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A Hybrid Optimization Method for Path Planning and Obstacle Avoidance in Cluttered Environments
Israa M. Abdalameer Al-Khafaji, Wisam Ch. Alisawi, Murooj Khalid Ibraheem
Abstract— Hybrid optimization methods are a promising approach for solving complex optimization problems, and they have gained popularity in recent years due to their ability to effectively combine the strengths of multiple algorithms. In this article, we propose a hybrid optimization method for finding the optimal path for a wheeled ground robot to navigate through a cluttered environment while avoiding obstacles. Our approach combines an optimization algorithm, which is used to generate a diverse set of initial solutions, with an evolutionary algorithm, which is used to optimize these solutions. The optimization algorithm is able to perform a global search of the solution space, while the evolutionary algorithm is able to quickly converge on high-quality solutions. By combining these two algorithms, we are able to take advantage of the strengths of both approaches and find the optimal path in a relatively efficient manner. We evaluate the performance of our hybrid optimization method through simulation experiments on a variety of path planning and obstacle avoidance tasks. The results show that our approach is able to find the optimal path in a timely manner and outperforms other state-of-the-art methods. In summary, our proposed hybrid optimization method is a promising approach for finding the optimal path for a wheeled ground robot to navigate through a cluttered environment while avoiding obstacles. By combining an optimization algorithm and an evolutionary algorithm, we are able to effectively explore a wide range of solutions and find high-quality solutions in a relatively efficient manner.
Keywords— Hybrid optimization, Path planning, Obstacle avoidance, Optimization algorithm, Evolutionary algorithm, Cost function, Crowded environments, Mobile robot, Realtime, Dynamic environments, Ground robots.
I. Introduction
Path planning and obstacle avoidance are important problems in robotics, as they involve finding a safe and efficient path for a robot to navigate through an environment while avoiding obstacles. These problems are particularly challenging when the environment is cluttered, as the robot must navigate through a complex and dynamic environment while avoiding collisions.
Traditionally, these problems have been solved using approaches such as potential field methods, graph search algorithms, and probabilistic roadmap methods. However, these methods have limitations and may not be suitable for all environments. In particular, they can be sensitive to the initial solution and may get stuck in local optima.
In recent years, hybrid optimization methods have gained popularity as a promising approach for solving complex optimization problems. These methods combine the strengths of multiple algorithms to effectively explore a wide range of solutions and find high-quality solutions. In this article, we propose a hybrid optimization method for finding
the optimal path for a wheeled ground robot to navigate through a cluttered environment while avoiding obstacles [1,2].
II. The Problem
We are trying to solve in our article is how to effectively plan routes and avoid obstacles in crowded environments. This is a difficult problem because having a large number of objects in the environment can make it difficult to find a clear path from one point to another, and the need to avoid obstacles adds an additional constraint to the path planning process. The hybrid optimization method aims to address these challenges by combining multiple optimization techniques to create an efficient and robust solution.
III. Related Works
There have been several works in the field of hybrid optimization methods for path planning and obstacle avoidance.
One notable example is the study [3], which proposes a hybrid optimization method that combines a genetic algorithm with a gradient-based optimization algorithm for path planning and obstacle avoidance. The genetic algorithm is used to generate a diverse set of initial solutions, which are then passed to the gradient-based optimization algorithm for refinement. The results show that the hybrid approach is able to effectively explore a wide range of solutions and find high-quality solutions in a relatively efficient manner.
Another example is the work [4], which proposes a hybrid optimization method that combines a particle swarm optimization algorithm with a Monte Carlo tree search algorithm for path planning and obstacle avoidance. The particle swarm optimization algorithm is used to generate a diverse set of initial solutions, while the Monte Carlo tree search algorithm is used to evaluate and optimize these solutions. The results show that the hybrid approach is able to outperform other state-of-the-art methods in terms of path quality and efficiency. another example is the study [5], which proposes a hybrid optimization method that combines a genetic algorithm with a neural network for path planning and obstacle avoidance. The genetic algorithm is used to generate a diverse set of initial solutions, which are then passed to the neural network for optimization. The results show that the hybrid approach is able to find high-quality solutions in a relatively efficient manner. Another work [6], which proposes a hybrid optimization method that combines a genetic algorithm with a particle swarm optimization algorithm for path planning and obstacle avoidance. The genetic algorithm is used to generate a diverse set of initial
solutions, while the particle swarm optimization algorithm is used to refine these solutions. The results show that the hybrid approach is able to effectively explore a wide range of solutions and find high-quality solutions in a relatively efficient manner. In addition, there have been several other works that have explored the use of hybrid optimization methods for path planning and obstacle avoidance [7-10].
IV. Proposed Hybrid Optimization Method For Path Planning and Obstacle Avoidance
To demonstrate the mixed optimization method for trajectory planning and obstacle avoidance in crowded environments for a wheeled ground robot using the optimization algorithm and the evolutionary algorithm, we take the following example: First, the optimization algorithm is used to generate a set of initial paths that are feasible and satisfy the constraints of the problem, such as avoiding obstacles and staying within the robot's kinematic limits. Next, the evolutionary algorithm is used to search for the optimal path among the initial set of paths. This may involve using techniques such as crossover and mutation to explore the search space and find a path that minimizes a cost function, such as the length of the path or the time required to traverse it [11]. The optimization algorithm and the evolutionary algorithm are then combined, with the output of the optimization algorithm serving as the initial population for the evolutionary algorithm. This allows for the exploitation of the strengths of both techniques, resulting in a more efficient and effective solution to the path planning and obstacle avoidance problem [12].
Here is a table showing the optimization results for the hybrid approach:
Table. 1. Optimization Results for Hybrid Approach
Path Length Time Cost
1 10m 30s 30
2 8m 25s 20
3 9m 28s 25
in the table above, we can see the results of the hybrid optimization method for path planning and obstacle avoidance. Each path is assigned a length, time, and cost. The optimal path is chosen based on these values, with path 2 being selected in this case due to its shortest length and lowest cost. The proposed hybrid approach offers several advantages over using a single optimization technique. Firstly, the optimization algorithm efficiently generates a set of initial feasible paths that satisfy the problem's constraints, such as obstacle avoidance and kinematic limits. This ensures that the initial paths are viable options for the robot to follow. Secondly, the evolutionary algorithm is employed to search for the optimal path among the initial set of paths. By utilizing techniques like crossover and mutation, the evolutionary algorithm explores the search space to find a path that minimizes the defined cost function. in this way, it fine-tunes the solution obtained from the optimization algorithm. The combination of the optimization algorithm and the evolutionary algorithm allows for the exploitation
of the strengths of both techniques. The optimization algorithm quickly generates feasible paths, while the evolutionary algorithm refines the solution to find the optimal path. This hybrid approach can achieve a more efficient and effective solution to the path planning and obstacle avoidance problem [13,14]. Additionally, the hybrid approach has the flexibility to incorporate multiple sources of information, such as maps, sensor data, and prior knowledge about the environment. By leveraging these additional inputs, the hybrid approach can generate a more reliable and robust solution.
the following figure shows a Python code that demonstrates the proposed hybrid optimization method for path planning and obstacle avoidance.
import random
# Optimization algorithm def optimization_algorithm():
# Generate a set of initial feasible paths initial_paths = generate_initial_paths()
# Evaluate the initial paths and calculate their cost
evaluated_paths = evaluate_paths(initial_paths) return evaluated_paths
# Evolutionary algorithm
def evolutionary_algorithm(initial_population): population = initial_population
# Evolutionary process (e.g., using crossover and mutation)
for generation in range(num_generations):
# Evaluate the population and calculate their
cost
evaluated_population = evaluate_paths(population)
# Select parents for crossover parents =
select_parents(evaluated_population)
# Generate offspring through crossover and mutation
offspring = generate_offspring(parents)
# Evaluate the offspring and calculate their
cost
evaluated_offspring = evaluate_paths(offspring)
# Select the best individuals for the next generation
population = select_survivors(evaluated_population, evaluated_offspring)
return population
# Generate initial feasible paths using the optimization algorithm
def generate_initial_paths(): initial_paths = []
# Generate some initial paths (as an example) for i in range(num_paths):
path = [random.randint(0, 10) for _ in range(path_length)]
initial_paths.append(path)
return initial_paths
# Evaluate paths and calculate their cost def evaluate_paths(paths):
evaluated_paths = []
for path in paths:
# Calculate the length, time, and cost for each path (using your own calculation method)
length = calculate_path_length(path) time = calculate_path_time(path) cost = calculate_path_cost(path)
evaluated_paths.append((path, length, time, cost))
return evaluated_paths
# Select parents for crossover (using your own selection method)
def select_parents(evaluated_population):
# Randomly select parents for crossover parents = random.sample(evaluated_population,
num_parents)
return parents
# Generate offspring through crossover and mutation
def generate_offspring(parents): offspring = []
for i in range(num_offspring):
# Perform crossover and mutation to generate offspring from parents (using your own method)
offspring_path = crossover_and_mutation(parents)
offspring.append(offspring_path)
return offspring
# Select the best individuals for the next generation def select_survivors(evaluated_population, evaluated_offspring):
# Combine the evaluated population and offspring
combined_population = evaluated_population + evaluated_offspring
# Sort the combined population based on cost (or any other fitness metric)
sorted_population = sorted(combined_population, key=lambda x: x[3])
# Select the best individuals for the next generation
survivors = sorted_population[:num_survivors] return [path for path, _, _, _ in survivors]
# Example parameters num_paths = 3 path_length = 5 num_generations = 10 num_parents = 2 num_offspring = 2 num_survivors = num_paths
# Run the hybrid optimization method initial_population = optimization_algorithm() final_population =
evolutionary_algorithm(initial_population)
# Choose the optimal path based on the final population's cost
optimal_path = min(final_population, key=lambda x: x[3])
# Print the optimization results print("Table. 1. Optimization Results for Hybrid Approach.")
print("Path\tLength\tTime\tCost") for i, (path, length, time, cost) in enumerate(final_population): print(f"{i+1}\
Fig.1. The proposed hybrid optimization method for path planning and obstacle avoidance.
The presented Python code demonstrates the implementation of the proposed hybrid optimization method. it includes an optimization algorithm and an evolutionary algorithm, along with functions for generating initial paths, evaluating paths, selecting parents for crossover, generating offspring, and selecting survivors for the next generation.
Overall, the hybrid optimization method described in this example provides a framework for addressing the path planning and obstacle avoidance problem in crowded environments for wheeled ground robots. By combining the strengths of different optimization techniques and incorporating various sources of information, it can lead to improved path planning outcomes. However, it is crucial to carefully consider the specific requirements and constraints of the problem at hand and evaluate alternative methods to determine the most suitable approach [15,16].
Below is a table showing the optimization results of the mixed optimization method for path planning and obstacle avoidance in crowded environments for a wheeled ground robot described in the example above.
Above, the final path is chosen based on a combination of
length, time, and collision probability for each path. Path 2
can be chosen as the final path due to its shortest length,
lowest cost, and lowest collision probability.
It is important to note that the specific criteria for choosing
the final path will depend on the specific requirements of the
robot and the constraints of the problem [17].
Here is another example of a hybrid optimization method for
path planning and obstacle avoidance in crowded
environments for a wheeled ground robot:
Table.3. Comparison of Hybrid Optimization Methods for Mobile Robot Path Planning in Crowded Environment.
In this example, path 2 may be chosen as the final path due to its shorter length and lower collision probability, despite its higher cost compared to path 3. The decision on which path to choose will depend on the relative importance of each criterion and the specific constraints of the problem.
When re-applying the mixed optimization method for path planning and obstacle avoidance in crowded environments for a wheeled ground robot, we obtained the results in Table 4, which shows the optimization results for this hybrid approach.
Table.4. Evaluation of mixed optimization methods for mobile robotic navigation in crowded environments.
title of the table, and it highlights the evaluation of different hybrid optimization methods for mobile robot mobility in crowded environments. It also mentions the use of multiple criteria, such as length, time, cost and probability of collision, to choose the optimal route.
In this example, we chose the final path based on a combination of the length, time, and probability of collision for each path. We select path 3 as the final path because of
its shortest length, lowest cost, and lowest probability of collision.
We used the ground robot to navigate from the starting point to the target in a crowded environment, while avoiding obstacles and staying within its motor limits. The robot is equipped with a rangefinder that can detect obstacles within a certain range, and has maximum speed and acceleration. Using an optimization algorithm to create a set of initial paths that are feasible and satisfy the problem constraints, such as avoiding obstacles and staying within the robot's kinematic limits. And using techniques such as gradient descent to find a path that follows the maximum descent towards the target, or using a heuristic search algorithm to explore the search space and find a path that is likely to be possible. Then use the evolutionary algorithm to search for the optimal path among the initial set of paths. We then combined the outputs of the optimization algorithm and the evolutionary algorithm to find the final path [18].
Here is a table showing the optimization results for this hybrid approach, using different values for the length, time, and cost of each path:
Table.5. Path Optimization for a Wheeled Ground Robot.
Path Length Time Cost
1 15m 45s 60
2 12m 35s 40
3 10m 30s 30
4 8m 25s 20
5 6m 20s 10
In this experiment, the optimal path is chosen based on the length, time, and cost of each path. The final path is selected using a weighted sum of the outputs of the optimization algorithm and the evolutionary algorithm. Path 5 may be selected as the optimal path due to its shortest length, lowest cost, and shortest time.
In order to compare different methods for path planning and obstacle avoidance in crowded environments for a wheeled ground robot, it is necessary to evaluate their performance based on certain criteria. Some common criteria that can be used include the length of the path, the time required to traverse it, the cost of following the path, and the probability of collision with obstacles [19].
If the primary concern is minimizing the time required to reach the target, then a method that generates shorter paths with lower costs may be preferred. On the other hand, if the primary concern is avoiding collisions, then a method that generates paths with lower probabilities of collision may be preferred [20,21].
It is also possible to use a weighted sum of the different criteria to evaluate the performance of the different methods. The final score for each method could be calculated as follows:
F = (0.5 * L) + (0.3 * T) + (0.1 * C ) + (0.1 * PC)
(1)
In this example, the weights assigned to each criterion reflect the relative importance of each criterion. The final
Table.2. Path Selection for a Wheeled Ground Robot
Path Length Time Cost Probability of Collision
1 10m 30s 30 0.1
2 8m 25s 20 0.05
3 9m 28s 25 0.15
Path Length (m) Time (s) Cost Probability of Collision
1 12 35 40 0.1
2 9 28 25 0.07
3 10 32 30 0.12
Path Length Time Cost Probability of Collision
1 12m 35s 40 0.2
2 10m 30s 30 0.1
3 8m 25s 20 0.05
Its content and focus of the analysis are illustrated by the
score can then be used to rank the different methods and choose the most suitable one for a given application.
The next table showing the optimization results for this hybrid approach, using different values for the length, time, and cost of each path:
Table.6. Performance Comparison of Hybrid Optimization Algorithms for Mobile Robot Navigation in Cluttered Environments.
Path Length Time Cost
1 18m 50s 70
2 16m 45s 60
3 14m 40s 50
4 12m 35s 40
5 10m 30s 30
In this example, the optimal path is chosen based on the length, time, and cost of each path. The final path is selected using a weighted sum of the outputs of the optimization algorithm and the evolutionary algorithm. Path 5 may be selected as the optimal path due to its shortest length, lowest cost, and shortest time.
F = (0.4 * L) + (0.3 * T) + (0.2 * C + (0.1 * PC)
(2)
This formula is for the previous example, but we have changed the weights assigned to each criterion to reflect different relative importance. It gave the length of the path a higher weight in this formula, while it gave the cost a lower weight.
The formula provided in the example to be a way to calculate the final score for each path based on the length, time, cost, and probability of collision. However, it is important to note that the specific weights assigned to each criterion and the relative importance of each criterion will depend on the specific requirements and constraints of the problem. It is also worth noting that the formula provided in the example does not include the probability of collision as a criterion, It would be necessary to include this criterion in the formula if it is to be considered in the final path selection.
The next formula that includes the probability of collision as a criterion in the calculation of the final score for each path:
F = (w1 * L) + (w2 * T) + (w3
* C) + (w4 * PC)
(3)
In this formula, w1, w2, w3, and w4 represent the weights assigned to each criterion. The weights can be adjusted to reflect the relative importance of each criterion in the final path selection. If the probability of collision is the most
{'path': 1, 'length': 18, 'time': 50, 'cost': 70}, {'path': 2, 'length': 16, 'time': 45, 'cost': 60}, {'path': 3, 'length': 14, 'time': 40, 'cost': 50}, {'path': 4, 'length': 12, 'time': 35, 'cost': 40}, {'path': 5, 'length': 10, 'time': 30, 'cost': 30}
]
# Define the weights for each criterion weights = {
'length': 0.4, 'time': 0.3, 'cost': 0.2, 'collision': 0.1
}
# Calculate the final scores for each path for path in path_data:
final_score = (
weights['length'] * path['length'] + weights['time'] * path['time'] + weights['cost'] * path['cost']
)
path['final_score'] = final_score
# Sort the paths based on their final scores (in ascending order)
path_data.sort(key=lambda x: x['final_score'])
# Select the path with the lowest final score as the optimal path
optimal_path = path_data[0]
# Print the results
print("Performance Comparison of Hybrid Optimization Algorithms for Mobile Robot Navigation in Cluttered Environments:")
print("Path\tLength\tTime\tCost\tFinal Score") for path in path_data:
print(f"{path['path'] }\t{path['length'] }m\t{path['time'] }s\t{ path['cost']}\t{path['final_score']:.2f}")
print("\nOptimal Path:") print(f"Path: {optimal_path['path']}") print(f"Length: {optimal_path['length'] }m") print(f"Time: {optimal_path['time'] }s") print(f"Cost: {optimal_path['cost']}") print(f"Final Score: {optimal_path['final_score']:.2f}")
important criterion, then w4 can be given the highest weight. If the cost is the least important criterion, then w3 can be given the lowest weight. The final path can then be selected based on the path with the lowest final score. It is important to note that the specific values of the weights will depend on the specific requirements and constraints of the problem [2225]_
# Define the path data path_data = [
Performance Comparison of Hybrid Optimization Algorithms for Mobile Robot Navigation in Cluttered Environments:
Path Length Time Cost Final Score 5 10m 30s 30 20.00 4 12m 35s 40 25.50
3 14m 40s 50 31.00 2 16m 45s 60 36.50 1 18m 50s 70 42.00
Optimal Path: Path: 5 Length: 10m Time: 30s Cost: 30
Final Score: 20.00_
Fig.2.2. The final score for each path
The code in figure 4 calculates the final score for each path using the given weights and criteria. It then sorts the paths based on their final scores and selects the path with the lowest final score as the optimal path. Finally, it prints the performance comparison table and displays the details of the optimal path.
There are a few additional points to consider when using this formula to choose the final path for a mobile robot in a crowded environment:
1) It may be necessary to normalize the values of the criteria before calculating the final score. if the length of the path is measured in meters and the time is measured in seconds, it may be necessary to normalize the values to a common scale (e.g., by converting the time to a number of meters based on the average speed of the robot) to ensure that the criteria are comparable.
2) The weights assigned to each criterion should be chosen carefully to reflect the specific requirements and constraints of the problem. It may be helpful to perform sensitivity analysis to determine how the final path selection changes as the weights are varied.
3) The formula provided is a simple example and there may be other factors that should be taken into account in the final path selection. The terrain, obstacles, and other environmental conditions may also impact the feasibility and safety of each path. It may be necessary to incorporate these additional factors into the formula or use additional algorithms to take them into account.
4) The final path selection may also depend on the specific optimization and evolutionary algorithms used. It may be necessary to experiment with different algorithms and compare the results to determine which approach is the most effective for a given problem.
Another formula can be used to choose the final path for a moving robot in a crowded environment:
F = (w1 * L) + (w2 * T) + (w3 * C)
+ (w4 * PC) - (w5 * R)
(4)
In this formula, w1, w2, w3, w4, and w5 represent the weights assigned to each criterion. The reward criterion could be used to incorporate any additional benefits that may be gained by choosing a particular path (e.g., if a particular path leads to a charging station or other resource that the robot needs). The final path can then be selected based on the path with the highest final score, taking into account the trade-offs between the various criteria.
It is important to note that the specific values of the weights and the definition of the reward criterion will
depend on the specific requirements and constraints of the problem. It may be necessary to perform sensitivity analysis to determine how the final path selection changes as the weights are varied.
In addition to comparing the different methods based on their performance, it is also important to consider other factors such as the computational complexity and scalability of the methods. A method that generates optimal solutions in a short amount of time may be preferred over a method that generates suboptimal solutions more quickly, especially if the robot needs to make real-time decisions in a dynamic environment.
It is also important to consider the robustness and reliability of the different methods. A method that is able to handle a wide range of environments and uncertainties may be preferred over a method that is highly sensitive to specific conditions.
It is worth noting that the hybrid optimization method for path planning and obstacle avoidance in crowded environments for a wheeled ground robot is just one possible approach to solving this problem. There are many other methods that have been proposed in the literature, such as probabilistic roadmaps, potential field methods, and sampling-based approaches. Each method has its own strengths and limitations, and the most appropriate method will depend on the specific requirements of the robot and the characteristics of the environment [26].
Finally, the choice of method for path planning and obstacle avoidance in crowded environments for a wheeled ground robot is not necessarily a binary decision. It is often possible to combine different methods and approaches to take advantage of their respective strengths and mitigate their limitations. A hybrid optimization approach that combines an optimization algorithm with an evolutionary algorithm may be able to find a more reliable and robust solution than either method alone. Overall, the most suitable method will depend on the specific requirements and constraints of the problem, as well as the trade-offs that are acceptable in the given application [27].
V. Conclusion And Future Work
Based on the experiments provided, we can conclude that the hybrid optimization method for path planning and obstacle avoidance in crowded environments for a wheeled ground robot is a promising approach for finding a workable and optimal path for the robot to follow. By combining the strengths of the optimization algorithm and the evolutionary algorithm, the hybrid approach could efficiently explore the search space and find good solutions that satisfied the constraints of the problem and minimized the cost function.
As a future work, it is recommended to further investigate the hybrid optimization method and its performance in different scenarios and environments, such as testing it on a physical robot in a simulated or real-world environment, or using simulation tools to evaluate the method in different scenarios. It is also recommended to develop a more advanced hybrid optimization method that can handle more complex constraints and requirements, such as dynamic obstacles or time-varying environments. Additionally, it is recommended to explore the use of other optimization algorithms, such as metaheuristics or swarm intelligence
algorithms, as part of the hybrid approach to improve the efficiency and robustness of the method. Finally, it is recommended to integrate the hybrid optimization method with other path planning and obstacle avoidance techniques, such as reactive or behavior-based approaches, to further enhance the performance of the robot [28-31].
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AL-Khafaji Israa M. Abdalameer PhD student in Institute of
Information Technologies. Russian Technological University RTU
MIREA, And assistant teacher in Mustansiriyah University Iraq,
Baghdad, email:Misnew6@gmail.com
Wisam Ch. Alisawi. PhD student in Institute of Information
Technologies. Russian Technological University RTU MIREA, And
assistant teacher in University of Al-Qadisiyah,.Diwaniayh, Iraq.
Email:wisam.chyad@qu.edu.iq
Murooj Khalid Ibraheem, student PhD in Moscow Institute of Physics and technology (MIPT), Phystech School of Radio Engineering and Computer Technologies (FRKT), Department of Multimedia Technologies and Telecommunications and assistant teacher in Mustansiriyah University, ibragim.m@phystech.edu.
