Free configuration space at the simple system

Today, I will show you  configuration spaces in the two link systems ; RR and RP.

figure.1

First RR system has two configuration space variables ; theta1, theta2 (unit: radian)

figure.2

Second RP system has two configuration space variables: theta1 , D(Distance) (unit: radian, meter, respectively)

figure.3

If we want to map the obstacle in the figure.1 onto each configuration space (figure.2 & figure.3 ), What I do?

First, in the RR system, it is possible that collision between obstacle and link.1 or collision between obstacle and link.2. In the first case, if collision between obstacle and link.1 is happen,  all positions of link.2 with all angles are impossible. In the second case, if a distance between second joint and center of obstacle is smaller than length of link.2, there are impossible angle sets.

According to the upper concepts, we can write plot script for finding free configuration space. Next figure is result.

(code.1: https://docs.google.com/open?id=0B7RItyl-gDWqaFBPbkJTR3oxQTA )

By  thinking similar concept that is used in the RR system, We can get a free configuration set in the RP system. Next figure is result

(code.2: https://docs.google.com/open?id=0B7RItyl-gDWqRGNZcVRGS3ZMX0k)