路径规划课件Chap4-Potential-Field howie[1].doc

路径规划课件Chap4-Potential-Field_howie[1].docRobotic Motion Planning:
Potential Functions
Robotics Institute 16-735
Mt p://voro . /~motion
Howie Choset
http://v oron /~choset
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The Basic Idea
• A really simple idea:
一 Suppose the goal is a point ge iH2 Q
一 Suppose the robot is a point r e iR2
一 Think of a "spring55 drawing the robot toward the goal and away from obstacles:
一 Can also think of like and opposite charges
Another Idea
• Think of the goal as the bottom of a bowl
• The robot is at the rim of the bowl
• What will happen?
The General Idea
Both the bowl and the spring analogies are ways of storing potential energy
The robot moves to a lower energy configuration
A potential function is a function U :讯111 —讯
Energy is minimized by following the negative gradient of the potential en ergy fun ction:
We can now think of a vector field over the space of all q's ・・・
一 at every point in time, the robot looks at the vector at the point and goes in that di recti on
Attractive/Repulsive Potential Field
U (q) = "att(g) + ^ 'rep(^)
Uatt is the "attractive" potential ■“ move to the goal
Urep is the “repulsive” potentiaI ・・・ avoid obstacles
Artificial Potential Field Methods:
Attractive Potential
Conical Potential
U (q)二驭(匕处曲)■
e⑷=掩爲)(q -叫】)•
Quadratic Potentiml ►
（g，g呂osi），
(b)
场ttS)= VDatt(q) — (q, qgoal)),
J
= C(q — Qgoal) ■>
Artificial Potential Field Methods:
Attractive Potential
Combined Potential
r ]
尹</2 (g)§goal)5 况(％ ^goal)二"goal) 如 9)= <
d；oal(d& ggoal) 一 9((^goal)25 ^(^J^goal) > ^goal•
Q q— qgoalh d・(q? q&oal)上 〃goaP
Wt(g)=
W — ^goal) d(q〕qgoal)
d&Qgoal) > dgoab
In some cases, it may be desirable to have di st a nee functions that grow more slowly to avoid huge velocities far from the goal
one idea is to use the quadratic potential near the
goal (< d*) and the conic farther away
One minor issue: what?
16-735,