The basic idea here is to try to construct a smooth function over the extent of the configuration space, which has high values when the robot is near to an obstacle and lower values when it's further away.     If we can construct such a function, we can use it's gradient to guide the robot to the desired configuration.  

 

 

 

 

 

 

 

 

 

  bowl-like shape

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 This is sometimes referred to as sensor based planning

 

laser sensor,...rangefinder

 

In fact, they can incorporated into real time control schemes, running at tens of hertz using local sensor data  

 

 

 downside is local minima

 

 

 

 

 

 

 

 

 

 

 

 

 

 hard to know local minima in advance

 

One way to view these artificial potential field based schemes is as a useful heuristic.

  

the use of a back tracking procedure to detect these situation

 

 

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visible graph approach 1

 

 

 

 trapezoidal decomposition approach 2

 

 

 

 grid based approach 3

 

 

 

 上面: discretize space and use dijkstra

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 下面：Tree search