The document discusses ant colony optimization (ACO) and its application in path planning for mobile robots, addressing traditional method limitations like robustness and adaptability. It outlines improvements in ACO through algorithms that focus on pheromone initialization, diffusion models, and advanced heuristics for effective pathfinding. The paper highlights the use of a rolling window method for local path planning and the advantages of adapting ACO for dynamic environments.

1. ANT COLONY OPTIMIZATION
AND PATH PLANNING
Wren Oswin
(SCT19CS062)
Guided by,
Dr. Jayasudha J.S,
Professor and Dean(Academics)

2. 2
1. Introduction
2. Ant Colony Optimization
3. Pheromone Initialization
4. Pheromone Diffusion Model
5. Fallback Strategy
6. Improved Heuristics
7. Improved Pheromone update
8. Local Path Planning
9. Conclusion
10. References
CONTENTS

3. INTRODUCTION
3
● Path planning for mobile robots aim to provide a collision-free,
optimal or approximate optimal path from the initial position
to the destination position
● Various methods have been researched to generate the optimal
path involving cell decomposition, roadmap approaches, and
potential field methods
● These methods suffer from a lack of robustness, adaptivity, and
local minimum solutions
● Heuristic methods have been promoted to overcome the
essential drawbacks of traditional methods

4. INTRODUCTION (CONTD.)
4
The representative methodologies include
• Artificial Neural Network
• Genetic Algorithms
• Ant Colony Optimization
• Particle Swarm Optimization
• Artificial Bee Colony
• Gradient-Based Optimizer
• Slime mould Algorithm
• Whale Optimization Algorithm

5. ANT COLONY OPTIMIZATION
5
● Probabilistic method for resolving computational problems, which can be reduced to
searching optimal paths through graphs
● Inspired by behavior of ants finding paths in the procedure of food searching or risk
avoidance
● It is a metaheuristic for difficult combinatorial optimization problems

6. ANT COLONY OPTIMIZATION (CONTD.)
6
● Ants can leave a type of material called a pheromone in the paths they pass
● They can sense the intensity of the pheromone and can thereby guide their own
direction of action in the process of foraging
● Main Characteristics
○ Distributed computing
○ Positive information Feedback
○ Heuristic Search

7. ANT COLONY OPTIMIZATION (CONTD.)
7
Figure A: Ants travelling on a
path with no obstacles
Figure B: An obstacle appears
on a path dividing the path into
two
Figure C: Ants choose both
paths for travel
Figure D: Ants choose the
shorter path

8. ANT COLONY OPTIMIZATION (CONTD.)
8
Steps followed in ACO -
● 'm’ants are randomly placed in the location (search space).
● Initial value of pheromone on each edge are equal
● The k-th(k = 1, 2, .. , m) ant chooses the next location to be
transferred to on account of the random proportion rule

9. ANT COLONY OPTIMIZATION (CONTD.)
9
• 𝝉ij is the pheromone of edge;
• α , parameter to regulate the influence of τ
• ηij is the heuristic factor (visibility of node j from i), which is the inverse of distance;
• ß, parameter to regulate the influence of η
• allowedk , The set of nodes which are not visited by ant k

10. ANT COLONY OPTIMIZATION (CONTD.)
10
• Pheromone release by ants on a valid edge
ρ is the volatilization
constant of pheromone
• Repeat steps until termination condition or a fixed number of iterations
• Display the optimal path
k

11. ANT COLONY OPTIMIZATION (CONTD.)
11
TSP-ACO()
1. Start
2. bestTour.length ← ∞, bestTour ← nil
3. do
3.1 Randomly place M ants on N cities
3.2 for each ant ‘a’
3.2.1 for n ← 1 to N
a. ant ‘a’ selects an edge it can visit according to probability distribution
3.3 update bestTour if currentTour.length < bestTour.length
3.4 For each ant a
3.4.1 for each edge(u,v) in the ant’s tour
a. Deposit pheromone ∝ 1/tour-length on edge (u,v)
4. Until some termination criteria
5. return bestTour
6. Stop

12. ANT COLONY OPTIMIZATION (CONTD.)
12
Primary data structures for implementing ACO
• Adjacency matrix or adjacency list for representing state space graph
• 2D Matrix to store edge costs - cost matrix
• 2D Matrix to store pheromone levels on each edge - pheromone matrix

13. ANT COLONY OPTIMIZATION (CONTD.)
13

14. ANT COLONY OPTIMIZATION (CONTD.)
14
● We select one of the nodes to travel to using the Roulette wheel technique

15. ANT COLONY OPTIMIZATION (CONTD.)
15
Strengths of Swarm Intelligence Algorithms:
● Flexible number of individuals, facilitating higher scalability
● Realize a relatively large-scale search, present excellent exploration
and exploitation capabilities
● No single agent is indispensable, malfunction in one part of system
won’t cause a complete failure, hence it is robust
● The ant colony algorithm can be run continuously and adapt to
changes in real time

16. ANT COLONY OPTIMIZATION (CONTD.)
16
Limitations of Swarm Intelligence algorithms:
● Time consuming, affected by factors such as
○ Size of population
○ Frequency of iteration and pattern of iteration
● Stagnation/premature convergence to local optimum due to lack of central
coordination

17. ANT COLONY OPTIMIZATION (CONTD.)
17
Extensions to classic ACO:
● Variable Pheromone initialization
● Pheromone diffusion model
● Fallback Strategy
● Improved Heuristics and pheromone update strategy

18. PHEROMONE INITIALIZATION
18
● In classical ACO, pheromone levels on edges were equally initialized and this hinders
the movement of ants for reaching optimum quicker. As a consequence, it takes a long
time to find a better solution from a great number of candidate solutions.
● In Adaptive Improved ACO, the non-uniform distribution of initial pheromone based
on A* algorithm is used to adjust the initial allocation of pheromone.
● A* search evaluates nodes by combining g(n), the cost to reach the node, and
h(n), the cost to get from the node to the goal

19. PHEROMONE INITIALIZATION (CONTD.)
19
● First, an optimal path obtained by A* algorithm is used for pheromone initialization.
The initial pheromone value can be defined as follows:
T* is the optimal path
found by A* algorithm
L* is the path length
of T*

20. PHEROMONE DIFFUSION MODEL
20
● The pheromone trails play an important role in the performance and
collaborative capability of the ACO
● In classic ACO, pheromone is only deposited on the edges that ants pass
through
● Leads to the problem of insufficient cooperation between ants and brings the
risk of entrapment in the local optimum
● It is usually more likely to get a better solution in the neighborhood of the
optimal solution than in other regions

21. PHEROMONE DIFFUSION MODEL (CONTD.)
21
● The pheromone diffusion model can enhance the exploration and collaboration capabilities
of the ant colony algorithm

22. PHEROMONE DIFFUSION MODEL (CONTD.)
22
● The initial pheromones on the optimal path constructed by A* algorithm are
diffused to the surrounding areas according to the pheromone diffusion model to
enhance the cooperation among ants.
Without pheromone
diffusion
With pheromone diffusion

23. FALLBACK STRATEGY
23
● There are many disconnected paths in practical application. It is difficult for the
classic ACO to converge to the optimal path, for the nodes are selected based on
parameters like pheromone weight, heuristic information weight
● An robot looking for the optimal path will fall back to the previous node to select
another node, if the current node leads to a disconnected path
● Fallback strategy makes ACO adaptable, but also less efficient
● Both heuristic information and pheromone update strategy needs to be modified

24. IMPROVED HEURISTICS
24
● Valuation function of A* was used to improve heuristic information, making the
improved ACO more accurate, efficient and directional in search
gij(t) is the cost from the current node i to the candidate node j at time t
hjn(t) is the minimum estimated cost from the candidate node j to the
destination n

25. IMPROVED PHEROMONE UPDATE
STRATEGY
25
● Classic ACO pheromone update strategy is prone to local optimum trap
● An addition of reward/penalty mechanism ensures ensures it doesn’t fall
into local optimum trap and ensures efficiency and effectiveness in iterative
updates

26. IMPROVED PHEROMONE UPDATE
STRATEGY (CONTD.)
26
𝜏
𝜏
Ng and Nb are the
number of ants to
be rewarded and
penalized,
respectively;
lg and lb are the path lengths to be
rewarded and penalized,
respectively.
P is pheromone intensity coeff.

27. LOCAL PATH PLANNING
27
• Local path planning refers to methods that take in information from the
surroundings in order to generate a simulated field where a path can be
found
• Uses Rolling Window Method - can calculate the maximum collision-
free speed required for the robot to reach the target
• RWM can be implemented in 3 steps :-
• Scene prediction
• Rolling window optimization
• Feedback initialization

28. LOCAL PATH PLANNING (CONTD.)
28
When there is no obstacle in the window,
the local sub-target point is determined
by calculation to be the intersection of
the mobile robot and the global end point
G at the boundary of the window.
When there is an obstacle in the window,
the local sub-target point position can be
obtained by calculation, which ensures
that the mobile robot can safely avoid the
obstacle and move toward the global end
point G.

29. LOCAL PATH PLANNING (CONTD.)
29
• For solving local path planning problem, we expand the rolling
window perception range into a circular area
• A particle is selected to simulate the mobile robot to execute the
obstacle avoidance strategy

30. LOCAL PATH PLANNING (CONTD.)
30
For dynamic obstacles with known motion rules, the following four scenarios are
considered for the particle and the dynamic obstacle in a rolling window period :-
1. The particle and the dynamic obstacle do not intersect in the motion
trajectory within a cycle perceived by the dynamic window.
2. The particle and the dynamic obstacle in one cycle have an intersection point
at the same time and they are moving sideways.
3. The particle and the dynamic obstacle in one cycle have an intersection point
at the same time and they are moving in opposite directions
4. The particle predicts that there is a dynamic obstacle moving in the same
direction with a higher speed behind it

31. LOCAL PATH PLANNING (CONTD.)
31
Side Collision avoidance
strategy

32. LOCAL PATH PLANNING (CONTD.)
32
Frontal Collision avoidance
strategy

33. LOCAL PATH PLANNING (CONTD.)
33
Rear-end Collision avoidance
strategy

34. LOCAL PATH PLANNING (CONTD.)
34
• When a dynamic obstacle is detected to change in speed, direction or
size during two consecutive environmental refreshing processes, it is
regarded as a dynamic obstacle with unknown motion law.
• For the problem of dynamic obstacle avoidance with unknown motion
rules, a second-level safety distance determination rule is implemented,
which improves the algorithm's obstacle avoidance function in complex
environments.
• The rule divides the distance between the moving particle and the
dynamic obstacle into two categories: controllable safety distance and
emergency safety distance

35. LOCAL PATH PLANNING (CONTD.)
35
Schematic diagram of regional division
• Reasonable values for two distances
can shorten the global path length
to the greatest extent and reduce
energy consumption
• When the moving particle is
determined to encounter a dynamic
obstacle with unknown motion law,
the velocity decreases to 1/2 of the
initial velocity

36. LOCAL PATH PLANNING (CONTD.)
36
Schematic diagram of regional division
• If distance between the moving particle and
the dynamic obstacle after the next
environmental information refresh meets the
requirement of controllable safety distance,
the particle point continues to move along the
planned path

37. LOCAL PATH PLANNING (CONTD.)
37
Schematic diagram of regional division
• If moving obstacle will enter the emergency
safety distance, It is assumed to be a static
obstacle, and the local path of the particle
from the current position to the next sub-target
point is planned and moved along the new
local path. At this time, the velocity of the
moving particle is restored to the initial
velocity.

38. LOCAL PATH PLANNING (CONTD.)
38
Schematic diagram of regional division
• In the process of particle moving along the new
planned path, it is judged whether the distance
between them meets the emergency safety
distance requirement after a certain refresh
time.
• If the requirement is met, the particle continues
to move along the new path.
• Otherwise, stop advancing immediately and
return along the passed path until the distance
between the two is greater than the emergency
safety distance again.
• After the obstacle gradually moves away, the
particle continues to move towards the target
point.

39. CONCLUSION
39
• Classic ACO is a reliable algorithm for solving path problems in static environments
• The elementary algorithm for ACO is sometimes time consuming and require novel
extensions to increase its convergence speed along with finding the most optimal
solution, and changes also need to be made for the pheromone update and initialization
phases
• Using the rolling window method and improved ACO is found to be effective in
Dynamic Path Planning for Robotic systems
• Future research on swarm intelligence algorithms can further improve the algorithms’
efficiency in solving optimization problems with high accuracy.

40. REFERENCES
40
1. Q. Jin, C. Tang and W. Cai, "Research on Dynamic Path Planning Based on the Fusion
Algorithm of Improved Ant Colony Optimization and Rolling Window Method," in
IEEE Access, vol. 10, pp. 28322-28332, 2022
2. X. Wang, H. Shi and C. Zhang, "Path Planning for Intelligent Parking System Based on
Improved Ant Colony Optimization," in IEEE Access, vol. 8, pp. 65267-65273, 2020
3. S. Zhang, J. Pu and Y. Si, "An Adaptive Improved Ant Colony System Based on
Population Information Entropy for Path Planning of Mobile Robot," in IEEE Access,
vol. 9, pp. 24933-24945, 2021
4. J. Tang, G. Liu and Q. Pan, "A Review on Representative Swarm Intelligence
Algorithms for Solving Optimization Problems: Applications and Trends," in
IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 10, pp. 1627-1643, 2021

41. THANK YOU