A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions
Abstract
:1. Introduction
2. Scholarly Contributions and Applications
- Definition: (Trajectory Planning)Given a function on a bounded variation, where and . If there exists a process that can retain the values , such that for M, then the process is called a continuous process, and ∂ is called trajectory planning.
- Definition: (Optimal trajectory Planning)Let optimal trajectory planning have a cost function , such that denotes the set of all paths. If definitions 1 is fulfilled to search the path and , such that ∂ is a set of all the feasible paths, then is called as optimal path and , and is optimal path planning.
3. Objectives and Content of This Review
- Consolidation of relevant work: The tendency to concurrently discern a vehicle’s environment, stabilize and restore its motion, and conduct the required driving maneuvers is an exceptional aptitude of human drivers. All over the world, researchers are working on replicating this maneuverable capability of human drivers into designing an autonomous vehicular system to provide a simplified design, comfort, and safety via ensuring the vehicle efficiency is not perturbed [49,50,51,52,53].
- Exploration of design space and Parametric Characterization through Numerical Solvers: Numerical solvers are considered the primitive and most predominant tool for determining the design space and modeling the conventional configuration for ground and aerial vehicles. Few papers on the environment modeling characterization through numerical solvers demonstrate that this area needs to be researched thoroughly. We provide this study in Section 4.
- Survey of trajectory optimization methodologies utilizing Bio-inspired and hybrid Technique: The selection modus operandi to execute trajectory optimization is the most critical question for computational and numerical studies. The development of numerical techniques for optimization directly relates to the exploration of space for ground and aerial vehicles. The trajectory optimization problem is treated as an optimal non-linear problem, so to formulate the optimal and desired trajectory for ground and aerial vehicles, plenty of optimization methods are present for utilization. Therefore, this urges us to conduct extensive research to highlight the optimization algorithms for performing trajectory optimization. We provide this study in Section 5 and Section 6.
- Limitations and the way forward: The paper’s contribution also lies in determining the factors that are not contributing to the optimal trajectory optimization for both ground and aerial vehicles. The drawbacks are categorized into two main areas: (i) the limitations in existing non-linear control techniques; (ii) the limitations in ground and aerial vehicles design. We provide this study at last in Section 7.
Techniques for Path Planning
4. Numerical Techniques
- Dynamic programming: Dynamic programming [80] is an optimization approach that transforms a complex problem into a sequence of simpler problems. The optimality criterion in continuous time is based on the Hamilton–Jacobi–Bellman partial differential equation.
- Indirect methods: In the indirect method [81], the calculus of variations is used to calculate the first-order optimality conditions of the original optimal control problem. The indirect approach solves the problem indirectly by converting the optimal control problem to a boundary-value problem. As a result, the optimal solution is found in an indirect method by solving a system of differential equations that satisfies endpoint and interior-point conditions.
- Direct methods: In a direct method, the state and control of the optimal control problem are discretized in some manner, and the problem is transcribed to a non-linear optimization problem or non-linear programming problem (NLP). Direct methods are divided into three categories: direct shooting [82], direct multiple shooting [83], and collocation. Direct collocation methods utilize a polynomial approximation to the integrated state equations between the nodes, whereas direct shooting methods directly integrate state equations. Arguably, the most powerful methods for solving general optimal control problems are direct collocation methods [79]. A direct collocation method is a state and control parameterization method, where the state and control are approximated using a specified functional form. The two most common forms of collocation are local collocation [84] and pseudospectral (global orthogonal) collocation [84]. In optimal control, local collocation has been employed using one of two categories of discretization: Runge–Kutta methods or the orthogonal collocation method [85,86,87]. In the pseudospectral method [88,89], the optimal control problem is transcribed to a non-linear programming problem (NLP) by parameterizing the state and control using global polynomials (basis function are Chebyshev or Lagrange polynomials) and collocating the differential-algebraic equations using nodes obtained from a Gaussian quadrature. The collocation points are the roots of an orthogonal polynomial (such as Chebyshev or Legendre polynomials) and/or a linear combination of an orthogonal polynomial and its derivatives.
4.1. Applications to Aerial Vehicles
4.2. Applications to Ground Vehicles
4.3. Application to Underwater Vehicle
4.4. Summary Numerical Techniques
5. Bio-Inspired Methods
Technique | Seminal Work | Source |
---|---|---|
Artificial Neural Network | It is based on Kohonen’s self-organizing maps. | [147,148] |
Fuzzy Logic | Presented by Professor Lofti Zadeh, in 1965, at the University of California, (refer Figure 6). | [147,148] |
Artificial Bee Colony Algorithm | Proposed by Karaboga, in 2005, for solving optimization problems. The algorithm mimics the bees colony behavior for the food search. They are divided into three groups: (i) employed bees, (ii) onlooker bees, and (iii) scouts. | [149,150,151] |
Genetic Algorithm | Derived from evolutionary algorithms, they involve different operators, e.g., mutation, crossover, and selection operator (refer to Figure 7). | [152,153,154,155,156,157,158,159,160] |
Simulated Annealing | It is a probabilistic method used for finding the global minimum of a function. It is considered the first metaheuristic algorithm inspired by the physical phenomena happening in the solidification of fluids, such as metals. | [161] |
Grey Wolf Optimizer | Assessing the nature of wolves, researchers were able to formulate mathematical expressions revealing their social behavior in terms of hierarchy distribution of roles in a pack, hunting, the search for prey, and attacking strategies. | [64,162] |
Moth Flame Optimization | Inspired by the behavior of moths in nature, its popularity lies in its simple implementation and no derivation involvement in the starting phase with fewer parameters, making it easy to implement and flexible for all kinds of applications. | [69,163] |
Whale Optimization | The hunting behavior hierarchy of whales inspires Whale Optimization. They out-stand because of their hunting strategy. Their foraging behavior is called the bubble-net feeding method. | [63,164,165] |
AntLion Optimizer | The life cycle of antlions includes two main phases: larvae and adult. Antlions undergo metamorphosis in a cocoon to become adults. They mostly hunt in larvae, and the adulthood period is for reproduction. | [68] |
5.1. Application to Aerial Vehicles
5.2. Application to Ground Vehicles
5.3. Application to Underwater Vehicles
5.4. Summary Bio-Inspired Techniques
6. Hybrid Algorithms
6.1. Application to Aerial Vehicle
6.2. Application to Ground Vehicles
6.3. Application to Underwater Vehicles
6.4. Summary of Hybrid Techniques
7. Challenges Involved in Path Planning Methods
7.1. Proposed Solutions
7.2. Way Forward
Algorithm 1 Coordinated Multi-robot exploration with WOA. |
|
8. Conclusions
- Consolidation of available information: A detailed review of the trajectory planning and optimization is presented from the application point of view on ground, aerial, and underwater vehicles. The DARPA challenge 2007 related to robotics, Lord Rayleigh work related to dynamic soaring in 1883, and some extensions related to the underwater vehicle are elaborated. Algorithms, i.e., numerical techniques for implementing the path planning, are discussed.
- Survey of trajectory optimization techniques: A comprehensive overview related to optimization algorithms and numerical techniques that have been utilized for performing trajectory formation and its optimization.
- Problem formulation and generation of optimal trajectories: An explanation of how different algorithms can be integrated to build a mathematical model for planning and the formation of trajectory components can be achieved presented with a literature survey.
- Limitations and a way forward: Though numerous works review robotics, aerial and underwater vehicle systems have been presented together with optimization techniques and numerical methods, and it has been observed no single algorithm produces desired results or accurate output; therefore, a hybridization of different algorithms has been used by researchers. Two optimization algorithms or two numerical methods together can be integrated, or a mix and match of techniques can be achieved for obtaining the desired characteristics results.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
UAV | Unmanned Aerial Vehicles |
AUV | Autonomous Underwater Vehicles |
UGVs | Unmanned Ground Vehicles |
SLAM | Simultaneous Localization and Mapping |
sUAV | Small Unmanned Aerial Vehicle |
UAAV | Unmanned Aerial-Aquatic Vehicle |
ROS | Robot Operating System |
UUV | Unmanned Underwater Vehicle |
iCab | Intelligent Campus Auto-mobile |
TEB | Time Elastic Band |
GP | Gaussian Process |
NED | North-West-Down |
FRU | Front-Right-Up |
NLP | Non-Linear Programming |
GESOP | Graphical Environment for Simulation and Optimization |
ALTOS | Aerospace Launch Trajectory Optimization Software |
IDVD | Inverse Dynamics in Virtual Domain |
PSOPT | Pseudo Spectral Optimizer |
SAK | Smart Adaption Kit |
GCM | Guidance and Control Module |
CEP | Circular Error Probable |
GPS | Global Positioning System |
LBL | Long Base Line |
DVL | Doppler Velocity Log |
IMU | Inertial Measurement Unit |
EM | Electromagnetic Field |
MEMS | Micro-Electromechanical Systems |
AHRS | Attitude Heading Reference System |
RBO-TMA | Reverse Bearing Only Target Motion Analysis |
SDC | State-Dependent Coefficient |
IN | Inertial Navigation |
PSO | Particle Swarm Optimization |
GWO | Grey Wolf Optimization |
ANN | Artificial Neural Network |
GA | Genetic Algorithm |
ALO | Ant Lion Optimization |
WOA | Whale Optimization |
CNN | Convolutional Neural Network |
SLI | Sylvester Law of Inertia |
NSGA II | Non-dominated sorting genetic algorithm II |
UWG | Underwater Glider |
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Control Panel | Sensor | Software | Testing Environment | Source |
---|---|---|---|---|
E-puck robot | IR, VGA camera, Bluetooth | Webots software | Urban | [37] |
Pioneer 3-DX | camera | Xilinx, GA-IP FPGA | Laboratory based | [38] |
Matlab(ROS system) | – | ROS (SLAM) | Willow Garage map | [39] |
Aria P3-DX | – | Saphira software | simple environment | [40] |
Pioneer 3-DX robot | sonar | ROS | simple environment | [41] |
Applications | |
---|---|
Ground Vehicle | Agriculture applications of grass cutting, land surveying, soil sampling, precision spraying, weeding, and harvesting of crops, Harvester Robots |
Aerial Vehicle | UAV Drones: Mapping and Surveying, Asset Inspection, Mining, Firefighting, Payload carrying, Aviation |
Underwater Vehicle | Sea-gliders, Drifters, propeller-driven vehicles |
Numerical Technique | Contributions | Source |
---|---|---|
Direct global collocation Pseudo spectral | The author proposed a guidance strategy for autonomous dynamic soaring utilizing Guass Pseudospectral OPtimization Software (GPOPS). | [126,127,128,129] |
Variable order orthogonal collocation method | Sachs calculated energy-neutral trajectories for trajectory optimization utilizing two other optimization software, namely ’BOUNDSCO’ and ’TOMP’. The first program ’BOUNDSCO’ is based upon multiple shooting methodology, whereas ’TOMP’ is based on a parameter optimization technique for determining optimal control. | [95,130,131] |
Graph-based Planner with Visibility Graph | Naazare et al. exhibited a graph-based path planner on a UAV to avoid collision in restricted areas. The trajectory builds a visibility graph of the environment using GPS information and finds the shortest path utilizing the A-star algorithm. The generated waypoints show the global localization. Furthermore, the trajectory planner can be used to successfully eliminate the difficulty of manually operating UAVs around restricted areas under challenging circumstances. | [46,132,133] |
Parametric characterization | Imran Mir et al. presented the integration of dynamic soaring with morphing capabilities for a small Unmanned Aerial Vehicle (sUAV). Variable span and variable sweep are two wing morphologies. The non-linear wind gradient profile and 3D point-mass UAV equations of motion have been utilized to model flight dynamics. Parametric characterization has been accessed to check the key performance parameters for various phases of flight dynamics. The results show that the morphing UAV can perform dynamic soaring in an area where fixed-configuration UAVs might not work. | [10,134,135,136] |
Runge–Kutta method | Thaer et al. studied the robotic arm control parameters with numerical solutions involved with the help of the Runge–Kutta method. The non-linear equations are incorporated with formulas of centrifugal effects, Coriolis, and gravitational torques. The method employed was an attempt to mitigate the error involved in the industrial robotic arm, which helps in the increased production system. The acquired results validate the effectiveness of the numerical method and help in analyzing the variations in position and velocity joints. The Runge–Kutta method output perfectly matches with true velocities. | [111] |
Laplace equation | Azali et al. solve the path planning issue iteratively using a numerical method. The Laplace equation is used to calculate the potential function. The author came up with a block iterative method known as 4 Point-EG for resolving the trajectory planning. The experiment shows that the proposed method can generate a clear path from the start to the goal positions and validates that 4 Point-EG works better as compared to previous methods involved in trajectory formation. | [114] |
MEMS-AHRS (Micro-electromechanical systems Attitude Heading Reference System | Nak Yong Ko et al. presented a new technique for attitude detection that accurately uses MEMS-AHRS for detecting the attitude in real-time. The authors proposed a depth measurement method whose robustness and accuracy are higher than the magnetic field and IMU sensors, which ultimately improves the efficiency of the attitude estimation. The technique involves quaternion to relate depth with attitude. The proposed method was tested using simulated data and performing different sea trials. The acquired results prove the efficiency of proposed method. | [122] |
Method | Contribution | Environment Modeling | Nature Environment | Source |
---|---|---|---|---|
GSA-ACO with two fuzzy logic | Castillo et al. used type-2 fuzzy logic in two different bio-inspired techniques: (i) Gravitational Search Algorithm GSA and (ii) Ant Colony Optimization ACO. The parameters such as elapsed rate and percentage of iterations involved in each of these algorithms are fine-tuned by using a type-2 fuzzy logic controller. By which the behavior of a model can be controlled to perform a local/global search task. To check the feasibility of said controller, benchmark functions are used where fuzzy controllers minimize the error occurring in simulations. | Simulation-based | 2D ground vehicle | [202] |
Fuzzy Controller | Lagunes et al. works on optimizing a fuzzy controller by using bio-inspired techniques. The inputs used are linear and angular velocity error and torque 1 and 2 to map the desired trajectory. For optimization purposes, the fireflies algorithm is integrated with a fuzzy system. | Simulation-based | 2D (ground vehicles) | [203] |
SMC Controller | Yu et al. combined two controllers, Sliding Mode Controller and Fuzzy Controller, to regulate the robotic dolphin. The SMC controller checks the line of sight for the robot, and for checking the stability of the algorithm, the Lyapunov function is incorporated to check the convergence properties system. The experimental results show that the said control strategy perfectly steers the mobile robot towards the goal direction. | Simulation-based | 2D ground vehicles | [204] |
PID and Fuzzy Logic Controller | Soliman et al. presented the comparison of the Omni wheel robot to achieve desire maneuverability. The kinematics model of the mobile robot is implemented on control algorithms, such as PID and Fuzzy Logic Controller. The author tested the proposed integration of controllers on hardware and validated the results obtained from simulations. | Simulation-based | 2D ground vehicles | [205] |
Fuzzy Logic Controller | Li et al. presented the Fuzzy Logic Controller based on robotic path planning. The referenced location of the obstacle and the formation of the angle between target and robot position are considered input parameters for driving fuzzy control and determining the accurate movement of the mobile robot. | Simulation-based | 2D ground vehicles | [206] |
Contribution | Hybrid Method | Source |
---|---|---|
Neuro-Fuzzy Method | Many researchers have worked on the obstacle avoidance for mobile robot. | [222,223,224,225,226,227,228,229] |
Neuro-Fuzzy Inference System | Authors proposed the adaptive neuro-fuzzy inference system (ANFIS) for ground vehicle navigation and obstacle avoidance. Khepera simulator (KiKs) was used for simulation purposes. Experimental works were done to check the feasibility of the controller. | [230] |
Multiple Adaptive Neuro-Fuzzy Inference System | The authors developed the adaptive fuzzy controller with two output parameters and four input parameters. Each adaptive fuzzy controller acts as a single Takagi-Sugeno type fuzzy inference system, where output is the velocity from the left and right wheels, and left and right obstacle distances with heading angle act as input parameters. The robustness of said controller is validated on the simulation platform. | [231] |
Hybrid Intelligent System (HIS) | Alves and Lopes proposed the integration of ANN with FL for controlling robot navigation and mitigating the noise production in the system when collecting data from sensors. According to the authors, the integration provides calibration and tuning of parameters not present in the neuro-fuzzy system. Simulations were performed to validate the results successfully. | [232] |
Dynamic Self-Generated Fuzzy Q-learning (DSGFQL) | The method was proposed for obstacle avoidance. The method was compared with dynamic fuzzy Q-learning (DFQL) and fuzzy Q-learning (FQL), and the Q-value clustering scheme was compared with the Genetic algorithm. The proposed method is said to produce the desired output and perform well when tested in simulations. | [233,234,235] |
Cause | Challenges | Source |
---|---|---|
Sensors/camera | The readings form these sensors are not accurate nor reliable as they are integrated with noise, temperature, and system oscillations, etc. This arises uncertainty in the system output, which causes unintentional error in the output of the algorithm. | [236,237,238] |
Noise occurrence | Plenty of research has been performed to mitigate and cater the noise occurrence in the vehicle system; however, this is still a challenge. These problems and plenty others widely disturb the implementation of any algorithm in real-time. | [240] |
Vision-Based | The problem lies in identifying pairs of points in the same dimension. This causes ambiguity in identifying points, which results in inconsistent interpretation of any image. | [241,242] |
ANN | This algorithm has numerous advantages, but they require a large data set of the surrounding area for the adjustment of hidden layers. The famous backpropagation algorithm has its own disadvantages, as it easily converges to the local minima problem. | [244,245] |
Approach | Comments | Local/Global | Improvement | Off/On Line | Environment Dimension | Simulation/Experiment |
---|---|---|---|---|---|---|
Dijkstra | (a) Low efficiency | Global/Local | / | off | 2D | Simulation |
(b) Robust and efficient success rate | ||||||
A-star | (a) Low cost | Global/Local | / | off | 2D | Simulation |
(b) Easy implementation and efficient | ||||||
(c) Involves interruption and susceptible to slow convergence | ||||||
PRM | (a) Precise Results and easy implementation | Global/Local | / | on | 2D/3D | Simulation/ Experiment |
(b) Search path is may not be the optimal path | ||||||
D-star | (a) Stable | Local | / | off | 2D | Simulation |
(b) Proven effective in obstacle avoidance | ||||||
D-star-Lite | (a) Fast and Robust | Local | / | off | 2D/3D | Simulation/ Experiment |
(b) Proven effective for dynamic path planning | ||||||
APF | (a) Simple and easy to implement | Local | Optimization path, improved stability, avoiding local minima | on/off | 2D/3D | Simulation/ Experiment |
(b) Fall into local minima problem |
Algorithms | Strengths | Challenges | Implementation | Time Complexity |
---|---|---|---|---|
Fuzzy Logic | (a) The fuzzy rules can be tuned for desirable requirement [3] | (a) Difficult to create membership functions | Real-time and simulation | |
(b) Control logic implementation is easy [252] | ||||
(c) Can be easily integrated with bio-inspired algorithms [3] | ||||
Neural Network | (a) Works best in real-time | (a) Difficult to handle buried neuron layers in the network [244] | Real-time and simulation | |
(b) Imitate human control logic easily | (b) Increase in layers increases complexity [244] | |||
(c) Use of backpropagation results in a local minimum problem [253] | ||||
(d) Acquiring a large data set in real-time is difficult [244] | ||||
Genetic Algorithm | (a) Faster convergence rate and optimization capability [46] | (a) Get stuck in local minima problem when environment complexity increase [254] | Simulation | |
(b) Combine well with other algorithms [46] | (b) Produce oscillations in system [255] | |||
(c) Because of easy implementation integrate well with other algorithms [181] | ||||
ABC | (a) Requires fewer control parameters [151] | (a) Slow convergence rate [256] | Simulation | |
(b) Requires less computational time [181] | ||||
(c) Because of easy implementation integrate well with other algorithms [181] | ||||
Simulated Annealing | (a) Good at approximating global optimum [161] | (a) Slow convergence rate [161] | Simulation | |
GWO | (a) Fast convergence rate [183] | (a) Implementation gets tricky when complex scenarios arise [185] | Simulation | |
(b) Lesser variable involvement [183] (c) Easily integrated with other algorithms [184] | ||||
Moth Flame | (a) Compared to other algorithms, it produces good solutions in complex scenarios [192] | (a) Has premature convergence rate [191] | Simulation | |
WOA | (a) Easy implementation with fast convergence rate [194] | (a) Difficult to handle in a complex environment [141] | Simulation | |
AntLion | (a) Produces good results in complex environment [195] | (a) Involvement of a lot of variables makes it difficult to handle when integrated with different algorithms [196] [74] | Simulation |
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Gul, F.; Mir, I.; Abualigah, L.; Sumari, P.; Forestiero, A. A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions. Electronics 2021, 10, 2250. https://doi.org/10.3390/electronics10182250
Gul F, Mir I, Abualigah L, Sumari P, Forestiero A. A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions. Electronics. 2021; 10(18):2250. https://doi.org/10.3390/electronics10182250
Chicago/Turabian StyleGul, Faiza, Imran Mir, Laith Abualigah, Putra Sumari, and Agostino Forestiero. 2021. "A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions" Electronics 10, no. 18: 2250. https://doi.org/10.3390/electronics10182250
APA StyleGul, F., Mir, I., Abualigah, L., Sumari, P., & Forestiero, A. (2021). A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions. Electronics, 10(18), 2250. https://doi.org/10.3390/electronics10182250