# Collision Free Smooth Path for Mobile Robots in Cluttered Environment Using an Economical Clamped Cubic B-Spline

## Abstract

**:**

## 1. Introduction

- Post smoothing collision checking and curve improvement.
- Economical control point adjustment technique.
- Automated knot vector generation according to planned path.
- Improved execution time and path length.
- More closer to the originally planned path.

## 2. Preliminaries

## 3. Related Work

## 4. Proposed Smoothing Algorithm

Algorithm 1: Clamped B-Spline Smoothing Algorithm. |

## 5. Results and Discussion

#### 5.1. Performance Metrics

**Total Path Length:**The total length of path (measured in meters) directly affects the total operational time to cover the distance and the total energy consumption of the mobile robot. Therefore, the short length of smooth path is also desirable leading to energy efficiency: 1 grid cell in grid occupancy map = 1 m.**Run Time:**The Computational time (measured in unit second) s required to compute the solution is a prominent efficiency indicator of the proposed approach.**Collision-free smoothness:**It is the most crucial metric as a smooth path obtained in minimal computational time with required continuity and short length will be of no use if it is not free from collision. Once the post smoothing process provides a collision free smooth path, it is applicable to follow.

#### 5.2. Experimental Cases

- Collision checking is performed after smoothness application until all collisions are eliminated.
- Post collision path improvement.
- Collision based control point adjustment. Point insertion is avoided in collision free curve segments. New control points are inserted only in segments where collision occurs, and hence offers a need based and efficient point insertion scheme.
- Automated knot vector generation.
- Approximation with more close following of the planned path.
- Obeys convex hull property and lies within a boundary of a planner generated path.
- No stitching or joining points required, one whole single curve represents the smooth curve for the path.

## 6. Conclusions and Future Directions

## Funding

## Conflicts of Interest

## Abbreviations

UAV | Unmanned Aerial Vehicle |

CAGD | Computer Aided Graphic Design |

RRT | Rapidly Exploring Random Tree |

RRT* | Rapidly Exploring Random Tree Star |

RRT*-AB | RRT*-Adjustable Bounds |

MEA* | Memory Efficient A* |

ROS | Robot Operating System |

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**Figure 5.**Phases of proposed smoothing approach using unstructured complex environment. (

**a**) Path generation by RRT*-AB, (

**b**) B-Spline application, (

**c**) Post smoothing collision, (

**d**) Mid-point insertion in segment of collision, (

**e**) Final smooth path.

**Figure 7.**Comparison of experimental results of proposed algorithm with the state-of-the-art spline-based algorithm [13], case 1 structured map, case 2 complex un-structured map, and case 3 dense structure environment. (

**a**) Case 1 Elbanhawi et al. [13], (

**b**) Case 1 Proposed, (

**c**) Case 2 Elbanhawi et al. [13], (

**d**) Case 2 proposed, (

**e**) Case 3 Elbanhawi et al. [13], (

**f**) Case 3 proposed.

Case | Metric | Elbanhawi et al. [13] | Proposed Approach |
---|---|---|---|

Case 1: Simple Structured Map | Collision Status | Collision free | Collision free |

Path Cost | 31 m | 29 m | |

Run Time | 0.24 s | 0.17 s | |

Case 2: Complex Un-structured Map | Collision Status | Collision | Collision free |

Path Cost | NA | 111 m | |

Run Time | NA | 0.22 s | |

Case 3: Dense Cluttered Un-Structured Map | Collision Status | Collision | Collision free |

Path Cost | NA | 119 m | |

Run Time | NA | 0.27 s |

**Table 2.**Feature comparison of the proposed approach with cubic spline-based state of the art [13].

Features | Elbanhawi et al. [13] | Proposed Approach |
---|---|---|

Collision detection and smooth path regeneration strategy | No | Yes |

Economical point insertion | No | Yes |

Suitable for unstructured complex environment | No | Yes |

Auto knot vector generation | No | Yes |

Features | Yang et al. [22] | Huh et al. [26] | Elbanhawi et al. [13] | Proposed Approach |
---|---|---|---|---|

Continuity | ${G}^{2}$ | ${G}^{2}$ | ${C}^{2}$ | ${C}^{2}$ |

Degree Independence | No | No | Yes | Yes |

Local Control | No | No | Yes | Yes |

Avoiding Stitching Discontinuity | No | No | Yes | Yes |

Curvature Management | No | No | Yes | No |

Collision Checking | Partially | No | No | Yes |

Tested on Unstructured map | No | No | No | Yes |

Post Smoothness Collision Checking and Elimination | Partially | No | No | Yes |

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**MDPI and ACS Style**

Noreen, I.
Collision Free Smooth Path for Mobile Robots in Cluttered Environment Using an Economical Clamped Cubic B-Spline. *Symmetry* **2020**, *12*, 1567.
https://doi.org/10.3390/sym12091567

**AMA Style**

Noreen I.
Collision Free Smooth Path for Mobile Robots in Cluttered Environment Using an Economical Clamped Cubic B-Spline. *Symmetry*. 2020; 12(9):1567.
https://doi.org/10.3390/sym12091567

**Chicago/Turabian Style**

Noreen, Iram.
2020. "Collision Free Smooth Path for Mobile Robots in Cluttered Environment Using an Economical Clamped Cubic B-Spline" *Symmetry* 12, no. 9: 1567.
https://doi.org/10.3390/sym12091567