# Autonomous Obstacle Avoidance and Trajectory Planning for Mobile Robot Based on Dual-Loop Trajectory Tracking Control and Improved Artificial Potential Field Method

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Kinematic Model of Mobile Robot

_{d}is the time at which the mobile robot reaches the location point (x

_{d}, y

_{d}).

## 3. Design of Control System

#### 3.1. Design of Position Control Law

#### 3.2. Design of Attitude Control Law

_{d}, by designing an attitude control law, ω.

_{d}.

#### 3.3. Autonomous Obstacle Avoidance Trajectory Planning

#### 3.4. Control System Block Diagram

## 4. System Closed-Loop Stability Analysis

_{d}that satisfies trajectory tracking control, the kinematic model can be written as follows:

_{d}are inconsistent, they will inevitably affect the stability of the position closed-loop system. If the influence of the angle tracking error is considered and ideal control laws v

_{1}and v

_{2}are adopted, and ${u}_{1}=v\mathrm{cos}{\theta}_{d}$ and ${u}_{2}=v\mathrm{sin}{\theta}_{d}$ are taken at this time, the design can be carried out according to control law Equations (3) and (14), which can be rewritten as follows:

_{1}and u

_{2}are bounded, v is thus bounded, Equation (15) of the closed-loop system satisfies the global Lipschitz condition, and then x

_{e}and y

_{e}are bounded at any finite time for any initial state.

## 5. Experiment and Result Analysis

_{d}y

_{d}] as x

_{d}= t, y

_{d}= sin($\frac{1}{2}$x) + $\frac{1}{2}$x + 1. Moreover, a = 3.0, b = 3.0, p

_{1}= 10.0, p

_{2}= 10.0, k

_{3}= 3.0, and η

_{3}= 0.5. For the switching term of attitude control law Equation (7), the saturation function is applied, and the boundary layer thickness is taken as 0.10.

#### 5.1. Experiment of the Certain Trajectory without Obstacle

#### 5.2. Experiment with Uncertain Trajectories and Multiple Obstacles

## 6. Conclusions and Future Work

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zheng, K.; Hu, Y.; Yu, W. A novel parallel recursive dynamics modeling method for robot with flexible bar-groups. Appl. Math. Model.
**2020**, 77, 267–288. [Google Scholar] [CrossRef] - Zheng, K.; Zhang, Q.; Hu, Y.; Wu, B. Design of fuzzy system-fuzzy neural network-backstepping control for complex robot system. Inf. Sci.
**2021**, 546, 1230–1255. [Google Scholar] [CrossRef] - Zheng, K.; Zhang, Q.; Peng, L.; Zeng, S. Adaptive memetic differential evolution-back propagation-fuzzy neural network algorithm for robot control. Inf. Sci.
**2023**, 637, 118940. [Google Scholar] [CrossRef] - Ayawli, B.B.K.; Chellali, R.; Appiah, A.Y.; Kyeremeh, F. An Overview of Nature-Inspired, Conventional, and Hybrid Methods of Autonomous Vehicle Path Planning. J. Adv. Transp.
**2018**, 2018, 8269698. [Google Scholar] [CrossRef] - Cowlagi, R.V.; Tsiotras, P. Curvature-Bounded Traversability Analysis in Motion Planning for Mobile Robots. IEEE Trans. Robot.
**2014**, 30, 1011–1019. [Google Scholar] [CrossRef] - Huang, L. Velocity planning for a mobile robot to track a moving target—A potential field approach. Robot. Auton. Syst.
**2009**, 57, 55–63. [Google Scholar] [CrossRef] - Lyu, D.S.; Chen, Z.W.; Cai, Z.S.; Piao, S.H. Robot path planning by leveraging the graph-encoded Floyd algorithm. Future Gener. Comput. Syst. Int. J. Escience
**2021**, 122, 204–208. [Google Scholar] [CrossRef] - Qin, H.; Shao, S.; Wang, T.; Yu, X.; Jiang, Y.; Cao, Z. Review of Autonomous Path Planning Algorithms for Mobile Robots. Drones
**2023**, 7, 211. [Google Scholar] [CrossRef] - Wei, H.; Wang, B.; Wang, Y.; Shao, Z.; Chan, K.C. Staying-alive path planning with energy optimization for mobile robots. Expert Syst. Appl.
**2012**, 39, 3559–3571. [Google Scholar] [CrossRef] - Zhong, X.; Tian, J.; Hu, H.; Peng, X. Hybrid Path Planning Based on Safe A* Algorithm and Adaptive Window Approach for Mobile Robot in Large-Scale Dynamic Environment. J. Intell. Robot. Syst.
**2020**, 99, 65–77. [Google Scholar] [CrossRef] - Zheng, K.; Hu, Y.; Wu, B.; Guo, X. New trajectory control method for robot with flexible bar-groups based on workspace lattices. Robot. Auton. Syst.
**2019**, 111, 44–61. [Google Scholar] [CrossRef] - Liu, L.; Wang, B.; Xu, H. Research on Path-Planning Algorithm Integrating Optimization A-Star Algorithm and Artificial Potential Field Method. Electronics
**2022**, 11, 3660. [Google Scholar] [CrossRef] - Li, J.; Liao, C.; Zhang, W.; Fu, H.; Fu, S. UAV Path Planning Model Based on R5DOS Model Improved A-Star Algorithm. Appl. Sci.
**2022**, 12, 11338. [Google Scholar] [CrossRef] - Hong, Z.H.; Sun, P.F.; Tong, X.H.; Pan, H.Y.; Zhou, R.Y.; Zhang, Y.; Han, Y.L.; Wang, J.; Yang, S.H.; Xu, L.J. Improved A-Star Algo-rithm for Long-Distance Off-Road Path Planning Using Terrain Data Map. ISPRS Int. J. Geo-Inf.
**2021**, 10, 785. [Google Scholar] [CrossRef] - Zhang, Z.; Jiang, J.; Wu, J.; Zhu, X. Efficient and optimal penetration path planning for stealth unmanned aerial vehicle using minimal radar cross-section tactics and modified A-Star algorithm. ISA Trans.
**2023**, 134, 42–57. [Google Scholar] [CrossRef] [PubMed] - Alshammrei, S.; Boubaker, S.; Kolsi, L. Improved Dijkstra Algorithm for Mobile Robot Path Planning and Obstacle Avoidance. Comput. Mater. Contin.
**2022**, 72, 5939–5954. [Google Scholar] [CrossRef] - Liu, L.-S.; Lin, J.-F.; Yao, J.-X.; He, D.-W.; Zheng, J.-S.; Huang, J.; Shi, P. Path Planning for Smart Car Based on Dijkstra Algorithm and Dynamic Window Approach. Wirel. Commun. Mob. Comput.
**2021**, 2021, 8881684. [Google Scholar] [CrossRef] - Wang, J.; Li, Y.; Li, R.; Chen, H.; Chu, K. Trajectory planning for UAV navigation in dynamic environments with matrix alignment Dijkstra. Soft Comput.
**2022**, 26, 12599–12610. [Google Scholar] [CrossRef] - Yu, L.; Jiang, H.; Hua, L. Anti-Congestion Route Planning Scheme Based on Dijkstra Algorithm for Automatic Valet Parking System. Appl. Sci.
**2019**, 9, 5016. [Google Scholar] [CrossRef] - Dian, S.; Fang, H.; Zhao, T.; Wu, Q.; Hu, Y.; Guo, R.; Li, S. Modeling and Trajectory Tracking Control for Magnetic Wheeled Mobile Robots Based on Improved Dual-Heuristic Dynamic Programming. IEEE Trans. Ind. Inform.
**2021**, 17, 1470–1482. [Google Scholar] [CrossRef] - Korayem, M.H.; Irani, M.; Charesaz, A.; Hashemi, A. Trajectory planning of mobile manipulators using dynamic programming approach. Robotica
**2013**, 31, 643–656. [Google Scholar] [CrossRef] - Luy, N.T. Robust adaptive dynamic programming based online tracking control algorithm for real wheeled mobile robot with omni-directional vision system. Trans. Inst. Meas. Control.
**2017**, 39, 832–847. [Google Scholar] [CrossRef] - Yoon, H.-S.; Park, T.-H. Motion planning of autonomous mobile robots by iterative dynamic programming. Intell. Serv. Robot.
**2015**, 8, 165–174. [Google Scholar] [CrossRef] - Chu, Z.; Wang, F.; Lei, T.; Luo, C. Path Planning Based on Deep Reinforcement Learning for Autonomous Underwater Vehicles Under Ocean Current Disturbance. IEEE Trans. Intell. Veh.
**2023**, 8, 108–120. [Google Scholar] [CrossRef] - Peng, Y.; Liu, Y.; Li, D.; Zhang, H. Deep Reinforcement Learning Based Freshness-Aware Path Planning for UAV-Assisted Edge Computing Networks with Device Mobility. Remote Sens.
**2022**, 14, 4016. [Google Scholar] [CrossRef] - Wang, J.; Shim, V.A.; Yan, R.; Tang, H.; Sun, F. Automatic Object Searching and Behavior Learning for Mobile Robots in Unstructured Environment by Deep Belief Networks. IEEE Trans. Cogn. Dev. Syst.
**2019**, 11, 395–404. [Google Scholar] [CrossRef] - Xiao, X.; Liu, B.; Warnell, G.; Stone, P. Motion planning and control for mobile robot navigation using machine learning: A survey. Auton. Robot.
**2022**, 46, 569–597. [Google Scholar] [CrossRef] - Zhang, L.; Zhang, Y.; Li, Y. Path planning for indoor Mobile robot based on deep learning. Optik
**2020**, 219, 165096. [Google Scholar] [CrossRef] - Luo, Q.; Wang, H.; Zheng, Y.; He, J. Research on path planning of mobile robot based on improved ant colony algorithm. Neural Comput. Appl.
**2020**, 32, 1555–1566. [Google Scholar] [CrossRef] - Miao, C.; Chen, G.; Yan, C.; Wu, Y. Path planning optimization of indoor mobile robot based on adaptive ant colony algorithm. Comput. Ind. Eng.
**2021**, 156, 107230. [Google Scholar] [CrossRef] - Lee, J.; Kim, D.-W. An effective initialization method for genetic algorithm-based robot path planning using a directed acyclic graph. Inf. Sci.
**2016**, 332, 1–18. [Google Scholar] [CrossRef] - Liu, L.; Wang, X.; Yang, X.; Liu, H.; Li, J.; Wang, P. Path planning techniques for mobile robots: Review and prospect. Expert Syst. Appl.
**2023**, 227, 120254. [Google Scholar] [CrossRef] - Chang, Z.; Zhang, Z.; Deng, Q.; Li, Z. Route planning of intelligent bridge cranes based on an improved artificial potential field method. J. Intell. Fuzzy Syst.
**2021**, 41, 4369–4376. [Google Scholar] [CrossRef] - He, Z.; Chu, X.; Liu, C.; Wu, W. A novel model predictive artificial potential field based ship motion planning method considering COLREGs for complex encounter scenarios. ISA Trans.
**2023**, 134, 58–73. [Google Scholar] [CrossRef] - Tian, Y.; Zhu, X.J.; Meng, D.S.; Wang, X.Q.; Liang, B. An Overall Configuration Planning Method of Continuum Hy-per-Redundant Manipulators Based on Improved Artificial Potential Field Method. IEEE Robot. Autom. Lett.
**2021**, 6, 4867–4874. [Google Scholar] [CrossRef] - Soltani, A.; Tawfik, H.; Goulermas, J.; Fernando, T. Path planning in construction sites: Performance evaluation of the Dijkstra, A∗, and GA search algorithms. Adv. Eng. Inform.
**2002**, 16, 291–303. [Google Scholar] [CrossRef] - Montiel, O.; Sepúlveda, R.; Orozco-Rosas, U. Optimal Path Planning Generation for Mobile Robots using Parallel Evolutionary Artificial Potential Field. J. Intell. Robot. Syst.
**2015**, 79, 237–257. [Google Scholar] [CrossRef]

**Figure 2.**The force acting on the mobile robot, where ${\mathit{F}}_{att}$ is the attraction force, ${\mathit{F}}_{req1}$ and ${\mathit{F}}_{req2}$ are the components of the repulsion force ${\mathit{F}}_{req}$, and

**F**is the summation of forces acting on the mobile robot.

**Figure 5.**The force acting on the mobile robot based on the improved artificial potential field method.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zheng, K.
Autonomous Obstacle Avoidance and Trajectory Planning for Mobile Robot Based on Dual-Loop Trajectory Tracking Control and Improved Artificial Potential Field Method. *Actuators* **2024**, *13*, 37.
https://doi.org/10.3390/act13010037

**AMA Style**

Zheng K.
Autonomous Obstacle Avoidance and Trajectory Planning for Mobile Robot Based on Dual-Loop Trajectory Tracking Control and Improved Artificial Potential Field Method. *Actuators*. 2024; 13(1):37.
https://doi.org/10.3390/act13010037

**Chicago/Turabian Style**

Zheng, Kunming.
2024. "Autonomous Obstacle Avoidance and Trajectory Planning for Mobile Robot Based on Dual-Loop Trajectory Tracking Control and Improved Artificial Potential Field Method" *Actuators* 13, no. 1: 37.
https://doi.org/10.3390/act13010037