the space C of all configurations of this robot.

the space C_free of all possible collision-free configurations.

PRM is a complete algorithm.

PRM is probabilistically complete assuming certain conditions on the shape of the free space.

three landmarks not creating a straight line

two landmarks

three landmarks

the number of actions undertaken by the local planner.

the average distance between the points sampled from the configuration space.

the visibility property of the free space, where the visibility is determined by the local planner.

assigning to the robot a large enough positive potential.

assigning to each obstacle the direction of motion of the robot near it (spin)

ensuring equal distribution of the potential on the onstacles.

cell decomposition

roadside following

wavefront

expands the tree and advances the motion towards q_goal

expands the tree and advances the motion towards q_goal or q_init

expands the tree and tries to build a new branch towards q_goal

using a quadtree data structure.

using an octree data structure.

using a binary tree.

is complete, but not optimal.

is complete and optimal, in opposition to the classic RRT.

is asymptotically optimal and has fast exploration properties like RRT.

represent a plausible next move of the robot.

represents an obstacle in C_free

represents a configuration of the robot.