# Predictive Dynamic Window Approach Development with Artificial Neural Fuzzy Inference Improvement

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. DWA Improvement

#### 3.1. Predictive DWA

#### 3.2. ANFIS Development

## 4. DWA Improves Results

#### 4.1. Map 1 Results

#### 4.2. Map 2

#### 4.3. Map 3

#### 4.4. Map 4

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Examples of different dynamic window approach (DWA) situations with different ${\mathsf{\alpha}}_{\mathrm{D}}$, ${\mathsf{\beta}}_{\mathrm{D}}$, and ${\mathsf{\gamma}}_{\mathrm{D}}$, as follows: (

**a**,

**c**) ${\mathsf{\alpha}}_{\mathrm{D}}=0.8$, ${\mathsf{\beta}}_{\mathrm{D}}=0.1$ and ${\mathsf{\gamma}}_{\mathrm{D}}=0.1$; (

**b**,

**d**) ${\mathsf{\alpha}}_{\mathrm{D}}=0.1$, ${\mathsf{\beta}}_{\mathrm{D}}=0.8$ and ${\mathsf{\gamma}}_{\mathrm{D}}=0.1$.

**Figure 5.**Artificial neuro-fuzzy inference system (ANFIS) scenarios for data acquisition, as follows: (

**a**) Map 1 with seven obstacles; (

**b**) map 2 with nine obstacles; (

**c**) map 3 with 14 obstacles; (

**d**) map 4 with 33 obstacles.

**Figure 7.**${\mathsf{\beta}}_{\mathrm{D}}$ selection depending on two different inputs, namely: (

**a**) Distance to the obstacle and (

**b**) AGV actual speed.

**Figure 8.**${\mathsf{\gamma}}_{\mathrm{D}}$ selection, depending on the distance to the goal position.

**Figure 9.**P-DWA ANFINS and DWA ANFIS values comparison during the execution, as follows: (

**a**) Heading comparison, (

**b**) distance to the obstacle comparison, (

**c**) speed comparison, and (

**d**) AGV trajectories with different algorithms.

**Figure 10.**DWA ANFINS parameters change during the scenarios, as follows: (

**a**) ${\mathsf{\alpha}}_{\mathrm{D}}$ change during the execution, (

**b**) ${\mathsf{\beta}}_{\mathrm{D}}$ change during the execution, (

**c**) ${\mathsf{\gamma}}_{\mathrm{D}}$ change during the execution, and (

**d**) AGV trajectories with different configurations.

**Figure 11.**DWA ANFINS parameters change during the scenarios, as follows: (

**a**) ${\mathsf{\alpha}}_{\mathrm{D}}$ change during the execution, (

**b**) ${\mathsf{\beta}}_{\mathrm{D}}$ change during the execution, (

**c**) ${\mathsf{\gamma}}_{\mathrm{D}}$ change during the execution, and (

**d**) the AGV trajectories with different configurations.

**Figure 12.**DWA ANFINS parameters change during the scenarios, as follows: (

**a**) ${\mathsf{\alpha}}_{\mathrm{D}}$ change during the execution, (

**b**) ${\mathsf{\beta}}_{\mathrm{D}}$ change during the execution, (

**c**) ${\mathsf{\gamma}}_{\mathrm{D}}$ change during the execution, and (

**d**) AGV trajectories with different configurations.

Algorithm | Reference | Advantages | Weakness |
---|---|---|---|

Dynamic window approach | [4] | Consider robot constraints to calculate an optimum path. | Use fixed weights and select one path per sample time. |

A vector field histogram | [5] | Places great emphasis on dealing with uncertainty from sensor and modeling errors. | Requires the kinematics and shape of the robot. |

TangentBug | [6] | Produces very short paths given purely local information. | Need ideal localization Heuristic function may cause navigation to become slower. |

PointsBug | [6] | Has better performance than TangentBug. | Require high accuracy localization based on output of trigonometric function. |

Swarm optimization | [7] | Allows searching for an optimum trajectory by using particles in search space. | Requires a constant computing to optimize a solution. |

Dynamic movements primitives | [8] | The complex movements are simplified by creating a set of primitive actions. | Requires updating all kernel weights and the quality of the path is compromised. |

Moving to a point with obstacle avoidance | [9] | Simple equations are used to avoid obstacles and it does not need the kinematics equations for motion calculation. | Use fixed weights in the main function. |

Model-based algorithms | [10,11,12,13] | The prediction step gives the chance to analyze the future and adjust the trajectory. | Require a perfect model of the plan to obtain a good prediction. |

Genetic Algorithms | [14] | Normally uses the robot kinematic and dynamic parameters to optimize the path. | Uses a high computational capacity to optimize the function. |

Ant colony optimization | [15] | Adopts a multiple agent to optimize the path resolution. | The probability distribution can change for each iteration and it is not optimized to real time, because of it requires uncertain time to converge. |

Ant algorithm with A* characteristic | [16] | A* accelerates the ant colony conversion and increases the smoothness of global path. | A premature convergence could happen, because of bad adjustment of the limits. |

Double Layer ant colony | [17] | Thanks to both executions the precision is increased. | The algorithms require a trajectory optimization to improve the path resolution. |

Predictive DWA with ANFIS (Developed in this article) | - | Improves Fuzzy logic controller by adopting ANFIS technique to adjust DWA weights and foresee the future implementing a prediction. | Require a perfect model of the plan to obtain a good prediction and adjustment of the prediction step. |

**Table 2.**Dynamic window approach (DWA) parameter and variable definition, as defined in the literature [4]. AGV—automated guided vehicle.

Description | Name | Units |
---|---|---|

Linear speed of vehicle | ${\mathrm{V}}_{\mathrm{agv}}$ | m/s |

Angular speed of vehicle | $\dot{\mathsf{\gamma}}$ | rad/s |

Alignment of the robot with the target direction | $\mathrm{heading}\left({\mathrm{V}}_{\mathrm{agv}},\dot{\mathsf{\gamma}}\right)$ | - |

Distance to obstacle | $\mathrm{dist}\left({\mathrm{V}}_{\mathrm{agv}},\dot{\mathsf{\gamma}}\right)$ | m |

Displacement speed | $\mathrm{vel}\left({\mathrm{V}}_{\mathrm{agv}},\dot{\mathsf{\gamma}}\right)$ | m/s |

Heading coefficient | ${\mathsf{\alpha}}_{\mathrm{D}}$ | rad^{−1} |

Ostacle distance coeffient | ${\mathsf{\beta}}_{\mathrm{D}}$ | m^{−1} |

Speed coefficient | ${\mathsf{\gamma}}_{\mathrm{D}}$ | s/m |

Fitness function | $\mathrm{G}\left({\mathrm{V}}_{\mathrm{agv}},\dot{\mathsf{\gamma}}\right)$ | - |

Normalization function | $\mathsf{\sigma}$ | - |

Description | DWA | P-DWA |
---|---|---|

Time to arrive at goal (s) | 34.2 | 32.95 |

Mean speed (m/s) | 0.79 | 0.82 |

Minimum distance to obstacle (m) | 0.67 | 0.69 |

${\mathsf{\alpha}}_{\mathrm{D}}$ | 0.5 | 0.5 |

${\mathsf{\beta}}_{\mathrm{D}}$ | 0.5 | 0.5 |

${\mathsf{\gamma}}_{\mathrm{D}}$ | 0.5 | 0.5 |

${\mathsf{\sigma}}_{\mathrm{D}}$ | 3 | 3 |

Sample time (s) | 0.05 | 0.05 |

Prediction Sample time (s) | - | 0.5 |

Description | DWA | P-DWA |
---|---|---|

Time to arrive at goal (s) | 41.25 | 34.9 |

Mean speed (m/s) | 0.65 | 0.83 |

Minimum distance to obstacle (m) | 0.44 | 0.65 |

${\mathsf{\alpha}}_{\mathrm{D}}$ | 0.5 | 0.5 |

${\mathsf{\beta}}_{\mathrm{D}}$ | 0.5 | 0.5 |

${\mathsf{\gamma}}_{\mathrm{D}}$ | 0.5 | 0.5 |

${\mathsf{\sigma}}_{\mathrm{D}}$ | 3 | 3 |

Sample time (s) | 0.05 | 0.05 |

Predictive window(s) | - | 0.5 |

Term | Definition |
---|---|

h | Heading value for each sample time |

H | Mean heading for each data acquisition |

v | Speed value for each sample time |

V | Mean Speed for each data acquisition |

d | Distance to the obstacle value for each sample time |

D | Mean Distance for each data acquisition |

ArriveGoal | The distance between the AGV and goal for each sample time |

X_{Goal} | X-position of the goal |

Y_{Goal} | Y-position of the goal |

X_{AGV} | X-position of the AGV |

Y_{AGV} | Y-position of the AGV |

n | Number of sample execution |

i | Number of sample time |

Fuzzy Type | Sugeno |
---|---|

And Method | Product of fuzzified input values |

Or Method | Probabilistic OR of fuzzified input values |

Defuzzy Method | Weighted average of all rule outputs |

Implication Method | Scales the consequent membership function by the antecedent result value |

Aggregation Method | Sum of the consequent fuzzy sets |

Description | P-DWA ANFIS | DWA ANFIS |
---|---|---|

Time to arrive at goal (s) | 31.55 | 33.95 |

Mean speed (m/s) | 0.86 | 0.8 |

Mean heading (°) | 151.55 | 150.96 |

Minimum distance to obstacle (m) | 0.69 | 0.74 |

Description | P-DWA ANFIS | DWA ANFIS |
---|---|---|

Time to arrive at goal (s) | 33.65 | 38.15 |

Mean speed (m/s) | 0.81 | 0.71 |

Mean heading (°) | 151.31 | 154.35 |

Minimum distance to obstacle (m) | 0.68 | 0.56 |

Description | P-DWA ANFIS | DWA ANFIS |
---|---|---|

Time to arrive at goal (s) | 46.7 | 50.7 |

Mean speed (m/s) | 0.59 | 0.54 |

Mean heading (°) | 153.47 | 156.20 |

Minimum distance to obstacle (m) | 0.47 | 0.46 |

Description | P-DWA ANFIS | DWA ANFIS |
---|---|---|

Time to arrive at goal (s) | 57.75 | 67.60 |

Mean speed (m/s) | 0.49 | 0.41 |

Mean heading (°) | 153.7 | 159.66 |

Minimum distance to obstacle (m) | 0.2 | 0.08 |

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**MDPI and ACS Style**

Teso-Fz-Betoño, D.; Zulueta, E.; Fernandez-Gamiz, U.; Saenz-Aguirre, A.; Martinez, R.
Predictive Dynamic Window Approach Development with Artificial Neural Fuzzy Inference Improvement. *Electronics* **2019**, *8*, 935.
https://doi.org/10.3390/electronics8090935

**AMA Style**

Teso-Fz-Betoño D, Zulueta E, Fernandez-Gamiz U, Saenz-Aguirre A, Martinez R.
Predictive Dynamic Window Approach Development with Artificial Neural Fuzzy Inference Improvement. *Electronics*. 2019; 8(9):935.
https://doi.org/10.3390/electronics8090935

**Chicago/Turabian Style**

Teso-Fz-Betoño, Daniel, Ekaitz Zulueta, Unai Fernandez-Gamiz, Aitor Saenz-Aguirre, and Raquel Martinez.
2019. "Predictive Dynamic Window Approach Development with Artificial Neural Fuzzy Inference Improvement" *Electronics* 8, no. 9: 935.
https://doi.org/10.3390/electronics8090935