RangeofAction.cdy

Please enable Java for an interactive construction (with Cinderella).

- G is the body of the spider
- Each foot of the robot can reach the points of the plane inside the disk of radius R
- This disk is called the range of action of the robot.

- Configuration: A position of the robot body G
- For some configuration, the placement of the robot is a set of pairings between some of the robot feet and some point of M,
M = {points p within the range of action}
- A placement is defined by I, the set of resting legs and by
p_i M, i I, the set of resting feet.
- We say that a placement is an l-leg placement if |I| = l

For a given configuration, a placement is said to be l-feasible if there is a set of indices I such that:
For all i I, d(G, p_i) ≤ R and |I| ≥ l
where d(A, B) is the Euclidean distance between two points A and B of the plane, i.e. there must be at least l-feasible sites in the range of action of the robot.
Spider Home

Created with Cinderella

For all i I, d(G, pi) ≤ R and |I| ≥ l

For all i I, d(G, p_i) ≤ R and |I| ≥ l