pose goes from being blocked to unblocked, or opposite

Since the critical changes happen at an exact point, the problem becomes discrete again when using them

(232) Skipping computational algebraic geometry because it is said implementation is very difficult & computationally expensive; the algorithms are powerful though

(249) Planning fro robots in 3D environments with noise is NEXPTIME hard (doubly-exponential)

(250) Davenport-Schinzel sequences are used for finding computational bounds for many problems, often uses the Ackerman function