Sampling demo: a tree grows through the configuration space of the two-link arm

This page grows a rapidly exploring random tree (RRT) from the start posture of the arm (links 0.4 m and 0.3 m) toward the goal posture, the positive-elbow solution of the tip target (0.5, 0.2) m. In the default model no part of either link may come within 5 mm of the disc, and the straight edge between the two postures is invalid. Each Step draws one random configuration, finds the nearest tree node, proposes a node at most 10° away in joint-space distance, then checks postures along the connecting edge at intervals of at most 1° per joint. Only a passing edge adds the proposed node; intermediate checking postures do not become tree nodes. Each posture drawn on the left is one point on the right. Hover over the right view to see the posture at the mouse.

Workspace, in meters

start posture goal posture sampled posture nearest tree node accepted extension rejected extension first invalid configuration on it, with a tie to the disc postures already checked the current check, with a tie from its closest point to the disc center a check that fails disc, radius 0.05 m 5 mm clearance ring

Configuration space, joint angles in degrees

forbidden: part of a link would come within 5 mm of the disc tree edges path found direct edge start to goal × sample, ○ nearest node, · checked configurations, × first invalid one ○ scheduled check, ● checked and valid, ● checked and invalid, ◯ the current check