A hybrid path planning algorithm combining A* and improved ant colony optimization with dynamic window approach for enhancing energy efficiency in warehouse environments

ACO in path planning

ACO is a heuristic algorithm inspired by the foraging behavior of ants and is extensively used in robot path planning. ACO utilizes artificial ants to deposit pheromones and find the shortest path.

Several studies have highlighted ACO’s effectiveness. Zhang et al. (2020) proposed a dynamic multi-role adaptive collaborative ant colony optimization (MRCACO), improving path length by 15% and convergence speed by 20%. Miao et al. (2021) developed an improved adaptive ant colony algorithm (IAACO), reducing path length by 12% and increasing real-time performance by 18%. Liu et al. (2019) enhanced ACO for dynamic environments, achieving 10% shorter and 30% smoother paths. Zhou & Wei (2024) proposed improvements addressing local optima and convergence, reducing convergence time by 22% and inflection points by 17%.

Despite its potential, ACO has limitations, such as local optima and parameter tuning needs. Integrating ACO with A* can leverage A*’s heuristic capabilities, improving robustness and performance in complex environments.

GA in path planning

GA has been extensively employed in robot path planning due to its robustness in handling complex optimization problems. GA operates by mimicking the process of natural evolution through selection, crossover, and mutation to evolve optimal or near-optimal solutions. For instance, Nazarahari, Khanmirza & Doostie (2019) introduced an enhanced GA that integrates an artificial potential field (APF) to generate initial feasible paths and then optimizes these paths regarding length, smoothness, and safety. Their algorithm demonstrated superior performance over A*, PRM, and PSO in different environments, improving path length, runtime, and success rate. Another example is Li, Hu & Liu (2021), who proposed an improved multi-objective GA (IMGA) for static global path planning. They employed a heuristic median insertion method to establish the initial population and designed a multi-objective fitness function considering path length, security, and energy consumption. Their simulations indicated a 17% reduction in the optimal path length compared to traditional GAs. Yifei et al. (2018) compared GA with discrete particle swarm optimization (DPSO) for optimizing the welding path of robots. The study found that GA achieved faster iterative efficiency with improved selection operators, while both algorithms generated optimal or near-optimal paths.

Hybrid approaches combining GA with other algorithms have also shown promising results. Ma et al. (2020) combined GA with Bezier curves to smooth paths, addressing redundant nodes and peak inflection points, resulting in shorter, smoother, and safer paths. Zhang et al. (2021) proposed a hybrid algorithm combining GA with the Firefly Algorithm (FA). This approach applied GA operations when FA fell into local optima, improving the overall accuracy and performance in path planning tasks. Additionally, Luan & Thinh (2023) developed a hybrid genetic algorithm (GA) featuring dynamic mutation rates and a switchable global-local search method. This method reduced premature convergence and produced smoothed paths directly without needing third-party smoothing algorithms.

Despite their advantages, GA has limitations such as slow convergence and susceptibility to local optima. Li et al. (2023) addressed these issues by improving the generation mechanism, crossover, and mutation strategies, enhancing the overall performance in path planning simulations. Comparative studies have shown the effectiveness of GA-based approaches. Cheng et al. (2020) utilized a multi-objective GA for reconfigurable robots, demonstrating its capability to generate Pareto-optimal solutions in dynamic environments. Their GA-based method outperformed others regarding safety, path length, and smoothness. Patle et al. (2018) introduced a matrix-binary code-based GA for mobile robot navigation, validating its effectiveness through accurate and experimental results. Their method provided optimal paths regarding path length and time efficiency compared to other intelligent navigation controllers. Overall, GA is a powerful tool in robot path planning, significantly enhanced through innovative operator strategies and hybrid approaches.

Particle swarm optimization in path planning

PSO is widely used in robot path planning for its simplicity and effectiveness in finding optimal paths. PSO simulates the social behavior of birds flocking or fish schooling to find optimal solutions. Xu, Cao & Song (2022) proposed an improved PSO algorithm with a quartic Bezier transition curve, demonstrating reduced path length and high-order smoothness. Sahu, Das & Kumar (2023) developed a hybrid algorithm integrating PSO, modified cuckoo search, and sine cosine algorithms, achieving optimal paths with minimal time and collision avoidance.

Huang et al. (2023) introduced an A*-PSO hybrid algorithm, optimizing key nodes generated by A* using PSO, resulting in reduced running times and improved path accuracy. Zhang et al. (2023) proposed a hybrid IACO-A*-PSO algorithm for radioactive environments, optimizing path length, radiation dose, and energy consumption.

Wang & Zhou (2019) combined A* with elastic PSO for shorter and more optimal paths, while Garip, Karayel & Erhan Çimen (2022) combined PSO with the firefly algorithm (FA) and cuckoo search (CS), showing superior performance. Lin et al. (2023) improved PSO with grey wolf optimization (GWO), enhancing exploration capabilities and convergence speed.

Despite their effectiveness, PSO algorithms can suffer from local optima and slow convergence. Integrating PSO with other optimization techniques, continuous research, and development further enhances its applicability and efficiency in complex and dynamic environments.

Comparison of optimization algorithms and feasibility of combining with A*

Various optimization algorithms have been explored for robot path planning, each with unique advantages and limitations. Among these, PSO, GA, and ACO are the most prominent methods. When integrated with the A* algorithm, these optimization techniques can significantly enhance path planning efficiency and effectiveness.

The A* algorithm, known for its heuristic-driven search, optimality, and completeness, excels in complex environments. Its ability to utilize heuristics to guide the search process efficiently, adapt to various grid structures, and handle dynamic obstacles makes it particularly effective in reducing energy consumption and improving navigation performance in cluttered settings.

Table 1 summarizes the key characteristics of these algorithms and their integration with A*, highlighting the benefits of combining these optimization techniques with A* for enhanced path planning in complex and dynamic environments.

Limitations of current advanced algorithms and necessity of the hybrid approach

While advanced algorithms such as A*, ACO, GA, and PSO offer significant benefits in path planning, each has specific limitations that hinder their effectiveness in complex and dynamic environments.

A* algorithm A* is optimal and complete, leveraging heuristics to find the shortest path. However, its computational cost increases significantly with problem size, making it less efficient for large-scale applications. Additionally, A* assumes a static environment, which limits its adaptability to dynamic changes.

Ant colony optimization (ACO) ACO is highly adaptable to dynamic environments and can handle large problem spaces through distributed computation. Nevertheless, it converges slowly and is sensitive to parameter tuning, requiring significant computational resources to achieve optimal performance.

Genetic algorithm (GA) GA is robust, effective in global search, and suitable for complex optimization problems. However, it suffers from slow convergence and can get trapped in local optima without sufficient population diversity, leading to suboptimal solutions.

Particle swarm optimization (PSO) PSO is simple to implement and converges quickly in simple search spaces. Despite these advantages, it is prone to local optima and requires careful parameter tuning to balance exploration and exploitation effectively.

Necessity of the hybrid approach A hybrid approach combining A*, ACO, GA, and PSO with the dynamic window approach (DWA) is proposed to address these limitations. This hybrid method enhances global and local search capabilities, balancing exploration and exploitation. The integration ensures robust path planning and real-time obstacle avoidance, making it suitable for dynamic warehouse environments.

The hybrid algorithm leverages the heuristic strengths of A*, the optimization capabilities of ACO, GA, and PSO, and the dynamic adaptability of DWA. This combination results in improved energy efficiency, computational efficiency, and adaptability, addressing the specific limitations of each algorithm.

By integrating these advanced algorithms, the hybrid approach offers a balanced and efficient solution for path planning in complex and dynamic environments, providing significant improvements over standalone algorithms.

Combination of A* with GA/PSO/ACO

The global path planning begins with the A* algorithm to find a primary path. This path is then optimized using GA, PSO, or ACO.

Improved ant colony optimization (IACO)

IACO introduces improvements over the standard ACO by initializing the pheromone levels on the initial path obtained from A*. This results in a more efficient search process.

DWA

DWA is used for local path planning to avoid obstacles dynamically. The robot’s velocity and direction are adjusted to ensure smooth, collision-free navigation. Key parameters include maximum speed (0.4 m/s), acceleration (0.1 m/s²), and a maximum turning angle of 30 degrees per time step. Figure 1 shows the working principle of the DWA algorithm.

Energy consumption calculation

Energy consumption is calculated based on the path’s terrain and the robot’s movement. For flat terrain, the energy consumption $E_{\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}}$ is given by:

$$E_{\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}}=\frac{G\cdot f\cdot \mathrm{\Delta }s}{{\eta }_T}$$where G is the weight of the robot, $f$ is the rolling resistance coefficient, $\mathrm{\Delta }s$ is the travel distance, and ${\eta }_T$ is the transmission efficiency.

For inclined terrain, the energy consumption $E_{\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ is:

$$E_{\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}=\frac{G\cdot (f\cdot \cos \varphi +\sin \varphi )\cdot \mathrm{\Delta }s}{{\eta }_T}$$where $\varphi$ is the slope angle of the terrain. For uphill movement ( $z_x>z_{x-1}$), $\varphi$ is positive, and for downhill movement ( $z_x<z_{x-1}$), $\varphi$ is negative.

Energy recovery on declines is calculated as follows:

$$E_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{y}}=k\cdot \left(\frac{G\cdot (\sin \varphi -f\cdot \cos \varphi )\cdot \mathrm{\Delta }s}{{\eta }_T}\right)$$where $k$ is the recovery efficiency factor. The total energy cost $E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ for the path is the sum of the energy costs for all segments:

$$E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\sum _{i=1}^n{E}_i.$$

Trajectory evaluation

After sampling, different simulated trajectories are generated based on various speeds and angular velocities. Each trajectory is scored, and the highest score is selected for the next planning period. The scoring rule is established by the evaluation function as shown in Equation:

$$G(v,\omega )=\sigma (\alpha \cdot h(v,\omega ))+\sigma (\beta \cdot d(v,\omega ))+\sigma (\gamma \cdot o(v,\omega ))$$where $\sigma$ represents normalization; $h(v,\omega )$ is the heading angle evaluation function calculated using the angle $\mathrm{\Delta }\theta$ or $(180-\mathrm{\Delta }\theta )$ between the predicted trajectory’s end orientation and the target direction; $d(v,\omega )$ is the distance evaluation function, evaluating the closest distance between the simulated trajectory and obstacles; and $o(v,\omega )$ is the velocity evaluation function, evaluating the linear velocity of the simulated trajectory. $\alpha$, $\beta$, and $\gamma$ are coefficients of the evaluation function.

Incorporating robot size Traditional DWA does not consider the robot’s actual size, often resulting in collisions during real-world navigation. To address this, robot size information is included. The coordinates of the robot’s four vertices are calculated based on the geometric center and size, generating a rectangular contour. This contour is then discretized into a set of points, and the distance $D(v,\omega )$ between these points and obstacles is calculated and normalized, replacing $d(v,\omega )$ in the evaluation function. This ensures the path quality is evaluated based on the distance between the robot’s contour and obstacles.

Radius Constraint Considering the mechanical structure of mobile robots, the path should satisfy the robot’s minimum turning radius requirement. Therefore, the turning radius is added as a constraint:

$$r=\frac{v}{\omega }$$

The evaluation function is updated as follows:

$$G(v,\omega )=\sigma (\alpha \cdot h(v,\omega )+\beta \cdot D(v,\omega )+\gamma \cdot o(v,\omega )+\delta \cdot r(v,\omega ))$$where $\delta$ is the coefficient of the evaluation function.

The DWA provides effective local obstacle avoidance but can easily fall into local optima. By integrating A*, IACO, and DWA, it is possible to achieve both global optimality and robust local obstacle avoidance. The integrated A*, IACO, and DWA path planning algorithm process is shown in Fig. 2.

This methodology comprehensively integrates global and local path-planning algorithms, ensuring energy-efficient and collision-free navigation in dynamic environments.

Experimental setup

The experiments were conducted in a warehouse environment, as depicted in Fig. 3. The map was loaded from a spreadsheet and initialized with specific start and goal coordinates. The map size and all nodes were set up accordingly, and the terrain elevation was calculated based on a given mathematical model. The yellow dashed line represents the initial static offline path, the blue square indicates sudden obstacles, and the red circle denotes randomly moving obstacles.

In this experiment, the start and goal points were slightly adjusted to serve as random seeds, allowing multiple trials to be conducted. Analysis of variance (ANOVA) was applied as a statistical significance test to determine whether the differences between the algorithms were meaningful or merely caused by random factors.

Algorithm integration

ACO + A* + DWA

• The A* algorithm was first used to find a global path from the start to the goal.

• The ACO algorithm was then applied to optimize this path by considering pheromone levels and heuristic information.

• Finally, the DWA was employed to locally adjust the path to avoid dynamic obstacles, ensuring smooth and collision-free navigation.

As shown in Fig. 4, the ACO algorithm, combined with A* and DWA, effectively optimizes and adjusts the path for dynamic environments.

GA + A* + DWA

• The GA optimized the path generated by the A* algorithm.

• The DWA further refined the path locally to handle dynamic obstacles.

Figure 5 illustrates the effectiveness of the GA in optimizing the path generated by the A* algorithm. Additionally, it shows how the DWA algorithm further refines the path to handle dynamic obstacles.

PSO + A* + DWA

• The PSO algorithm optimized the path found by the A* algorithm.

• The DWA was used for local path adjustments to avoid obstacles.

As shown in Fig. 6, the PSO algorithm optimized the path found by the A* algorithm, and the DWA was used for local path adjustments to avoid obstacles.

Algorithm parameters

The parameters for the algorithms used in this study are as follows:

DWA for local path planning

The DWA algorithm was employed to handle local obstacle avoidance. The robot’s velocity and direction were dynamically adjusted to ensure safe navigation around obstacles. The key parameters for the DWA were:

• Maximum speed: 0.4 m/s

• Acceleration: 0.1 m/s²

• Maximum turning angle: 30 degrees per time step

This methodology comprehensively integrates global and local path-planning algorithms, ensuring energy-efficient and collision-free navigation in dynamic environments.

ANOVA analysis

This section presents the ANOVA results for the robot navigation performance metrics, including time, energy, path length, and number of turns. The study examines the effects of the algorithm, the map complexity, and their interaction on these performance indicators.

Energy consumption

The energy consumption for each algorithm in the primary and complex map scenarios is shown in Fig. 7A. IACO+A*+DWA exhibits the lowest energy consumption in basic and complex scenarios, highlighting its superior efficiency in path planning. This makes IACO+A*+DWA the most energy-efficient algorithm among those tested.

Time taken

The time taken by each algorithm to reach the goal is presented in Fig. 7B. Despite the slight increase in time in the complex scenario, IACO+A*+DWA remains competitive with the other algorithms. Its performance in the basic scenario is particularly noteworthy, maintaining a balance between speed and energy efficiency.

Turns and path length

Figures 7C and 7D present the path length and the number of turns for each algorithm, respectively. IACO+A*+DWA generates shorter paths with fewer turns in both primary and complex scenarios. This contributes significantly to its lower energy consumption and competitive completion times. The reduction in the number of turns and path length further underscores the algorithm’s effectiveness in optimizing route planning.