Topic 9 Potential fields: Follow your potential
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1 Topic 9 Potential fields: Follow your potential
2 Path Planning B: Goal Find intermediate poses forming a path to the goal ) How can we find such paths? 2) Define pose and controls? Path on a graph: vertices - robot poses A: Start edges - traversable connection between poses (note edges are directed)
3 Approaches to path planning Search (fixed graph) DFS, BFS, Dijkstra, A* Search (build graph): Probabilistic Road Maps Rapidly-exploring Random Trees Optimization (local search): Potential fields, gradient descent
4 Potential field volcanic on fire Energy potential converges at goal heating up How do we define this potential? colder a little warmer cold
5 Potential Energy Energy stored in a physical system For objects acting only w.r.t. gravity PE = mass*height*gravity
6 Convergent Potentials let s call these attractor landscapes Start Start Goal Goal basin of attraction
7 2D potential navigation z: height indicates potential at location x = Start x d = Goal basin of attraction x-y plane: robot position
8 Cone Attractor x d = Goal Attractor Start w: weight (x d -x): direction x d -x : distance u = w(x d -x)/ x d -x x = Start Goal top view side view
9 Cone Attractor x d = Goal Attractor x d -x Start w: weight (x d -x): direction x d -x : distance (x d -x) u = w(x d -x)/ x d -x x = Start Goal top view side view
10 Cone Attractor x d = Goal Attractor x d -x Start w: weight (x d -x): direction x d -x : distance (x d -x) unit vector (x d -x)/ x d -x u = w(x d -x)/ x d -x x = Start Goal top view side view
11 Cone Attractor x d = Goal Attractor x d -x Start w: weight (x d -x): direction x d -x : distance (x d -x) unit vector (x d -x)/ x d -x u = w(x d -x)/ x d -x w x = Start Goal top view side view
12 Bowl Attractor x d = Goal Start u = exp(- x d -x /w) (x d -x) Goal x = Start top view side view
13 exp(-d/w) exp(-d/0) exp(-d/w) : influence of potential exp(-d/) exp(-d/0.5) exp(-d/.0) d = distance exp(-d/2)
14 Multiple potentials Output of potential field is a vector potential 2 (x) potential (x) How to combine or select between multiple potentials?
15 Multiple potentials i potential i (x) Output of potential field is a vector potential 2 (x) potential (x) Combine multiple potentials through vector summation u = i potential i (x) or u = potential (x)+ potential (x)
16 describe performance for this case Goal Current
17 describe performance for this case Goal Obstacles Repellors Current
18 describe performance for this case how do we deal with repellors? Goal Obstacles Repellors Current
19 Cone Repellor potential problems Obstacle Repellor Goal reverse direction u = w(x-x d )/ x d -x x = Start Start top view side view
20 Bowl Repellor Obstacle Repellor Goal u = exp(- x-x d /w) (x d -x) Start x = Start top view side view
21 describe performance for this case Goal Current
22 describe performance for this case Goal Current
23 describe performance for this case Goal Current
24 matlab example /course/cs48/pub/pfield.m How to address local minima?
25 [Prin. of Robot Motion] Wavefront planning Combine search with potential field Start: mark with 0 0 Goal: mark with 2
26 [Prin. of Robot Motion] Wavefront planning Obstacles: mark with 0
27 [Prin. of Robot Motion] Wavefront planning 0 BFS away from goal, mark depth unless
28 [Prin. of Robot Motion] Wavefront planning 0
29 [Prin. of Robot Motion] Wavefront planning 0
30 [Prin. of Robot Motion] Wavefront planning 0
31 [Prin. of Robot Motion] Wavefront planning 0
32 [Prin. of Robot Motion] Wavefront planning
33 [Prin. of Robot Motion] Wavefront planning Once start reached, follow potential to goal
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