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
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
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
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
Good Afternoon, I’m Wren Oswin and the topic I have chosen for my Seminar is “Ant Colony Optimization and Path Planning”
These are the contents of the seminar, I’ll start with an introduction to path planning and why Heuristic methods are preferred over traditional/classical methods, then I’ll teach what is Ant Colony Optimization and then we look at the extensions of Ant Colony Optimization which can increase its effectiveness. And finally we look at how collision detection is performed during path planning.
As we know, there are many research topics when it comes to mobile robots, such as SLAM, path planning and trajectory tracking. So, what does one mean when they talk about the process of Path Planning? Path planning for mobile robots or any autonomous robot in general, aims to provide a collision-free, optimal or approximate optimal path from the initial position to the destination position. Some of the traditional methods for path planning are cell decomposition, roadmap approaches and potential field methods. These traditional methods lack robustness, adaptivity and may trap the solution in local minima. So to counter these disadvantages, Heuristic methods have been developed and they’re found to be better than classical methods.
These are some of the Heuristic approaches
the ant colony optimization algorithm is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. As the name suggests, it is inspired by the behavior of ants finding paths in the process of food searching or risk avoidance(Give bread crumb example). Ant colony optimization is a metaheuristic for difficult combinatorial optimization problems. I will say what a metaheuristic is after defining what a heuristic is. Heuristics is a technique designed for solving a problem more quickly when classic methods are too slow or for finding an approximate solution when classic methods fail to find any exact solution. Heuristics are often problem-dependent, that is, you define an heuristic for a given problem. Metaheuristics are problem-independent techniques that can be applied to a broad range of problems. An heuristic is, for example, choosing a random element for pivoting in Quicksort algorithm. A metaheuristic knows nothing about the problem it will be applied, it can treat functions as black boxes. And as to why it is mentioned combinatorial optimization, we’ll be seeing in the following slides
Distributed computing is a model in which components of a software system are shared among multiple computers or nodes. Even though the software components may be spread out across multiple computers in multiple locations, they're run as one system.
Positive information feedback means that when an sub problem is solved by reaching a partial solution, the other agents receive this feedback and adjust their paths accordingly.
Heuristic search is class of method which is used in order to search a solution space for an optimal solution for a problem
Exploration refers to searching the unexplored area of the feasible region while exploitation refers to the search of the neighborhood of a promising region.
the term of premature convergence means that a population for an optimization problem converges too early, resulting in the solution being suboptimal.
it could be obviously noticed that the pheromone diffusion strategy increases the pheromone concentration of the adjacent areas of the optimal solution, enlarges the searching range, and reduces the
probability of premature convergence. ACS without pheromone diffusion mechanism has a smaller
standard deviation. This could be because the pheromone
diffusion strategy leads to a more dispersed distribution
of feasible solutions. Even so, the ACS with pheromone
diffusion mechanism slightly outperforms the original ACS
according to convergence speed and success rate.
Scene prediction: The mobile robot predicts the motion trajectory of dynamic obstacle by obtaining information within the sensing range, and determines whether a collision will occur based on its own motion law.
Rolling window optimization: According to the prediction results and environmental information, the corresponding strategy is adopted to find the local sub-target points and the mobile robot move accordingly. The detection range is continuously updated with the movement of the robot, entering a new detection cycle.
Feedback Initialization: Each rolling plan provides the latest data for the next local path selection, and initializes the obstacles in the sensing range in view of the known information
The particle decelerates and brakes, and restarts after the dynamic obstacle passes the virtual collision point and meets the safety distance.
The predicted virtual collision point is regarded as a static obstacle to avoid, and then according to the improved global path planning algorithm, the local path of the particle from the current position to the next sub-target point is planned.
Numerous swarm intelligence algorithms exist and they can be integrated with other mathematical models or other algorithms to counter limitations, if any