《An Empirical Study of Optimal Motion Planning》

sampling-based, grid-based, and trajectory optimization methods

varying dimensionality, number of homotopy classes, and width and length of narrow passages在这些方面作比较

评价标准convergence rates, and performance variations with respect to geometric characteristics

holomorphic 全纯的

homology 同调  cohomology 上同调

homomorphism 同态

homeomorphism 同胚

homotopy 同伦 homotopic 同伦的

homogeneous 齐次的

homologous 相应的

Grid search works well in low-dimensional problems, but performance drastically degrades as dimension grows. Trajectory optimization is highly susceptible to “nuisance” homotopy classes.Sampling-based planners are fairly consistent across dimensions.

the lazy planners L-PRM* and FMM spend a much smaller fraction of time collision checking

some planners that operate on alternate representations that permit obstacle distance / penetration depth tests (e.g., CHOMP [19]). It would be worthwhile to study how obstacle representation could provide more powerful sources of information to guide planning in hard problems