# Efficient and Safe Robotic Autonomous Environment Exploration Using Integrated Frontier Detection and Multiple Path Evaluation

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## Abstract

**:**

## 1. Introduction

- We propose an integrated frontier detection and maintenance method. A complete environmental exploration can be achieved by sufficient frontier detection and incrementally maintaining reachable and informative frontiers.
- A multiple path generation method is proposed using the wavefront propagation trend of the fast-marching method and a well-designed velocity field to generate safe paths with a good view.
- A multi-object utility function is proposed for frontier evaluation to obtain the optimal path, improving exploration efficiency. A path smoothing method with dynamic parameter adjustment improves the smoothness of the optimal path.

## 2. Related Works

#### 2.1. Frontier Detection Methods

#### 2.2. Decision-Making Methods

#### 2.3. Path-Planning Methods

## 3. Problem Statement

**Problem**: Given occupancy grid map $\mathcal{M}$ find the next most promising frontier $f$ with the optimal path ${T}^{*}$ which is followed by the robot.

## 4. Proposed Method

#### 4.1. Method Overview

Algorithm 1. Autonomous Exploration. | |

Input: $\mathcal{M}$, RobotLocation, LidarData,${F}_{w}$←∅, ExplorationFlag←True | |

Output: Complete map of environment | |

1 | whileExplorationFlag=True∧(ReplanTrigger=True∨TimingTrigger=True) do |

2 | DistanceMap←UpdatingEuclideanDistanceMap($\mathcal{M}$); |

3 | $F$←Frontier Detection and Maintenance(${F}_{w}$,$\mathcal{M}$, |

DistanceMap, RobotLocation, LidarData); | |

4 | if $F$ = ∅ then |

5 | ExplorationFlag = False; |

6 | break; |

7 |
end |

8 | OptimalPath←Multiple paths planning andevaluation($F$,$\mathcal{M}$, DistanceMap, RobotLocation); |

9 | SmoothPath←Smooth the path$({\phi}_{1}$,${\phi}_{2}$, DistanceMap, OptimalPath); |

10 | Publish Smooth Path to Path Tracking Module; |

11 | end |

#### 4.2. Frontier Detection and Maintenance

Algorithm 2. Frontier Detection and Maintenance. | |

Input: $\mathcal{M}$, RobotLocation, LidarData, ${F}_{w}$, DistanceMap | |

Output: $F$ | |

1 | ${F}_{o}$←∅, ${F}_{l}$←∅; |

2 | ActiveArea← AquireActiveArea ($\mathcal{M}$, RobotLocation, LidarData); |

3 | ${F}_{o}$← SearchFronteirsOnOGM (ActiveArea); |

4 | SetObstacle (RobotLocation, DistanceMap); |

5 | foreach frontier f in {${F}_{o}$,${F}_{w}$} do |

6 | if GetDistance(f)<safe dist ∨ (GetNearestObsCood (f)= |

RobotLocation∧|| f- RobotLocation || <${D}_{l}$) ∨GetInformationCost< | |

InfoThreshhold then | |

7 | remove f; |

8 | end |

9 | end |

10 | ${F}_{l}$← AquireFrontiersUsingLidarDate (LidarData, RobotLocation); |

11 | foreach frontier f in${F}_{l}$do |

12 |
if GetInformationCost<InfoThreshhold then |

13 | remove f; |

14 | end |

15 | end |

16 | RemoveObstacle(RobotLocation, DistanceMap); |

17 | if {${F}_{o}$,${F}_{l}$,${F}_{w}$}= ∅ then |

18 | $F$←∅; |

19 | return; |

20 | else |

21 | $F$← Cluttering(${F}_{o}$,${F}_{l}$,${F}_{w}$); |

22 | ${F}_{w}$←∅, ${F}_{w}$←$F$; |

23 | end |

#### 4.3. Multiple Paths Planning and Evaluation

#### 4.3.1. Multiple Path Generation Using Fast Marching

**.**Select $t$ frontiers closest to the robot in the set $F$ as the set ${F}_{d}$, ${F}_{d}=\{{f}_{1},{f}_{2},\cdot \cdot \cdot ,{f}_{t}\}$ and ${F}_{d}\subseteq F$.

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

#### 4.3.2. Path Evaluation

**.**Lidar data acquisition cost $L$

#### 4.3.3. Path Smoothing and Tracking

Algorithm 3. Smooth the path. | |

Input: ${\phi}_{1}$,${\phi}_{2}$, DistanceMap, OptimalPath | |

Output: SmoothPath | |

1 | OptTimes←0; |

2 | BsplinePath←GenerateBspline (OptimalPath); |

3 | SmoothPath←BsplinePathOptimization (BsplinePath); |

4 | whilePathCheck(SmoothPath)∧OptTimes < MaxOptTimesdo |

5 | OptTimes + +; |

6 | ${\phi}_{2}$←${\phi}_{2}$(MaxOptTimes—OptTimes)/MaxOptTimes; |

7 | SmoothPath←BsplinePathOptimization (BsplinePath); |

8 | end |

9 | ifOptTimes = MaxOptTimes then |

10 | ${\phi}_{2}$←0; |

11 | SmoothPath←BsplinePathOptimization (BsplinePath); |

12 | end |

## 5. Experimental Research and Results

#### 5.1. Experiment Setup

#### 5.2. Performance Comparison in Simulation

#### 5.2.1. The Autonomous Exploration Process

#### 5.2.2. Performance Comparison and Result

#### 5.3. Real-World Experiments

## 6. Discussion

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The schematic diagram shows the removal of inefficient frontiers through updating the distance map locally. (

**a**) Shows the robot with lidar data and updated $\mathcal{M}$ in the simulation environment. (

**b**) Shows the actual distance map and the acquired frontiers. (

**c**) Shows the change of the distance map by adding a virtual obstacle on the robot’s position to remove inefficient frontiers.

**Figure 3.**(

**a**) Schematic diagram showing the frontiers detection process using lidar data. (

**b**) Green dots are the newly added potentially accessible frontiers.

**Figure 4.**The schematic diagram shows the multiple path generation using fast marching. (

**a**) The cyan-colored squares represent the frontiers generated by the Frontiers Processing module. (

**b**) The velocity field of the environment. (

**c**) The wavefront propagates from the robot’s location (green dot) to the target point (blue dot). The red area represents the range of the wave, and the green dashed line represents the wavefront. (

**d**) The yellow line represents the generated multiple paths from the robot position to the unexplored frontiers.

**Figure 9.**Comparison of the exploration efficiency of different methods in different environments. From left to right: Laboratory, Corridor, and Office.

**Figure 10.**The performance of different path planning methods. A green dot represents the starting point, and a red dot represents the target point. (

**a**–

**c**) correspond to the performance of different methods in the first three sets of experiments. (

**d**–

**f**) correspond to the fourth set of experiments. (

**d**) shows the randomly generated 100 valid target points. (

**e**,

**f**) show the performance of different methods of the two experiments.

**Figure 12.**The performance of exploration experiments with the shortest path under different parameters.

References | Map Type | Frontiers Detection | Decision Making | Path Planning | Experimental Scenario | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Occupancy Grid Map | Topological Map | Feature Map | Occupancy Grid Map | Lidar Data | Lidar Detection Range | Lidar Data Quality | Actual Path | Movement Consistency | Multiple Path Generation | Path Smoothing | Path Clearance | Simulation | Real-World | |

[11] | √ | – | – | √ | – | – | – | – | – | – | – | – | √ | √ |

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Our work | √ | – | – | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ |

$\mathcal{M}$ | Occupancy grid map. |

$f$ | Single frontier. |

${F}_{w}$ | The frontier warehouse is used to store the frontiers obtained in each exploration cycle. |

${F}_{o}$ | Stores the frontiers obtained from the active area of occupancy grid map $\mathcal{M}$. |

${F}_{l}$ | Stores frontiers acquired using lidar data. |

$F$ | The clustered frontiers. |

${F}_{s}$ | Frontiers with valid paths. |

${\theta}_{Max}$ | The maximum angular deviation that can be followed. |

${k}_{P}$, ${k}_{\phi}$, ${k}_{I}$ | The coefficient in utility function, where ${k}_{\phi}$ is only related to the physical characteristics of the robot. |

${D}_{l}$ | Lidar max range. |

$\mu $ | The confidence range ratio. |

$T$, $\tau $ | $T$ represents the path which is composed of waypoint $\tau $. |

$d(\xb7)$ | Distance function, obtain the distance between any position on the map and the obstacle. |

Method | Exploration Distance(m) | Exploration Time(s) | ||||||
---|---|---|---|---|---|---|---|---|

Avg | Std | Max | Min | Avg | Std | Max | Min | |

Laboratory: 15 m × 15 m, Lidar: Filed of view 270°, Max range 6 m | ||||||||

RRT-exploration (Geta = 4) | 86.1 | 6.9 | 97.0 | 75.7 | 346.3 | 27.3 | 410.0 | 313.5 |

RRT-exploration (Geta = 6) | 80.9 | 5.1 | 90.4 | 75.1 | 366.6 | 71.6 | 515.5 | 293.0 |

Nearest Frontier | 68.6 | 7.4 | 77.3 | 53.8 | 382.6 | 54.0 | 486.0 | 323.0 |

Proposed (2,1) | 58.8 | 5.9 | 67.6 | 50.9 | 304.7 | 22.6 | 334.5 | 262.5 |

Proposed (1,1) | 56.6 | 3.3 | 62.2 | 51.5 | 280.6 | 22.9 | 310.0 | 245.5 |

Corridor: 20 m × 15 m, Lidar: Filed of view 360°, Max range 8 m | ||||||||

RRT-exploration (Geta = 4) | 97.6 | 9.8 | 115.4 | 81.6 | 499.0 | 87.1 | 618.5 | 394.0 |

RRT-exploration (Geta = 6) | 89.5 | 7.0 | 97.7 | 74.6 | 460.0 | 59.4 | 556.5 | 388.0 |

Nearest Frontier | 88.2 | 5.6 | 94.7 | 77.3 | 430.8 | 33.4 | 497.5 | 369.0 |

Proposed (2,1) | 77.9 | 2.4 | 82.6 | 74.1 | 346.2 | 24.2 | 398.5 | 316.0 |

Proposed (1,1) | 80.9 | 3.3 | 85.6 | 75.0 | 336.6 | 15.9 | 360.0 | 301.0 |

Office: 20 m × 20 m, Lidar: Filed of view 360°, Max range 6 m | ||||||||

RRT-exploration (Geta = 4) | 132.3 | 17.9 | 163.8 | 109.4 | 517.6 | 73.7 | 656.0 | 462.0 |

RRT-exploration (Geta = 6) | 129.5 | 18.1 | 146.4 | 96.0 | 535.2 | 64.5 | 619.0 | 442.0 |

Nearest Frontier | 73.5 | 1.8 | 78.1 | 71.9 | 434.9 | 34.9 | 475.5 | 356.5 |

Proposed (2,1) | 67.6 | 1.7 | 71.1 | 64.9 | 339.2 | 22.1 | 377.5 | 307.0 |

Proposed (1,1) | 69.6 | 4.1 | 76.3 | 63.4 | 323.8 | 19.4 | 363.5 | 284.5 |

Method | Time (ms) | Length (m) | Clearance (m) | Success Rate | Continuity |
---|---|---|---|---|---|

1 | |||||

RRT* | 89.5 | 26.7 | 1.0 | 100% | ${C}^{0}$ |

Proposed Method | 54.9 | 27.0 | 1.2 | 100% | ${\mathit{C}}^{\mathbf{2}}$ |

2 | |||||

RRT* | 181.8 | 37.8 | 1.1 | 100% | ${C}^{0}$ |

Proposed Method | 60.3 | 38.7 | 1.4 | 100% | ${\mathit{C}}^{\mathbf{2}}$ |

3 | |||||

RRT* | 332.7 | 34.0 | 0.9 | 98% | ${C}^{0}$ |

Proposed Method | 56.8 | 34.3 | 1.1 | 100% | ${C}^{2}$ |

4 | |||||

RRT* | 46.3 | 21.2 | 1.0 | 99% | ${C}^{0}$ |

Proposed Method | 33.0 | 20.7 | 1.2 | 100% | ${\mathit{C}}^{\mathbf{2}}$ |

Method | Exploration Distance(m) | Exploration Time(s) | Completeness of the Mapping | Smoothness Comparison | |
---|---|---|---|---|---|

Proposed(2,1) | |||||

1 | 64.7 | 438.0 | 0.998 | 0.32 | |

2 | 57.0 | 435.0 | 0.982 | 0.31 | |

3 | 57.4 | 402.5 | 0.996 | 0.37 | |

Avg | 59.7 | 425.2 | 0.992 | 0.33 | |

Proposed(1,1) | |||||

1 | 54.0 | 394.0 | 0.996 | 0.33 | |

2 | 63.4 | 454.0 | 1.013 | 0.33 | |

3 | 59.8 | 408.0 | 0.996 | 0.31 | |

Avg | 59.1 | 418.7 | 0.997 | 0.32 |

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**MDPI and ACS Style**

Sun, Y.; Zhang, C.
Efficient and Safe Robotic Autonomous Environment Exploration Using Integrated Frontier Detection and Multiple Path Evaluation. *Remote Sens.* **2021**, *13*, 4881.
https://doi.org/10.3390/rs13234881

**AMA Style**

Sun Y, Zhang C.
Efficient and Safe Robotic Autonomous Environment Exploration Using Integrated Frontier Detection and Multiple Path Evaluation. *Remote Sensing*. 2021; 13(23):4881.
https://doi.org/10.3390/rs13234881

**Chicago/Turabian Style**

Sun, Yuxi, and Chengrui Zhang.
2021. "Efficient and Safe Robotic Autonomous Environment Exploration Using Integrated Frontier Detection and Multiple Path Evaluation" *Remote Sensing* 13, no. 23: 4881.
https://doi.org/10.3390/rs13234881