All algorithms of path planning

1. Path planning of mobile robots
with stationery obstacles
Chivukula Sairam Satwik
224156005

2. What is Path planning?
• Path planning- Determining a path from an initial configuration to a
goal configuration such that the robot doesn't collide with any
obstacles
• Path planning is an important primitive for autonomous mobile
robots that lets robots find the shortest or otherwise optimal path
between two points.

3. Goal of Path Planning
1. Optimal Path estimation
• Calculate the optimal path taking potential uncertainties in the actions into
account
• Quickly generate actions in the case of unforeseen objects
2. Collision avoidance
• Determine collision-free trajectories using geometric operations

4. Map Representation
• Path planning requires a map of the environment and the robot to be
aware of its location with respect the map.
• Map representation have
two complementary
approaches:
• Discrete approximation and
• Continuous approximation.

5. Discrete Approximation
• In a discrete approximation, a map is sub-divided into chunks of equal
(e.g., a grid or hexagonal map) or differing sizes (e.g., rooms in a
building). The latter maps are also known as topological maps.
• Discrete maps lend themselves well to a graph representation. Here,
every chunk of the map corresponds to a vertex (also known as
“node”), which are connected by edges, if a robot can navigate from
one vertex to the other.

6. • Computationally, a graph might be stored as an adjacency or
incidence list/matrix.
• Each cell represents a node in the graph
• If a robot can move from one cell to
another, then those nodes are connected
in the graph
• Cells that would result in a collision are
not included in the graph
• Search the resulting graph

7. Continuous Approximation
• A continuous approximation requires the definition of inner
(obstacles) and outer boundaries, typically in the form of a polygon,
whereas paths can be encoded as sequences of real numbers.

8. • Discrete maps are the dominant
representation in robotics.
• The most common map is the
occupancy grid map. In a grid map,
the environment is discretized into
squares of arbitrary resolution.

9. Path Planning Algorithms
• The problem is to find an optimum path considering the following
parameters:
• minimum cumulative edge cost (Physical distance travelled)
• delay in a networking application
• Any other parameter related to experimental environment
• Path planning in discrete environment can be carried out by using
algorithms like BFS, DFS but most commonly used are Dijkstra’s, A*,
D* and RRT.
• Path planning in continuous environment can be carried out by
using Potential Fields approach.

10. BFS (Breadth First Search)
• Searches through every node on
one level before moving down
to the next level

11. Pseudo Code
DFS (root node) {
create stack
create list of visited nodes
mark root node as visited
push root node into stack
while (stack is not empty) {
x = stack . top ()
stack . pop ()
for (all immediate neighbors of x) {
if (not visited) {
push into stack
mark as visited
}
}
}
}

12. DFS (Depth First Search)
• Searches deep within the first
node before moving to the next

13. Pseudo Code
DFS (root node) {
create queue
create list of visited nodes
mark root node as visited
enqueue root node
while (queue is not empty) {
x = queue . pop ()
queue . pop ()
for (all immediate neighbors of x) {
if (not visited) {
enqueue
mark as visited
}
}
}
}

14. Dijkstra’s Algorithm