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🔥 Content Introduction
This article proposes a robot trajectory planning method based on the Penguin Optimization Algorithm (POA). It first explains the basic principles of the Penguin Optimization Algorithm and analyzes its advantages in global search and local development. For the objectives of shortest path and obstacle avoidance in robot trajectory planning, a corresponding mathematical model is constructed. The feasible trajectories of the robot are encoded as individuals in the Penguin Optimization Algorithm, and by simulating the foraging and migration behaviors of penguins in their natural environment, the optimal trajectory is searched in the solution space. Simulation results show that compared to traditional Particle Swarm Optimization and Genetic Algorithms, the robot trajectory planning method based on the Penguin Optimization Algorithm exhibits superior performance in terms of path length and obstacle avoidance success rate, effectively solving the robot trajectory planning problem and providing technical support for efficient robot operation.
Keywords
Penguin Optimization Algorithm; Robot Trajectory Planning; Shortest Path; Obstacle Avoidance; Intelligent Optimization Algorithm
1. Introduction
Robots are increasingly applied in various scenarios such as industrial production, logistics transportation, and service fields, and trajectory planning is one of the key technologies for robots to achieve efficient and safe operation. Robot trajectory planning aims to plan an optimal path from the starting point to the target point while satisfying constraints such as obstacle avoidance, minimum time, and minimum energy consumption.
Traditional trajectory planning methods, such as the artificial potential field method and A* algorithm, can achieve good results in simple environments, but they face issues such as high computational load and susceptibility to local optima in complex environments. With the development of intelligent optimization algorithms, Particle Swarm Optimization and Genetic Algorithms have been widely used in robot trajectory planning, but there is still room for improvement in search efficiency and accuracy. The Penguin Optimization Algorithm is a novel intelligent optimization algorithm inspired by the collective behavior of penguins, possessing strong global search and local development capabilities, and its application in robot trajectory planning is expected to improve the quality and efficiency of planning.
2. Principles of the Penguin Optimization Algorithm
The Penguin Optimization Algorithm simulates the foraging, migration, and social behaviors of penguins in their natural environment. In the algorithm, each solution in the search space is viewed as a penguin, and the position of the penguin corresponds to the parameters of the solution. The algorithm mainly includes the following steps:
- Initialize the population: Randomly generate a certain number of penguin individuals in the solution space to form the initial population. Each penguin individual’s position represents a potential solution, i.e., a possible trajectory of the robot.
- Calculate fitness: Define a fitness function based on the objectives of robot trajectory planning (such as path length, obstacle avoidance, etc.) and calculate the fitness value of each penguin individual. A higher fitness value indicates a better corresponding trajectory.
- Foraging behavior: Simulate the behavior of penguins randomly searching for food within a certain range by randomly perturbing the current individual position to generate a new individual position. If the fitness of the new position is better than the original position, update the individual position.
- Migration behavior: Penguins migrate based on environmental changes and group information. In the algorithm, a certain probability is used to select some penguin individuals to move closer to the current global optimal individual, simulating the migration behavior of penguins and accelerating the convergence speed of the algorithm.
- Social behavior: Penguins communicate information with each other, which in the algorithm manifests as individuals learning from each other. By exchanging partial information between individuals, new individuals are generated, enhancing the global search capability of the algorithm.
- Update the population: Repeat the above foraging, migration, and social behaviors to continuously update the positions and fitness values of the penguin population until the termination condition is met (such as reaching the maximum number of iterations or convergence of fitness values).
3. Modeling the Robot Trajectory Planning Problem
(1) Environment Modeling
Model the robot’s working environment as a two-dimensional or three-dimensional space, using methods such as grid method or Voronoi diagram method to discretize the environment. For example, using the grid method, the working environment is divided into equally sized grids, each representing a position unit. Different attribute values are assigned based on whether there are obstacles within the grid, such as 0 indicating no obstacle and 1 indicating an obstacle.
(2) Objective Function
(3) Encoding of Solutions
Encode the robot’s trajectory as individuals in the Penguin Optimization Algorithm. Integer encoding can be used, where the sequence of grid numbers passed through on the path is arranged to form a coding string, which corresponds to the position of a penguin individual. For example, in a 10×10 grid environment, if the robot’s path passes through grids (2, 3), (3, 4), and (4, 5) in order, its encoding would be [23, 34, 45].
4. Robot Trajectory Planning Process Based on the Penguin Optimization Algorithm
- Initialization: Set algorithm parameters such as the number of penguin populations, maximum number of iterations, foraging range, and migration probability, randomly generate the initial population, and encode each individual according to the coding rules.
- Calculate fitness: Calculate the fitness value of each penguin individual based on the fitness function.
- Execute algorithm operations: Sequentially perform foraging behavior, migration behavior, and social behavior operations to update the positions and fitness values of the penguin individuals.
- Check termination conditions: Check if the maximum number of iterations has been reached or if the fitness values have converged. If the termination conditions are met, stop the algorithm; otherwise, return to step 2 to continue execution.
- Output results: The trajectory corresponding to the individual with the optimal fitness value in the final population is taken as the robot’s optimal planned trajectory.
5. Conclusion
This article applies the Penguin Optimization Algorithm to robot trajectory planning, achieving efficient trajectory planning for robots in complex environments by constructing appropriate mathematical models and algorithm processes. Simulation results indicate that this method outperforms traditional Particle Swarm Optimization and Genetic Algorithms in terms of path length, obstacle avoidance success rate, and convergence speed. Future work may further optimize the parameter settings of the Penguin Optimization Algorithm and apply it to robot trajectory planning in three-dimensional spaces or dynamic environments, expanding the algorithm’s application scope.
⛳️ Operation Results
🔗 References
[1] Guo Qingda, Wan Chuanheng, Shi Buhai. Research on Time-Optimal Trajectory Planning and Simulation of Industrial Robots Based on Genetic Algorithm[J]. Computer Measurement and Control, 2014, 22(4):3. DOI:10.3969/j.issn.1671-4598.2014.04.084.
[2] Liu Nengguang, Ren Tianran, Chai Cangxiu, et al. Two-Level Planning of Painting Robot Trajectory Based on Genetic Algorithm[J]. Mechanical Design and Manufacturing, 2008(6):3. DOI:CNKI:SUN:JSYZ.0.2008-06-073.
[3] Zuo Fuyong, Hu Xiaoping, Xie Ke, et al. SCARA Robot Trajectory Planning and Simulation Based on MATLAB Robotics Toolbox[J]. Journal of Hunan University of Science and Technology: Natural Science Edition, 2012, 27(2):4. DOI:10.3969/j.issn.1672-9102.2012.02.009.
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Traveling salesman problem (TSP), vehicle routing problem (VRP, MVRP, CVRP, VRPTW, etc.), three-dimensional path planning for drones, drone collaboration, drone formation, robot path planning, grid map path planning, multimodal transport problems, electric vehicle routing problem (EVRP), two-layer vehicle routing problem (2E-VRP), oil-electric hybrid vehicle routing problem, ship trajectory planning, full path planning, warehouse patrol.
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