# Dynamic Path Planning for Mobile Robots by Integrating Improved Sparrow Search Algorithm and Dynamic Window Approach

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## Abstract

**:**

## 1. Introduction

## 2. Global Path Planning

#### 2.1. Basic SSA

#### 2.2. MISSA: Sparrow Search Algorithm Improved through Integration of Multiple Strategies

- (1)
- To address the imbalanced distribution of the population and the inadequate diversity in the basic SSA, logistic–tent chaotic mapping is employed to initialize the sparrow population, ensuring an even distribution and improving algorithm traversal. In order to enhance the diversity within the population and improve both the quality of the initial solution and search precision, an elite-inverse learning strategy is implemented.
- (2)
- To tackle the problem of inadequate position updating in the sparrow population, a dynamic self-adaptive adjustment strategy for position updating is employed. This strategy refines the position update equations for both producers and scroungers, bolstering the algorithm’s optimization prowess.
- (3)
- Given that the basic SSA tends to get trapped in local optima, a Lévy flight strategy is utilized to update the position of the scroungers. The incorporation of an optimal position perturbation strategy boosts the algorithm’s capability to evade local optima.

#### 2.2.1. Initialization of Population Using Logistic–Tent Chaotic Mapping

#### 2.2.2. Elite Opposition-Based Learning Strategy

#### 2.2.3. Dynamic Self-Adaptive Position Update Strategy

- (1)
- Improved Formula for Producer Position Update

- (2)
- Improved Formula for Scrounger Position Update

#### 2.2.4. Optimal Position Perturbation Strategy

#### 2.2.5. Improved Algorithm Flow

- Step 1: Initialize parameters. These include population size, maximum number of iterations, proportion of producers, proportion of scouters, warning threshold, and safety threshold.
- Step 2: Initialize the population through the application of logistic–tent chaotic mapping, calculate the fitness value for each sparrow, sort them, and identify the current best and worst fitness values along with their corresponding sparrow positions.
- Step 3: Apply the EOBL strategy proportionate to the number of producers, combined with fitness value sorting, to select top-ranked sparrows as producers and update their positions according to Equations (13) and (14).
- Step 4: The remaining sparrows function as producers and update their positions using Equation (17).
- Step 5: Based on the proportion of scouters, randomly select scouters from the sparrow population and update their positions by using Equation (5).
- Step 6: Compute the fitness value for each sparrow and sort them. When the sparrow individuals gather to a certain extent, apply the Cauchy perturbation strategy to disturb the optimal sparrow position.
- Step 7: Compare the newly perturbed fitness value with the original value and update individual positions accordingly.
- Step 8: Determine whether the maximum iteration count has been reached. If true, end the loop, output, and record the optimal result. If not, proceed to step 3.
- Step 9: Output the global optimal path and its corresponding fitness value.

## 3. Integration of Enhanced DWA for Dynamic Path Planning

#### 3.1. Improvements to the DWA

#### 3.1.1. Establishment of Robot Kinematic Model

#### 3.1.2. Velocity Sampling

- (1)
- Robot’s Maximum and Minimum Velocities:

- (2)
- Robot’s Intrinsic Constraints

- (3)
- Constraints on Obstacle Safety Distance

#### 3.1.3. Adaptive Velocity Adjustment Strategy

#### 3.1.4. Optimization of DWA’s Evaluation Function

#### 3.2. Fusion Algorithm for Dynamic Path Planning

## 4. Simulation and Experimental Results Analysis

#### 4.1. Environment Modeling

#### 4.2. Simulation Experimental Environment

#### 4.3. Simulation Comparative Experiment of MISSA Global Path Planning

#### 4.3.1. Environment Model 1

#### 4.3.2. Environment Model 2

#### 4.4. Analysis of Random Obstacle Avoidance in the Fusion Algorithm

#### 4.5. Dynamic Path Planning with the Fusion Algorithm

#### 4.6. Experimental Validation

## 5. Conclusions

- Initially, logistic–tent chaotic mapping is utilized to initialize the sparrow population, generating a relatively evenly distributed and stable initial population. Subsequently, an elite reverse learning strategy is employed to select producers, which forms the foundation for algorithm stability. Following this, a dynamic self-adaptive position update strategy is integrated to enhance the optimization capability of the algorithm. This improvement involves refining the position update formulas for both producers and scroungers. Additionally, the Lévy flight strategy is applied to update the positions of scroungers, accompanied by the incorporation of a best position perturbation strategy to further enhance the algorithm’s ability to escape local optima. Through comparative experiments in static environments and obstacle avoidance experiments in various dynamic environment scenarios, the results demonstrate that the global paths planned by MISSA outperform those generated by the other three comparative algorithms in terms of path length, total rotation angle, and algorithm runtime. These findings underscore MISSA’s robust path optimization capability and stability.
- The evaluation function of the DWA is refined, and an adaptive velocity adjustment strategy is introduced. Subsequently, MISSA is integrated with the optimized DWA, utilizing the key points of the global path generated by MISSA as local sub-goals for the DWA. This integration results in the development of MISSA-DWA. Through path-planning experiments conducted in diverse dynamic environments and scenarios, it is concluded that the integrated MISSA-DWA algorithm not only devises globally optimal paths but also excels in generating smooth paths while dynamically navigating around obstacles. It effectively avoids unidentified obstructions, ensuring the secure arrival of the robot at the target destination. This enhancement significantly improves the efficiency and safety of the robot’s movement.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**The trajectories of four path-planning algorithms within environment model 1: (

**a**) ACO; (

**b**) IACO; (

**c**) SSA; (

**d**) MISSA. The initial point is depicted by a red dot, while the termination point is denoted by a green dot.

**Figure 7.**The trajectories of four path-planning algorithms within environment model 2: (

**a**) ACO; (

**b**) IACO; (

**c**) SSA; (

**d**) MISSA. The initial point is depicted by a red dot, while the termination point is denoted by a green dot.

**Figure 8.**Diagram illustrating the trajectory for random obstacle avoidance in path-planning scenarios: (

**a**) without random obstacles; (

**b**) with one added random obstacle; (

**c**) including two random obstacles; (

**d**) including two random obstacles.

**Figure 9.**Dynamic obstacle avoidance effect of the MISSA-DWA fusion algorithm in environment 1: (

**a**) avoiding the random obstacle; (

**b**) avoiding the dynamic obstacle; (

**c**) completed dynamic path planning to reach the target point.

**Figure 10.**MISSA-DWA fusion algorithm’s dynamic obstacle avoidance effect. (

**a**) Simulation diagram 1 in environment 2; (

**b**) simulation diagram 2 in environment 3; (

**c**) simulation diagram 3 in environment 4; (

**d**) simulation diagram 4 in environment 4.

**Figure 11.**Obstacle avoidance process in a static environment.(

**a**) obstacle avoidance process 1; (

**b**) obstacle avoidance process 2; (

**c**) reaching the target point.

**Figure 12.**Path planning in a static environment. (

**a**) the mobile robot starts to move (

**b**) obstacle avoidance process 1. (

**c**) obstacle avoidance process 2.

**Figure 14.**Obstacle avoidance process in a dynamic environment 1. (

**a**) obstacle avoidance process 1. (

**b**) obstacle avoidance process 2. (

**c**) reaching the target point.

**Figure 15.**Path planning in dynamic environment 1. (

**a**) the mobile robot starts to move (

**b**) obstacle avoidance process 1. (

**c**) obstacle avoidance process 2.

**Figure 17.**Obstacle avoidance process in dynamic environment 2. (

**a**) obstacle avoidance process 1. (

**b**) obstacle avoidance process 2. (

**c**) reaching the target point.

**Figure 18.**Path planning in a dynamic environment 2. (

**a**) obstacle avoidance process 1. (

**b**) obstacle avoidance process 2. (

**c**) obstacle avoidance process 3.

SSA | Number of Sparrows | Maximum Iterations | Search Dimensions | Alarm Threshold | Producer Ratio | Producer Ratio |

Parameters | 60 | 300 | 16 | 0.8 | 0.3 | 0.2 |

ACO | Number of Ants | Maximum Iterations | Pheromone Factor | Heuristic Function Factor | Pheromone Evaporation Factor | Pheromone Constant |

Parameters | 60 | 300 | 2 | 6 | 0.1 | 5 |

**Table 2.**Comparison of performance indicators for algorithms (ACO, IACO, SSA, and MISSA) under environment model 1.

Algorithm | Path Length/m | Total Rotation Angle | Time/s | |||
---|---|---|---|---|---|---|

Minimum | Average | Minimum | Average | Minimum | Average | |

ACO | 28.1416 | 30.3926 | 425 | 743.45 | 0.4178 | 1.8917 |

IACO | 27.9073 | 29.8455 | 126 | 187.37 | 2.9614 | 8.5572 |

SSA | 28.3411 | 32.7429 | 218 | 318.74 | 0.3796 | 1.7083 |

ISSA | 27.1290 | 27.7306 | 48 | 61.85 | 0.3282 | 0.9935 |

**Table 3.**Comparison of performance indicators for algorithms (ACO, IACO, SSA, and MISSA) under environment model 2.

Algorithm | Path Length/m | Total Rotation Angle | Time/s | |||
---|---|---|---|---|---|---|

Minimum | Average | Minimum | Average | Minimum | Average | |

ACO | 37.8701 | 43.3414 | 748 | 1436.17 | 1.8795 | 4.5309 |

IACO | 36.6226 | 38.6631 | 585 | 1062.82 | 3.2852 | 9.7443 |

SSA | 36.1751 | 39.5893 | 472 | 776.16 | 0.7164 | 1.9656 |

ISSA | 34.3719 | 34.8701 | 316 | 327.63 | 0.5681 | 1.3124 |

Quantity of Random Obstacles | Path Length/m | Time/s |
---|---|---|

No random obstacles | 74.155 | 106.58 |

One random obstacle | 74.763 | 109.69 |

Two random obstacles | 75.232 | 113.73 |

Three random obstacles | 76.206 | 117.62 |

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## Share and Cite

**MDPI and ACS Style**

Hou, J.; Jiang, W.; Luo, Z.; Yang, L.; Hu, X.; Guo, B.
Dynamic Path Planning for Mobile Robots by Integrating Improved Sparrow Search Algorithm and Dynamic Window Approach. *Actuators* **2024**, *13*, 24.
https://doi.org/10.3390/act13010024

**AMA Style**

Hou J, Jiang W, Luo Z, Yang L, Hu X, Guo B.
Dynamic Path Planning for Mobile Robots by Integrating Improved Sparrow Search Algorithm and Dynamic Window Approach. *Actuators*. 2024; 13(1):24.
https://doi.org/10.3390/act13010024

**Chicago/Turabian Style**

Hou, Junting, Wensong Jiang, Zai Luo, Li Yang, Xiaofeng Hu, and Bin Guo.
2024. "Dynamic Path Planning for Mobile Robots by Integrating Improved Sparrow Search Algorithm and Dynamic Window Approach" *Actuators* 13, no. 1: 24.
https://doi.org/10.3390/act13010024