Abstract
The goal of trajectory planning is to shorten the flight distance as much as possible on the premise of ensuring the safety of UAV in flight. Therefore, the research of trajectory planning has broad prospects and great significance. As the key technology of trajectory planning, optimization algorithm has increasingly become one of the focuses of scholars at home and abroad. The dynamic programming algorithm is characterized by high computational efficiency and global optimization in trajectory planning. In 3D trajectory planning, as the spatial search space expands, the number of grid points increases faster, and time complexity of the dynamic programming algorithm is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). It often leads to a “Curse of Dimension” phenomenon, which lowers its computational efficiency drastically. To solve this problem, this paper divides the entire planning space into stages based on Bellman's optimality principle. A dynamic programming-genetic algorithm(DPGA) is proposed by using genetic algorithm(GA) in each stage for optimization, while using dynamic programming algorithm(DP) in global planning. The global optimization ability of the algorithm is verified through convergence analysis. Moreover, based on a series of simulation experiments, it shows that the improved algorithm proposed in this paper is more efficient than the dynamic programming algorithm and genetic algorithm alone in global optimization.
Highlights
Path planning is one of the core issues of UAV control theory[1]
As a kind of swarm intelligence algorithm, the genetic algorithm has the following advantages in trajectory planning: (1) High efficiency: Because genetic algorithm has probability mechanism, its operation efficiency is less affected by the size of search area; (2) Wide application: the crossover and mutation operations of the two positions of Xi and Xi+1 in the curve C are independent of each other, so we can split and reconstruct the individual, and combine with different algorithms; (3) Parallelism: the entire search process is based on populations, which can compare and select multiple individuals at the same time, and perform parallel calculations to improve efficiency
This paper proposes a dynamic programminggenetic algorithm; By dividing the search area into several stages, the whole trajectory planning problem is divided into a series of subproblems with nodes on both sides of the plane as boundary conditions; The new algorithm uses genetic algorithm to solve the optimal solution of each subproblem and uses dynamic programming algorithm to globally optimize the optimal solution of each subproblem in order of stages
Summary
Path planning is one of the core issues of UAV control theory[1]. Its goal is to plan a optimal trajectory from the starting point to the terminate point according to the current complex mission environment, meeting the shortest flying range, successful obstacle avoidance, and various physical manoeuvrability constraints of the aircraft conditions. While in 3D dimensional space, when the spatial planning space expands, the time for solution in tradictional algorithms may grow explosively It means that the exact algorithms are difficult for complex 3D environment [5]. Heuristic algorithms such as the ant colony algorithms [6,7,8,9], genetic algorithms[10], particle swarm algorithms [11,12], and simulated annealing algorithms have been widely used in solving problems of trajectory planning. In terms of time complexity, the new algorithm achieves dimensionality reduction through the division of stages, and uses the mechanism of genetic algorithm to avoid the "Curse of Dimension" problem caused by the spatial combination of discrete states. In Sectioin VI and VII, the results are summarized, and the future research direction and work are prospected
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