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simple RRT：

For its search, it requires the following threedomain-specific function primitives:

Function Extend (env:environment,current:state,target:state):state 可以应用很多启发式的方法，并且the better the heuristic,the fewer nodes the planner will need to expand on average, since it will not need to rely as much on random exploration.
Function Distance (current:state,target:state):real
Function RandomState ():state

extend RRT

Some optimizations over the basic described in existing work are bidirectional search to speed planning, and encoding the tree points in an efficient spatial data structure

ERRT没有采用双向搜索的策略，但是采用了KDtree作为空间的数据结构。

①a more general biased distribution

相较于simpleRRT，这种算法增加了一种判断，向已知点进行拓展的

Typical values used in this work were P[goal] = 0.1 and P[waypoint] = 0.6.

②adaptive beta search

RRT planner is building a greedy approximation to a minimum spanning tree, and does not care about the path lengths from the initial state。

The distance metric can be modified to include not only the distance from the tree to a target
state, but also the distance from the root of the tree, multiplied by some gain value.

距离度量不仅仅是树到目标点的距离，还引入了到根的距离乘上gain value

这个值越大，将会导致更少的path从根到叶，也会减少空间扩展的数量，

value=1，将会永远从根节点开始扩展，value=0，RRT。

When the planner starts, beta is set to 0.Then on successive replans, if the previous run found
a plan, beta is incremented, and decremented otherwise.

In addition the value is clipped to between 0 and 0.65.

This adaptive bias schedule reflects the idea that a bad plan is better than no plan initially, and once a plan is in the cache and search is biased toward the waypoints, nudges the system to try to shorten the plan helping to improve it over successive runs.

dynamic RRT

D* efficiently repair previous solutions when changes occur in the environment

保留有效的部分，把无效的部分重新计算，DRRT也是利用了相似的思想

①We begin with an RRT generated from an initial configuration to a goal configuration (Fig. 3(a)).

②When changes occur to the configuration space (e.g. through receiving new information),
we mark all the parts of the RRT that are invalidated by these changes (Fig. 3(b) and (c)).

③We then trim the tree to remove all these invalid parts (Fig. 3(d)).

④At this point, all the nodes and edges remaining in the tree are guaranteed to be valid, but
the tree may no longer reach the goal. Finally, we grow the tree out until the goal is reached once more

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