Journal of Robotics and Control (JRC) Volume 6.
Issue 4, 2025 ISSN: 2715-5072.
DOI: 10.
18196/jrc.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Alami Essaadoui 1 .
Youssef Baba 2 .
Oussama Hamed 3* .
Mohamed Hamlich 4 .
Chafik Guemimi 5 .
Ali EL Kebch 6
1,2,3,4,5,6
University of Hassan II.
Ensam.
CCPS Laboratory.
Casablanca.
Morocco Univ.
Aix-Marseille.
Laboratoire dAoInformatique et SysteAmes.
Marseille.
France Email: 1 alami70@yahoo.
fr, 2 youssefbaba@gmail.
com, 3 oussama.
hamed@univ-amu.
hamlich@gmail.
com, 5 guemimichafik@gmail.
com, 6 alibec ma@yahoo.
*Corresponding Author AbstractAiPath planning in cluttered and uncertain environments remains a significant challenge in robotics, autonomous navigation, and logistics optimization.
This paper proposes a novel Adaptive Hybrid PSO-ACO Planner, which synergistically combines Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) to compute efficient paths in grid-based environments with static obstacles.
Unlike traditional fixed-phase hybrids, our approach features a dynamic switching strategy between PSO and ACO based on real-time convergence behavior, allowing the algorithm to maintain progress and escape local Additionally, adaptive parameter tuning is integrated to enhance the balance between global exploration and local exploitation throughout the search.
The switching logic is governed by two criteria: a stagnation threshold that triggers phase transitions and a progress-dependent adaptation mechanism that adjusts search intensities over time.
PSO dominates the early search phase, rapidly exploring the solution space, while ACO refines promising paths through pheromone-guided optimization in later stages.
The proposed planner also includes a path reconstruction module to ensure solution completeness and robustness.
Experimental evaluations on grid-based environments demonstrate that the proposed method consistently achieves higher path quality and faster convergence compared to standalone PSO and ACO approaches.
Quantitative results demonstrate notable improvements in path efficiency and overall success rate across a range of obstacle These advancements establish the Adaptive Hybrid PSOACO Planner as a robust and efficient tool for real-time and practical deployment in autonomous robot navigation systems.
KeywordsAiPath Planning.
Hybrid Metaheuristics.
Particle Swarm Optimization (PSO).
Ant Colony Optimization (ACO).
Adaptive Switching.
Robot Navigation I NTRODUCTION Path planning is one of the most critical tasks in the field of robotics and autonomous navigation.
Whether in the context of mobile robots, unmanned ground vehicles, or autonomous delivery systems, the ability to compute an efficient and collisionfree path from a starting point to a desired goal remains a fundamental challenge .
Ae.
This task becomes particularly complex in environments with static or dynamic obstacles, limited perception, or uncertainty .
Ae.
Robots operating in such environments often deal with sensor noise, limited field-of-view, and dynamically changing surroundings, making static planning approaches insufficient.
In these scenarios, a robot must intelligently explore the environment, reason about constraints, and adapt its trajectory in real time to ensure safe and successful navigation .
Ae.
The importance of reliable and optimized path planning extends across a wide range of practical applications.
In industrial settings, automated guided vehicles (AGV.
depend on efficient path planning to move goods within warehouses .
Ae.
urban mobility, self-driving cars must continuously plan their paths to navigate traffic while ensuring passenger safety .
Ae .
In emergency and rescue missions, mobile robots are deployed in unknown terrains where path planning must be robust against unexpected barriers and limited sensor coverage .
Ae .
Therefore, the effectiveness of path planning algorithms has a direct impact on the operational performance, reliability, and safety of robotic systems .
Ae.
Over the years, numerous approaches have been proposed for solving the path planning problem.
Classical methods such as DijkstraAos algorithm and A* provide deterministic solutions but often struggle with scalability and adaptability in complex or dynamic environments .
Ae.
Metaheuristic techniques, including Particle Swarm Optimization (PSO).
Ant Colony Optimization (ACO), and Genetic Algorithms (GA), have gained popularity due to their flexibility and global search capabilities .
Ae.
However, these algorithms also suffer from limitations.
PSO
can rapidly explore the search space but may converge prematurely to suboptimal solutions .
, .
ACO is powerful for local exploitation but tends to slow down as the search progresses .
Ae.
Journal Web site: http://journal.
id/index.
php/jrc Journal Email: jrc@umy.
Journal of Robotics and Control (JRC) ISSN: 2715-5072 Hybrid models that combine these algorithms have been introduced, yet most of them rely on fixed or manually defined transitions, lacking real-time adaptability and responsiveness to convergence behavior .
Ae.
Despite their promise, existing hybrid PSO-ACO approaches fall short in dynamic decision-making.
They typically use static, fixed-sequence integration strategies, which are insensitive to real-time convergence behavior and unable to adapt based on performance feedback.
Furthermore, many approaches introduce significant implementation complexity and computational cost, without adequately addressing their scalability in realworld robotic systems.
To overcome these limitations, this paper proposes an adaptive Hybrid PSO-ACO Path Planner that integrates PSO and ACO in a cooperative and adaptive framework .
Ae.
The novelty of this approach lies in its dynamic phaseswitching mechanism, which allows the planner to alternate between PSO and ACO based on the observed stagnation of convergence and the progress of optimization.
PSO dominates the early search stage to encourage broad exploration, while ACO enhances promising paths using pheromone-based reinforcement during the later stages.
The algorithm also incorporates adaptive parameter tuning to continuously balance exploration and exploitation throughout the search process.
The decision to transition between PSO and ACO is governed by two key factors: .
a stagnation threshold that indicates when progress has plateaued, and .
a progress-driven adaptation mechanism that tunes algorithmic parameters to maintain diversity early and promote convergence Initially, the algorithm employs PSO to explore the gridbased environment broadly, generating candidate paths through particle movements influenced by both global and personal When improvement stalls or the search becomes localized, the planner transitions to ACO, where pheromone trails guide the search through high-quality regions.
This switching process is bidirectional, allowing the system to re-invoke PSO if needed, and ensures that both exploration and exploitation are applied effectively and at the right moments.
Additionally, the planner integrates adaptive parameter tuning, a visibility-based heuristic, and a path completion and enhancement module that reconstructs or extends paths to ensure full connectivity from start to goal.
The main contributions of this work are: .
an adaptive hybrid path planning framework that adaptively switches between PSO and ACO based on stagnation and progress, ensuring robustness and flexibility in complex environments.
a progress-aware parameter adjustment scheme that balances exploration and exploitation throughout the search.
a path validation and enhancement mechanism that ensures solution completeness and quality without requiring a full While our experiments are conducted in static grid-based environments, the proposed framework is designed with extensibility in mind.
Future work will focus on dynamic scenarios, continuous space navigation, and real-time deployment using ROS-Gazebo on physical robots.
We also aim to investigate the influence of noisy sensors and uncertainty-aware models to further enhance real-world applicability.
Furthermore, we acknowledge that while our method improves adaptability, it introduces additional algorithmic complexity and computation This trade-off is discussed further in the conclusion.
The proposed method has been rigorously evaluated and compared against standalone PSO.
ACO, and other hybrid variants such as PSO-GA and GA-ACO.
The results demonstrate that the Adaptive Hybrid PSO-ACO Planner consistently achieves superior performance in terms of path optimality, success rate, convergence behavior, and overall reliability.
These findings confirm the effectiveness of the approach and underscore its potential for real-world applications in autonomous navigation systems.
The rest of the paper is structured as follows: Section 2 explains the theoretical background of PSO and ACO and details the proposed dynamic hybrid methodology.
Section 3 discusses the experimental results and benchmarks.
Finally.
Section 4 concludes the paper and outlines directions for future II.
R ELATED W ORKS
Path planning in cluttered and dynamic environments is still one of the most challenging tasks in mobile robotics.
Several nature-inspired optimization algorithms have been proposed to solve this problem, among them PSO and ACO are considered two of the most widely used approaches.
PSO is a populationbased stochastic optimization method introduced by Kennedy and Eberhart .
It mimics the social behavior of bird flocking and has shown fast convergence during the initial search However, standard PSO often suffers from premature convergence and lacks robustness in complex environments.
overcome these limitations, hybrid versions of PSO with other metaheuristics have been proposed.
ACO, developed by Dorigo and Gambardella .
, is inspired by the pheromone trail behavior of ants.
It is well adapted for solving discrete and combinatorial problems such as gridbased path planning.
ACO performs well in terms of solution refinement but requires more iterations to converge, especially in large search spaces.
To enhance performance, recent studies have proposed combining PSO and ACO into hybrid frameworks.
These hybrid approaches exploit the global exploration capacity of PSO and the local exploitation capability of ACO.
In .
, a two-layer strategy was proposed for wheeled mobile robots by combining an improved ACO algorithm for global path generation with a Dynamic Window Approach (DWA) for local obstacle avoidance.
Another work in .
Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 proposed a hybrid PSO-DWA method for unmanned surface vehicles, where adaptive parameter control was introduced to improve convergence and reduce oscillation near obstacles.
In the context of aerial vehicles, .
developed a hybrid dung beetle optimization algorithm for 3D path planning that integrates chaotic mapping and adaptive inertia to overcome local minima.
A recent work in .
introduced a dynamic PSO-based planner, named OkayPlan, which considers obstacle kinematics in real time.
It formulates the problem as a constrained optimization task and solves it using a modified PSO scheme.
All these works demonstrate that hybrid and adaptive methods can significantly improve the efficiency and reliability of autonomous navigation in uncertain environments.
Despite these improvements, most hybrid strategies adopt static switching rules or fixed weights between phases, which limits their responsiveness to stagnation or sudden changes in the environment.
In contrast, the method proposed in this paper introduces an adaptive hybrid PSO-ACO planner that dynamically switches between phases based on convergence A stagnation-based logic is used to alternate between PSO and ACO phases, while adaptive parameter adjustment ensures balanced exploration and exploitation during the entire planning process.
Compared to existing approaches, this strategy improves robustness and convergence speed in dense obstacle environments.
M ETHOD
This section presents the principal techniques used in this Two nature-inspired algorithms are first introduced: PSO and ACO.
These methods have demonstrated effectiveness in solving complex path planning problems.
Afterwards, the proposed adaptive hybrid approach, which combines both techniques in an adaptive framework, is detailed.
The method alternates between PSO and ACO phases based on the systemAos performance, allowing efficient exploration of the search space and rapid convergence toward an optimal path.
where pEbest,i is the personal best position found by particle i.
Egbest is the global best position found so far by the swarm.
O is the inertia weight, and c1 , c2 are cognitive and social learning coefficients respectively.
The variables r1 , r2 are random numbers uniformly distributed in .
, .
The main steps of the PSO procedure used in this work are summarized in the following pseudocode.
Algorithm 1: Particle Swarm Optimization Input: Objective function f , particles N , iterations T , inertia weight O, coefficients c1 , c2 Output: Global best solution Egbest Initialize positions pEi and velocities Evi randomly for each particle i = 1, .
A Set p Ebest,i Ia pEi , and Egbest Ia arg mini f (E pbest,i ) A For t = 1 to T :
Ae For each particle i:
O Sample r1 , r2 O U.
, .
O Update velocity: Evi Ia OEvi c1 r1 (E pbest,i Oe pEi ) c2 r2 (Egbest Oe pEi ) O Update position: pEi Ia pEi Evi O If f (E pi ) < f (E pbest,i ), then pEbest,i Ia pEi O If f (E pi ) < f (Egbest ), then Egbest Ia pEi A Return E In this work.
PSO is employed for initial exploration and for enhancing candidate paths by refining selected waypoints in the solution space.
Ant Colony Optimization ACO is a nature-inspired algorithm based on the behavior of real ants searching for food.
Each ant constructs a path by moving from node to node according to a probabilistic rule that combines pheromone intensity and heuristic information.
The movement probability from a node i to a node j is given by:
[Eij ] .
j ] Pij = P [Eik ] .
k ] Particle Swarm Optimization .
kOONi In PSO, each particle represents a potential solution in the search space, and all particles move within the space by adjusting their velocities and positions based on their own experience and the experience of neighboring particles.
The velocity Ev and position pE updates of a particle are governed by the equations:
Evi .
= OEvi .
c1 r1 (E pbest,i Oe pEi .
) c2 r2 (Egbest Oe pEi .
) .
pEi .
= pEi .
Evi .
Here.
Eij is the pheromone value on edge .
, .
, and ij represents the heuristic information.
In this method, ij is defined as:
ij = dij A .
where dij is the Euclidean distance from node j to the goal, and A is a small constant added to avoid division by zero.
To improve navigation in cluttered environments, the heuristic component is further combined with a visibility map that evaluates the number of free neighboring cells.
Therefore, the Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 total movement probability toward a neighbor j includes an exploration component and is computed as:
Pj Oy (Ej1.
5 ) A .
0 ) A j A .
Oe A) .
where j is the visibility of node j, is the exploration factor, and A OO .
, .
represents the normalized progress through the optimization cycles.
After all ants complete their tours, the pheromone matrix is updated using the following rule:
Eij Ia .
Oe ) A Eij OIEij where is the evaporation rate, and OIEij is the pheromone deposited by ant k, defined as:
A O, if edge .
, .
is in the best path of ant k .
OIEij = Lk Here.
Q is a constant.
Lk is the length of the path generated by ant k, and O is a reinforcement coefficient applied to elite The main steps of the ACO procedure implemented in this work are summarized below.
Algorithm 2: Ant Colony Optimization Input: Graph G = (V.
E), pheromone matrix E , heuristic matrix , number of ants m, parameters , , .
O, .
Output: Best path found.
Initialize pheromone levels Eij uniformly.
For iteration t = 1 to T :
Ae For each ant k = 1, .
, m:
O Build a complete path using:
Pij P [Eij ] .
j lOON [Eil ] .
l ] O Adjust ij with visibility if needed.
Ae Update pheromone values: Eij Ia .
Oe ) A Eij .
ij , where k=1 OIE( A O, if .
, .
OO best path of ant k .
OIEij = Lk A Return the best path found so far.
This pheromone-guided learning process allows the ants to collectively refine the solution space, reinforcing paths that are shorter, safer, and more complete.
When used in alternation with PSO, the ACO phase plays a critical role in fine-tuning the best candidate paths identified during the global exploration autonomous robot navigation.
The objective is to efficiently compute collision-free paths in static, grid-based environments while avoiding premature convergence and stagnation.
Unlike conventional hybridization strategies that operate on fixed sequencing, the proposed method employs a dynamic switching mechanism regulated by convergence indicators and adaptive progress metrics.
This allows the planner to seamlessly transition between PSO and ACO phases based on real-time performance feedback, ensuring consistent search diversity and refined exploitation throughout the optimization horizon.
Although the hybridization does not offer formal convergence guarantees, it is grounded in adaptive metaheuristics literature and supported by strong empirical results.
The stagnationaware switching mechanism and dynamic parameter adaptation collectively form a responsive framework that maintains search diversity and avoids premature convergence.
This limitation has been clearly stated and suggested for future theoretical .
Overview of the Planner: The navigation environment is modeled as a 2D occupancy grid , where each cell is labeled as either free .
or occupied .
The robot starts at a defined position and seeks to reach a target position while avoiding obstacles.
The planning procedure is executed across multiple optimization cycles, wherein each cycle consists of either a PSO-driven or ACO-driven path generation phase.
The selection of which optimization method to apply in each cycle is determined by the stagnation-aware switching logic.
Each generated path is evaluated based on completeness, feasibility, and optimality .
n terms of path lengt.
Only valid paths that successfully connect to are considered for updating the best-known solution .
The planner is equipped with path enhancement, reconstruction, and visualization modules to ensure the quality and interpretability of generated solutions.
Switching Mechanism Based on Stagnation Monitoring:
In the proposed hybrid framework, maintaining continuous progress in the optimization process is essential for avoiding premature convergence and escaping local optima.
To this end, a dynamic phase-switching mechanism is introduced, governed by a stagnation counter denoted .
This counter is incremented whenever successive optimization cycles fail to improve the length of the best-found path.
Let be the index of the current optimization cycle, and the length of the best complete path at cycle .
The evolution of the stagnation counter is defined as:
Adaptive Hybrid Path Planning Strategy This section details the development of the Adaptive Hybrid Metaheuristic Path Planning Algorithm, which intelligently integrates PSO and ACO within an adaptive framework for if Lbest c < Lbest c Oe 1 1, .
The counter is compared to a predefined stagnation threshold Once the threshold is reached (), the algorithm triggers a phase Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 transition to alternate between the two optimization strategies:
ACO,
if = PSO
Ia0
PSO,
if = ACO Let be the current optimization cycle and the total number of allowed cycles.
The normalized progress is defined by:
The switching logic described above is summarized in Fig.
which visually represents the decision process used to alternate between PSO and ACO phases in response to stagnation.
This scalar value serves as a temporal indicator of the optimization phase.
Three principal parameters are modulated by this progression variable: the exploration factor , the restart probability , and the elite emphasis .
Each plays a distinct role in regulating the behavior of the PSO and ACO modules.
Cmax A OO .
, .
Exploration Factor :
A(A) = max.
2, 0.
7 A .
Oe A)) .
This parameter influences the degree of randomness and visibility-driven bias in the ACO phase.
At early stages (), a higher promotes broad exploration.
As , decreases to concentrate search efforts near promising regions.
Restart Probability :
Ar (A) = max.
1, 0.
3 A .
Oe A)) Fig.
Flowchart illustrating the stagnation-based switching mechanism.
When the best path length no longer improves, a stagnation counter is incremented and compared to a predefined threshold s .
Once this threshold is reached, the planner switches between PSO and ACO phases adaptively Here, denotes the current operating phase of the algorithm.
The switching rule ensures that the system periodically introduces structural changes in the search behavior, allowing the algorithm to escape from regions where progress stalls due to suboptimal path convergence.
This adaptive alternation is especially beneficial in grid-based path planning problems where complex obstacle configurations can create deceptive basins in the search landscape.
PSO is better suited for global exploration during early cycles, rapidly covering large portions of the environment.
On the other hand.
ACO excels in fine-tuning and local exploitation due to its cumulative pheromone-based memory.
By switching between these phases in response to stagnation, the planner maintains a balance between intensification and diversification throughout the optimization horizon.
The switching logic and parameter scheduling are synchronized in a dual-feedback loop that governs both the strategy and behavior of the search dynamically.
This mechanism operates in conjunction with progressdependent parameter adjustment strategies to form a fully dynamic optimization engine capable of adapting its behavior over time without external supervision.
Adaptive Parameter Scheduling: To improve the efficiency and responsiveness of the hybrid optimization process, an adaptive scheduling strategy is integrated into the algorithm.
This mechanism adjusts key parameters in real-time according to the normalized optimization progress, enabling a smooth transition from exploration to exploitation as the search evolves.
Primarily used in PSO, this parameter determines the likelihood of particle reinitialization.
A higher value early in the search encourages diversity.
as the search matures, declines to reinforce exploitation.
Elite Emphasis :
e (A) = 1.
This coefficient amplifies the reinforcement of elite paths in ACO.
Increasing during late stages strengthens convergence by directing ants toward the most successful trajectories.
Together, these adaptive parameters define a dynamic behavioral profile.
Initially, the system emphasizes exploration to discover diverse regions.
As progress accumulates, the search gradually shifts to intensification near high-quality paths.
sensitivity study in results section evaluates how these adaptive rules perform across a variety of grid sizes and obstacle The results confirm that the planner remains robust and effective even with parameter variation.
Path Validation and Reconstruction: To ensure the feasibility and completeness of generated solutions, each candidate path P = .
0 , n1 , .
, nk } is subjected to a strict validation This process enforces two critical conditions:
Start and Goal Alignment: The path must begin at the designated start node S and terminate at the goal node Go .
Formally:
n 0=S n k=G o Obstacle Avoidance: Every node ni OO P must lie within a free cell of the occupancy grid G, i.
, no part of the path may intersect any obstacle or invalid region.
Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 If either of these conditions is violated .
articularly if the goal is not reache.
, the planner initiates a greedy path reconstruction process to attempt a rapid correction.
Starting from the last node nk of the incomplete path, a greedy search is executed to extend the trajectory to the goal:
P A = greedy path.
G .
If the greedy extension P A is successful, the final corrected path is assembled by appending the extension to the original path while avoiding node duplication:
Pfinal = P O P A .
:] .
In scenarios involving dense or irregular obstacle configurations, direct greedy reconstruction may fail due to occluded corridors or dead-ends.
In such cases, the system introduces intermediate waypoints selected near the midpoint between the current path and the goal.
These waypoints serve as subgoals, dividing the reconstruction into smaller, more tractable subproblems.
The resulting path is composed of concatenated greedy P final = greedy path.
k, .
O greedy path.
G .
where w is a valid intermediate waypoint located within a navigable corridor.
This modular reconstruction strategy significantly enhances the plannerAos robustness.
Rather than discarding partially valid paths and reinitializing the entire optimization process, the planner preserves useful subpaths and incrementally repairs Nonetheless, the greedy reconstruction mechanism may face limitations in highly dynamic or non-uniform environments.
Future work will explore integrating local replanning, backtracking, or learning-based heuristics to improve repair reliability under real-world uncertainty.
This approach reduces computational waste and improves convergence in complex, high-obstacle environments.
Formal Description of the Proposed Algorithm: The following algorithm summarizes the core execution flow of the proposed adaptive hybrid planner.
It integrates the adaptive scheduling of key parameters, stagnation-aware phase switching, and path validation mechanisms described previously.
The optimization alternates between PSO and ACO phases, progressively refining the solution while responding to search The final path is either the best valid trajectory discovered or a reconstructed extension of an incomplete one.
Algorithm 3: Adaptive Hybrid PSO-ACO Path Planning Input: Occupancy grid G, start node S, goal node Go , maximum cycles Cmax , stagnation threshold s Output: Optimized path Pbest Initialize: Pbest Ia OI.
Lbest Ia O.
Ia 0.
Ia PSO For each cycle c = 1 to Cmax :
Ae Compute progress ratio A Ia c/Cmax Ae Update parameters: A(A).
Ar (A), e (A) Ae If = PSO:
O If Pbest = OI: Pnew Ia global exploration() O Else: Pnew Ia path enhancement(Pbest ) Ae Else if = ACO: Pnew Ia aco phase(A) Ae If Pnew is valid and complete:
O If |Pnew | < Lbest : Pbest Ia Pnew .
Lbest |Pnew |.
Ia 0 O Else: Ia 1 Ae Else: Ia 1 Ae If Ou s :
O If = PSO: Ia ACO O Else: Ia PSO O Ia0 A If Pbest Pbest complete path to goal(Pbest ) A Return: Pbest Ia Ia IV.
R ESULTS AND D ISCUSSIONS
This section presents a detailed evaluation of the proposed Dynamic Hybrid PSO-ACO Planner, benchmarked against several path planning algorithms in grid-based environments.
The hybrid modelAos dynamic phase-switching, adaptive parameter tuning, and path enhancement capabilities were tested under consistent conditions and validated using both statistical performance metrics and simulated visual scenarios.
Simulation Environment and Setup All simulations were performed on a 20 y 20 grid with a static obstacle density ranging from 20% to 35%.
Obstacles were randomly generated but remained fixed for each comparative experiment.
The planner employs both 4-directional and 8-directional movement strategies.
The performance was measured across 50 independent runs per method.
Path Quality Evaluation The first criterion involves analyzing the path length generated by each algorithm.
Fig.
2 illustrates the average path lengths over 50 runs, highlighting the hybrid modelAos ability to produce shorter and more efficient paths compared to standalone PSO and ACO.
Although the A* algorithm produces the shortest paths, its deterministic design is not adaptable to real-time or uncertain The PSO-ACO planner, by contrast, achieves near-optimal results while retaining the flexibility of metaheuristic methods.
The relatively low standard deviation of the PSO-ACO solution also confirms its stability across trials.
These findings illustrate the hybrid plannerAos capacity to converge to high-quality solutions without excessive variability.
Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 performance indicator.
Success rate, convergence speed, and algorithmic stagnation provide insight into the robustness and responsiveness of a given method.
Table I presents the comparative performance of various algorithms across these metrics.
The Adaptive Hybrid PSO-ACO planner achieved the highest success rate among all metaheuristic strategies .
%).
Fig.
Comparison of execution time across different path planning algorithms Error bars indicate standard deviation over 50 independent runs Computational Efficiency Evaluating and comparing the average execution times of different path planning strategies is crucial to assess their practical applicability.
Fig.
3 summarizes the mean and standard deviation of execution time required by each algorithm under identical conditions.
The classical A* algorithm recorded the fastest time, completing in an average of 0.
1 seconds, attributed to its greedy and deterministic nature.
However, this advantage comes at the expense of flexibility and global optimality in more complex or changing environments.
Moreover, the hybrid approach required fewer iterations to find the first valid path .
2 on averag.
, significantly outperforming its standalone counterparts.
This efficiency is further reinforced by its low stagnation count, demonstrating that dynamic phase switching and adaptive parameter tuning effectively maintain optimization momentum and avoid local These results underscore the proposed methodAos capacity to deliver both high reliability and convergence efficiency in cluttered environments.
TABLE I.
P ERFORMANCE M ETRICS PER A LGORITHM : S UCCESS R ATE .
AVERAGE
I TERATIONS TO F IRST VALID PATH .
AND S TAGNATION C OUNT
Algorithm
PSO
ACO
PSO-ACO
GA-ACO
PSO-GA
Success Rate (%) Iterations to Path 5A2.
2A1.
2A1.
4A2.
1A1.
Stagnation Count In addition to reporting average values, we now include 95% confidence intervals for all key performance metrics.
Fig.
shows the success rate distributions with confidence bands across 30 trials per algorithm.
Significant differences were found in all comparisons.
< 0.
Fig.
Execution time comparison of various path planning algorithms.
The proposed PSO-ACO framework demonstrates a good balance between efficiency and solution Error bars represent standard deviation over 50 runs The proposed hybrid PSO-ACO algorithm offers a promising trade-off.
By dynamically alternating between explorationdriven PSO and exploitation-focused ACO, it preserves computational tractability while maintaining superior solution quality.
Notably, it achieves an average execution time of 1.
2 seconds only marginally higher than standalone PSO but significantly more efficient than GA-ACO or PSO-GA hybrids.
This efficiency, combined with its robustness and adaptiveness, renders it suitable for near real-time applications.
Success Rate and Stability In autonomous navigation, the plannerAos reliability in consistently computing feasible and complete paths is a crucial Fig.
Success rate comparison across five algorithms with 95% confidence intervals computed over 30 trials.
Path Smoothness and Safety Margin Two key indicators are considered: path smoothness, representing the average angular variation along the trajectory, and the safety margin, quantifying the mean clearance from surrounding obstacles.
As shown in Table II, the proposed PSOACO hybrid planner achieves a remarkable balance between these two metrics.
It outperforms standalone PSO and ACO in path smoothness .
12 radian.
, approaching the performance Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 of more exploitative strategies like GA-ACO.
This reflects the methodAos ability to generate feasible and fluid paths that respect the physical constraints of mobile platforms.
In terms of safety, the hybrid strategy preserves a generous average distance from obstacles .
41 unit.
, suggesting a cautious yet efficient navigation style.
The hybrid algorithm thus demonstrates its aptitude for navigating dense environments without compromising manoeuvrability.
TABLE II.
PATH S MOOTHNESS AND S AFETY M ARGIN PER A LGORITHM
Algorithm
PSO
ACO
PSO-ACO
GA-ACO
PSO-GA
Smoothness .
18 A 0.
14 A 0.
12 A 0.
10 A 0.
15 A 0.
Safety Margin 05 A 0.
35 A 0.
41 A 0.
30 A 0.
25 A 0.
Runtime and Memory Usage Analysis To evaluate the computational feasibility of the proposed adaptive hybrid framework, we conducted a performance analysis in terms of runtime and memory consumption across various map sizes and obstacle densities.
The results, summarized in Fig.
5, show that the algorithm scales reasonably well, with runtime increasing from 0.
82s for a 50x50 grid to 5.
76s for a 200x200 grid.
Similarly, memory usage grows from 15.
9MB.
Although the hybrid nature of the approach introduces additional overhead compared to standalone planners, the method remains tractable for offline or semi-static planning dominates across evaluation criteria and how efficiently it uses computational resources.
TABLE i.
C ONVERGENCE .
D OMINANCE ,
AND E FFICIENCY M ETRICS PER A LGORITHM
Algorithm
PSO
ACO
PSO-ACO
GA-ACO
PSO-GA
Convergence Rate (%) Dominance Ratio (%) Memory Usage (MB) 32 A 4
48 A 6
45 A 5
55 A 8
50 A 6
Progress Gradient Oe0.
9 A 0.
Oe1.
1 A 0.
Oe1.
5 A 0.
Oe0.
8 A 0.
Oe1.
2 A 0.
The hybrid PSO-ACO method exhibits strong convergence behavior, successfully reaching optimal or near-optimal paths in 95% of trials.
This performance is further validated by its high dominance ratio .
%), meaning it outperformed other methods in the majority of the evaluation metrics.
Although it consumes more memory than the deterministic A* algorithm, its usage remains moderate and justifiable given its enhanced flexibility and pathfinding reliability.
The progress gradient, defined as the average rate of improvement in the path length per iteration, is steepest for the hybrid planner.
This indicates effective learning and iterative refinement of solutions through dynamic switching and adaptive In contrast, the GA-based hybrids tend to stagnate earlier, reflecting less efficient search behaviors in comparison.
These findings support the conclusion that the hybrid PSO-ACO planner offers a strong compromise between computational cost and intelligent performance modulation, achieving competitive results in diverse and constrained environments.
Simulation-Based Validation To further validate the practical effectiveness of the proposed Dynamic Hybrid PSO-ACO planner, a series of simulations were conducted under varying environmental conditions.
These include changes in obstacle density and the type of allowed robot movements .
-directional vs.
8-directiona.
The visual outcomes from these simulations are presented in a sequence of figures, each illustrating the robotAos computed trajectory from the start to the goal position under a specific configuration.
Fig.
Runtime and memory usage of the hybrid PSO-ACO algorithm across increasing map sizes.
Convergence Behavior and Additional Metrics To complete the characterization of algorithmic performance.
Table i summarizes key metrics related to convergence dynamics, dominance, memory usage, and progress gradients.
These indicators collectively capture not only how reliably an algorithm converges to a solution, but also how consistently it Fig.
6 to Fig.
9 illustrate the plannerAos behavior using 4directional movement with obstacle ratios of 0.
35, 0.
30, 0.
20, respectively.
As the obstacle density decreases, the planner demonstrates progressively more direct and efficient In high-density scenarios .
Fig.
, the robot circumvents tight corridors with a preference for safer paths.
The trajectory shows strong clearance from obstacles, reflecting the plannerAos sensitivity to visibility and risk metrics.
As seen in Fig.
9, at 20% density, the path becomes significantly straighter and shorter.
This confirms that the planner not only adapts to cluttered environments but also capitalizes on free space when available, minimizing unnecessary directional The visual clarity of the paths also indicates the benefit of PSO-based global exploration during the initial search Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 Fig.
10 to Fig.
13 depict the planner operating under 8directional movement for the same obstacle densities.
The increased degrees of freedom result in visibly smoother and more compact paths.
In particular.
Fig.
11 and Fig.
12 reveal that the robot takes advantage of diagonal shortcuts to reduce path length while maintaining a reasonable safety margin.
Fig.
Trajectory generated with 4-directional movement and 35% obstacle density.
The planner follows a cautious path through narrow corridors, maintaining high clearance from obstacles Interestingly, under denser configurations .
Fig.
, the use of 8 actions allows the robot to bypass dead-ends and local traps more gracefully compared to the 4-directional constraint.
This flexibility complements the adaptive switching mechanism, enabling the hybrid planner to make fine-grained adjustments in tight situations.
The visual simulations reinforce the quantitative metrics discussed earlier.
The planner reliably constructs valid, safe, and efficient paths across a wide range of scenarios.
Its responsiveness to both obstacle layout and movement capability validates the core premise of the hybrid strategy combining exploration and exploitation dynamically, and modulating behaviors through learned heuristics.
The comparative visual clarity and consistency across figures demonstrate not only robustness but also scalability.
Fig.
Trajectory under 30% obstacle density.
The path is more direct while preserving safety, reflecting adaptive trade-offs in medium-density terrain Fig.
Trajectory generated with 8-directional movement and 35% obstacle density.
The planner utilizes diagonal actions to navigate compact corridors and avoid dead-ends.
Fig.
Trajectory under 25% obstacle density.
The hybrid planner exploits wider passages, producing a shorter, smoother route Fig.
Trajectory under 30% obstacle density with 8-directional movement.
The path becomes smoother and shorter, leveraging diagonal transitions.
Fig.
Trajectory under 20% obstacle density.
The resulting path is highly efficient and nearly straight, highlighting minimal environmental constraint To aid interpretability.
Table IV summarizes the core performance metrics across all tested algorithms.
The PSO-ACO method consistently outperforms both standalone and hybrid baselines in terms of success rate, path smoothness, and stability, while maintaining a reasonable runtime overhead.
Alami Essaadoui.
Adaptive Particle Swarm and Ant Colony Optimization Path Planning for Autonomous Robot Navigation Journal of Robotics and Control (JRC) ISSN: 2715-5072 adjustment of parameters and phase-switching logic enables the algorithm to avoid premature convergence and navigate around obstacles more effectively.
Additionally, intelligent path reconstruction and feasibility verification routines contribute to generating complete, smooth, and safe trajectories.
Fig.
Trajectory under 25% obstacle density.
The hybrid planner optimizes turns and reduces total length using diagonal shortcuts.
Fig.
Trajectory under 20% obstacle density.
With minimal clutter, the planner computes a direct and fluid path to the goal.
This holistic advantage reinforces the effectiveness of the proposed strategy.
TABLE IV.
S UMMARY OF P ERFORMANCE M ETRICS ACROSS T ESTED
A LGORITHMS .
T HE P ROPOSED PSO-ACO H YBRID D EMONSTRATES S UPERIOR
P ERFORMANCE IN S UCCESS R ATE .
PATH S MOOTHNESS .
AND S TABILITY
Algorithm
PSO
ACO
GA-ACO
PSO-GA
PSO-ACO
Success Rate (%) Smoothness .
Stability C ONCLUSION In this paper, we have proposed an Adaptive Hybrid Metaheuristic Planner based on the combination of PSO and ACO for autonomous robot path planning in cluttered environments.
Unlike conventional hybrid models with fixed roles, our method incorporates an adaptive switching strategy driven by convergence behavior and stagnation detection.
This mechanism ensures continuous optimization by dynamically balancing exploration and exploitation as the search progresses.
The proposed approach exploits the fast global convergence of PSO during the initial search phase, while leveraging the local refinement capability of ACO in later stages.
The adaptive Extensive simulations conducted on grid-based environments with varying obstacle densities confirm the superiority of the proposed planner over standalone methods and traditional hybrid approaches.
The results consistently demonstrate significant improvements across all key metrics including success rate, path smoothness, and planning stability highlighting the robustness of the approach in static scenarios.
While the current implementation is designed for offline or semi-real-time applications, we acknowledge that the proposed method does not yet meet the requirements for real-time deployment.
No formal timing guarantees or worst-case complexity bounds were evaluated in this study, and the computational overhead introduced by hybridization may limit applicability on resource-constrained robotic platforms.
These aspects will be addressed in future work.
Moreover, extending this framework to dynamic environments will require architectural modifications such as the integration of receding-horizon control, obstacle motion prediction, and adaptive replanning mechanisms.
Future research will also explore the incorporation of sensor uncertainty, localization drift, and kinematic constraints, with the aim of deploying the planner on physical robotic platforms and validating its performance under real-world navigation conditions using simulation platforms like Gazebo or Webots.
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