# Review of Autonomous Path Planning Algorithms for Mobile Robots

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## Abstract

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## 1. Introduction

## 2. Path Planning Algorithm

#### 2.1. Algorithms Based on Graph Search

#### 2.1.1. A* Algorithm

#### 2.1.2. Dijkstra’s Algorithm

#### 2.2. Heuristic Intelligent Search Algorithm

#### 2.2.1. Genetic Algorithm

#### 2.2.2. Ant Colony Algorithm

#### 2.2.3. Particle Swarm Optimization

#### 2.3. Algorithm Based on Local Obstacle-Avoidance

#### 2.3.1. Dynamic Window Approach

#### 2.3.2. Artificial Potential Field Method

#### 2.3.3. Time Elastic Banding Algorithm

#### 2.4. Algorithm Based on Artificial Intelligence

#### 2.4.1. Neural Networks

#### 2.4.2. Reinforcement Learning

#### 2.4.3. Brain-like Navigation

#### 2.5. Sampling-Based Algorithms

#### 2.5.1. Rapidly-Exploring Random Tree

#### 2.5.2. Probabilistic Roadmap Method

#### 2.6. Planner-Based Algorithms

#### 2.6.1. Covariant Hamilton Optimization Motion Planning

#### 2.6.2. Trajectory Optimization for Motion Planning

#### 2.7. Constraint Satisfaction Problem-Based Algorithms

#### 2.7.1. Chance Constrained Programming

#### 2.7.2. Model Predictive Control

#### 2.7.3. Quadratic Programming

#### 2.7.4. Soft-Constrained Programming

#### 2.8. Other Algorithms

#### 2.8.1. Differential Evolutionary Algorithm

#### 2.8.2. Biogeography Optimization Algorithm

#### 2.8.3. Level Set Approach

#### 2.8.4. Fast Marching Method

#### 2.8.5. Fuzzy Logic Method

#### 2.9. Discussion

## 3. Multi-Robot

## 4. Ground Robot, Unmanned Aerial Robots Cooperative

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Flow chart of genetic algorithm evolution [21].

**Figure 4.**The bird’s swarm searching for the optimal food source represents the particle swarm optimization process.

Algorithms | Mechanism | References | Year | Improvements | Advantages | Limitations |
---|---|---|---|---|---|---|

A* | Find the shortest path to the current node but to the destination | [9] | 2020 | Incorporate the A* algorithm into linear time logic. | Reduces the number of nodes and the time to generate paths. | / |

[11] | 2019 | The risk cost and distance cost functions are simplified, and the critical path points are extracted, which are combined with the window method | Reduces the number of A* nodes and eliminates the need for speed space modeling | Most parameters are determined in simulation experiments | ||

[13] | 2021 | The turning cost function is added, the generated trajectory is optimized, and the maximum search distance and maximum path length are limited | Reduces search time, path length, and number of nodes | / | ||

[14] | 2019 | New cost function designed using ray tracing technique to simulate reflection paths | Provides a safe path based on position error prediction | Energy loss to the unmanned aerial robot when there are sharp turns in the path | ||

[15] | 2019 | A cost function is designed that considers both path length and risk cost | Minimizing the risk to the crowd | There is no guarantee that the path is the optimal solution | ||

[16] | 2016 | Fusing sparse A* algorithms with bio-inspired neurodynamic models | Mitigates the computational bulk of the A* algorithm during 3D track planning | More complex dynamic impediments such as air resistance are not taken into account | ||

GA | Populations generate new populations through crossover and mutation | [21] | 2017 | Combined with Q-learning algorithms and designed for continuous environments with R-values and actions | Autonomously finding suitable obstacle avoidance routes and using Q-learning algorithms for dynamic obstacle avoidance | Q-learning algorithms need to learn from mistakes and robots need to experience failures to find a route |

[22] | 2013 | Combining co-evolutionary mechanisms with improved genetic algorithms | Faster convergence by avoiding local optimum problems | Currently only running in known static environments | ||

[23] | 2015 | Combines genetic algorithms and particle swarm optimization algorithms for global path planning in autonomous underwater robots and uses current factors as evaluation factors for genetic algorithms | Reduces energy consumption of autonomous underwater robots when navigating in a wide range of marine environments | No consideration of the impact of autonomous underwater robot movement on the performance assessment | ||

[24] | 2010 | Combined with dynamic planning, use a B-spline curve to optimize the path | Optimizes path length, minimum turning call, and a maximum pitch angle | / | ||

[25] | 2018 | Combining mixed integer linear programming with genetic algorithms | Better paths can be achieved through lower energy costs | / | ||

[27] | 2016 | Combining genetic algorithms and fuzzy logic | Improving the accuracy of route planning | Its cost function takes slightly longer to run | ||

ACO | Ants move toward areas of high pheromone concentration | [28] | 2017 | Introduced probability multiplication factor | Reduced computational effort and smoother paths | The planned path closely follows the edge of obstacles |

[29] | 2020 | Propose an adaptive pheromone volatility factor strategy; propose a load balancing strategy | Improved efficiency of algorithm operation | Planned paths through the corners of adjacent obstacles | ||

[30] | 2018 | RA and AACO navigation controller designed; RA-AACO hybrid controller designed using the logic RA and AACO logic | Enabling path planning for humanoid robots | 6–7% error in the planned path length and time spent | ||

[31] | 2020 | Introduction of particle swarm optimization algorithms to improve pheromone update rules | Improved search efficiency and shorter optimization paths | Slow convergence rate | ||

[32] | 2018 | Combined with the A* algorithm | The optimal path is obtained | As the number of search dimensions increases, there is a risk of falling into a local optimum | ||

[33] | 2022 | Transformation of the path planning task into a multi-objective optimization task with multiple constraints, introducing an exact population intelligence search method that improves ant colony optimization | Improving the effectiveness of unmanned aerial robot mission planning | / | ||

[35] | 2017 | Two different pheromone table encodings for MTS-ACO are proposed and a minimum time search heuristic function is designed | Better route planning solutions in less time | The trajectories obtained can only be flown directly by drones with specific capabilities | ||

PSO | Individual and group collaboration and information sharing | [37] | 2021 | Introduction of adaptive fractional speed | Enhanced ability to step out of the local optimum solution | Computationally intensive, unstable numerical oscillations, and difficulty in model optimization |

[38] | 2016 | Combination of improved particle swarm optimization algorithm and gravitational search algorithm | Optimized path length, number of turns, and arrival events | Focusing only on evacuation path optimization problems with a single evacuation path | ||

[39] | 2019 | Converts inertial weighting factors and learning factors from linear to non-linear to describe the obstacle with a penalty function | Reduced energy consumption of autonomous underwater robots in underwater environments | May fall into a local optimum solution | ||

[40] | 2019 | Introduction of adaptive laws and quantum behavior for global time optimization | Improved search performance | Slow convergence at later stages | ||

[42] | 2022 | A combination of a selfish population optimizer and a particle swarm optimizer is proposed | Simplifies the structure of SHO and improves SHO search capabilities | / | ||

[43] | 2021 | Parallel evolution of segmented paths using DC strategies to transform high-dimensional problems into multiple parallel low-dimensional problems | Ability to search for viable routes in complex environments with a large number of waypoints, providing better stability | / | ||

Dijkstra | Finding the shortest path in a directed graph | [18] | 2022 | The error caused by the sensor is considered | Generates the planning path with the minimum cumulative error | Inadequate handling in large environments |

[19] | 2019 | Introduction of equivalent paths | Optimal paths were calculated | No experimental results for verification | ||

DWA | Sampling of the surroundings (robot speed, motion parameters, and position) at the current moment | [45] | 2020 | Add two new evaluation functions that use Q-learning to adaptively learn the parameters of DWA | The shortcomings of the original evaluation function have been modified to enhance global navigation with strong self-learning and self-adaptation | The planned path is not optimal |

[46] | 2019 | A dynamic collision model is proposed | Consider the movement of other obstacles and predict future environmental collisions | May provide incorrect modeling when dealing with a large number of dynamic obstacles | ||

[47] | 2012 | Abandoned weighted objective function and used model predictive control | The navigation function is defined as the optimization objective based on the configuration space | Limitations when applied to robots with constrained kinematics | ||

APF | Changing the direction of motion of a robot by repulsive and gravitational forces | [49] | 2015 | Combining the bacterial evolutionary algorithm with the artificial potential field method the bacterial potential field method is proposed | No need to calculate the global optimal path enhancing the local and global controllability of the robot in dynamic environments | Trajectory planning is highly dependent on the hardware architecture of the robot |

[50] | 2020 | Use reinforcement learning to adjust the parameters of a potential field | It has better running time and cost function value | / | ||

[51] | 2020 | Addition of a distance correction factor to the repulsive potential field function; combined with the positive hexagonal bootstrap method | Reduced calculations during navigation | Obstacle avoidance in 3D environments was not considered in the experiment | ||

[52] | 2022 | Improved calculation of the direction of combined forces using the space vector method | Improved computational efficiency of algorithms and reduced cost of obstacle avoidance for autonomous underwater robots | No consideration of the mechanical constraints of the autonomous underwater robot and the size of the obstacle | ||

[53] | 2021 | A method of moving around the nearest obstacle is introduced, and a parallel search algorithm is proposed | Avoiding the trap of local minima in artificial potential fields | / | ||

[54] | 2022 | Proposing a new and improved attraction to enhance the sensitivity of unmanned aerial robots to wind speed and direction | A modified wind resistance gravitational function that takes into account any small changes in relative displacement caused by the wind causing the unmanned aerial robot to drift in a certain direction | / | ||

Neural Network | An information processing system that mimics the structure and function of the brain’s neural networks | [61] | 2014 | Introduction of directional automatic wave control and accelerated neuronal discharge based on dynamic thresholding techniques | Improved path query times, the model uses parameters independent of configuration space and neuron properties | Training neural networks offline is time-consuming |

[62] | 2019 | Combining Q-learning algorithms with convolutional neural networks | Improved path planning performance | Limited to a single scenario, if the target changes it will not work without a large amount of additional training data | ||

[63] | 2015 | Online compensation of range errors using multilayer neural networks and estimation of robot paths and states of environmental maps using Gaussian weighted integration of third-order volume rules | Mitigation of error accumulation caused by inaccurate linearization of the SLAM non-linear functions and incorrect range models | / | ||

TEB | Start point and target point states are specified by the global planner, with N robot poses inserted between, and movement times defined between points | [58] | 2020 | Proposing actively timed elastic bands, incorporating a hybrid inverse velocity barrier model into the objective function of the TEB algorithm | Drive mobile robots to actively avoid dynamic obstacles | There is a tendency to oversteer in corners with partial meandering |

[59] | 2022 | Add penalty function factor constraint, acceleration jump suppression constraint, end-smoothing constraint | Reduced maximum impact on the robot, smooth and accurate arrival at the target point and reduced end impact | Small improvement compared to static weights | ||

reinforcement learning | Train intelligence to take action to maximize their returns | [67] | 2020 | Combining deep Q-learning with experience replay mechanisms and heuristic knowledge | Solves the “dimensional catastrophe” problem, avoiding blind exploration and faster convergence to the optimal action strategy | Only possible in idealized environments |

[68] | 2020 | Increase the choice of extension points, introduce the idea of biased targets, use task return functions, target distance functions, and angle constraints | Reduces the number of invalid nodes and improves the performance of the RRT algorithm | The algorithm has limited generalization capabilities | ||

[70] | 2017 | Designed a learning-based mapless path planner | Training the planner by asynchronous deep reinforcement learning methods so that training and sample collection can be performed in parallel | Insufficient theoretical support and low sample sampling rate | ||

[72] | 2022 | A line-of-sight-based guidance method is used to generate the target angle for path tracking and to generate the error relative to the carrier coordinate system | Facilitates the filtering of irrelevant environmental information and the generation of corresponding policies, enabling more efficient policy approximation | Considers the effect of only a single environmental variable | ||

[73] | 2020 | A deep reinforcement learning method for unmanned aerial robot path planning based on global situational information is proposed, using competing dual-depth Q networks | Higher cumulative rewards and success rates can be achieved | For most winged tactical drones, this option is not suitable | ||

[76] | 2021 | A multi-step competitive DDQN-based algorithm is proposed to design locally optimal unmanned aerial robot paths using the constructed coverage graph | Improved stability and faster convergence of the algorithm | / | ||

Rapid-exploration Random Tree | Built by the random spanning tree method, connecting the generated tree to the trunk of the starting point | [87] | 2019 | Extending the retrospective scope of the two optimization processes of the RRT* algorithm; combined with a sampling strategy | Guaranteed better paths and faster convergence with the same time and space complexity | More computing resources required |

[89] | 2019 | Assessing the feasibility of RRT extensions and exploration through fuzzy controllers combined with six-degree-of-freedom nonlinear models | Handling of random and uncertain information Highly competent | High chance and low accuracy | ||

[91] | 2018 | Combining bi-directional artificial potential field methods with the idea of bi-directional bias sampling | Reduced invalid spatial sampling and increased convergence speed | / | ||

Other Algorithms | [106] | 2022 | Designed path evaluator | Helps autonomous underwater robots use ocean currents to avoid collisions | No consideration of the cost of local paths | |

[107] | 2018 | Using differential evolutionary algorithms to optimize control points for B spline generation | Effective handling of obstacles in three-dimensional space | Failure to consider the complexity of the underwater terrain | ||

[113] | 2016 | Derivation of stochastic dynamic orthogonal level set equations that can be used in dynamically varying current fields | Minimises energy consumption and optimizes the optimal path | The final path is vulnerable to currents | ||

[114] | 2020 | A new discrete iterative equation is derived by localizing the traditional level set function and introducing a polynomial distance regularisation (P-DRE) term | Improved computational efficiency of the level set algorithm | The simulation does not provide performance results in the case of obstacle avoidance | ||

[116] | 2015 | Introduction of multiple constraints and decision criteria to process water flows according to velocity profiles | Reduces path search time and generates 3D smooth paths | / | ||

[118] | 2019 | Introduction of ADRC to manage current disturbances | Improved adaptability of autonomous underwater robots to the marine environment | If the initial values are not set correctly, the control system will be unstable | ||

[119] | 2018 | Optimizing the value of the affiliation function for fuzzy logic using the quantum particle swarm algorithm | Presents a certain resistance to interference and does not require an accurate mathematical model | Insufficient steady-state accuracy in practical applications |

Algorithms | Mechanism | References | Year | Improvements | Advantages | Limitations |
---|---|---|---|---|---|---|

Multi-robot | Cooperation between multiple robots to complete a predetermined task | [121] | 2022 | Constructed a motion situational awareness map, created a rotational potential field, set up a rejection potential function and a robot priority model | The situational awareness map ensures that the robot makes the best decisions at all times, solving the local minima and targeting unreachability problems of the artificial potential field method | Robot control methods are not optimal |

[122] | 2016 | Proposed shortest distance algorithm based on the relative orientation | Ensures smooth and collision-free robot trajectories | The simulation does not provide performance results in the case of obstacle avoidance | ||

[123] | 2022 | Thiessen polygons are used to model and partition the environment, the GRF algorithm is introduced to refine the search, and a multi-robot task allocation method based on an improved market mechanism is used to dynamically allocate exploration target points | The ability to achieve rapid deployment of functional modules and rapid portability of algorithms between various types of multi-robot systems. | Error between simulation results and prototype experimental results | ||

[124] | 2020 | Integration of population-based frameworks and elite selection methods into evolutionary path planning; introduction of simulated annealing methods and particle swarm optimization | Generates trajectories with higher sampling values, a lower standard deviation, and shorter execution times | The method is not applied to 3D workspaces | ||

[125] | 2022 | Combines a novel B-spline data framework with a particle swarm optimization-based solution engine | Robust for handling interference and abnormal operation, providing fast obstacle avoidance | / | ||

[131] | 2018 | An angle-coded particle swarm optimization algorithm is proposed to design multiple constraints that combine the shortest path and safe unmanned aerial robot operation | Accelerated particle swarm convergence that generates safe and reliable paths for each unmanned aerial robot in a formation | / |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/drones7030211

**AMA Style**

Qin H, Shao S, Wang T, Yu X, Jiang Y, Cao Z.
Review of Autonomous Path Planning Algorithms for Mobile Robots. *Drones*. 2023; 7(3):211.
https://doi.org/10.3390/drones7030211

**Chicago/Turabian Style**

Qin, Hongwei, Shiliang Shao, Ting Wang, Xiaotian Yu, Yi Jiang, and Zonghan Cao.
2023. "Review of Autonomous Path Planning Algorithms for Mobile Robots" *Drones* 7, no. 3: 211.
https://doi.org/10.3390/drones7030211