Purpose

With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a new path planning approach to drone navigation based on topology in an uncertain environment. The main objective of this study is to use the Ricci flow evolution equation of metric and curvature tensor over angular Riemannian metric, and manifold for achieving navigational goals such as path length optimization at the minimum required time, collision-free obstacle avoidance in static and dynamic environments and reaching to the static and dynamic goals. The proposed navigational controller performs linearly and nonlinearly both with reduced error-based objective function by Riemannian metric and scalar curvature, respectively.

Design/methodology/approach

Topology and manifolds application-based methodology establishes the resultant drone. The trajectory planning and its optimization are controlled by the system of evolution equation over Ricci flow entropy. The navigation follows the Riemannian metric-based optimal path with an angular trajectory in the range from 0° to 360°. The obstacle avoidance in static and dynamic environments is controlled by the metric tensor and curvature tensor, respectively. The in-house drone is developed and coded using C++. For comparison of the real-time results and simulation results in static and dynamic environments, the simulation study has been conducted using MATLAB software. The proposed controller follows the topological programming constituted with manifold-based objective function and Riemannian metric, and scalar curvature-based constraints for linear and nonlinear navigation, respectively.

Findings

This proposed study demonstrates the possibility to develop the new topology-based efficient path planning approach for navigation of drone and provides a unique way to develop an innovative system having characteristics of static and dynamic obstacle avoidance and moving goal chasing in an uncertain environment. From the results obtained in the simulation and real-time environments, satisfactory agreements have been seen in terms of navigational parameters with the minimum error that justifies the significant working of the proposed controller. Additionally, the comparison of the proposed navigational controller with the other artificial intelligent controllers reveals performance improvement.

Originality/value

In this study, a new topological controller has been proposed for drone navigation. The topological drone navigation comprises the effective speed control and collision-free decisions corresponding to the Ricci flow equation and Ricci curvature over the Riemannian metric, respectively.

中文翻译：

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不确定环境下的拓扑无人机导航

目的

随着对监控和智能交通的需求不断增加，无人机技术已成为机器人研究人员关注的焦点。本研究旨在为不确定环境中的基于拓扑的无人机导航引入一种新的路径规划方法。本研究的主要目的是利用角黎曼度量上的度量和曲率张量的 Ricci 流演化方程，以及流形来实现导航目标，例如在所需的最短时间优化路径长度、静态和动态中的无碰撞避障。环境并达到静态和动态目标。所提出的导航控制器通过黎曼度量和标量曲率分别以减少的基于误差的目标函数线性和非线性地执行。

设计/方法/方法

基于拓扑和流形应用的方法建立了最终的无人机。轨迹规划及其优化由 Ricci 流熵上的演化方程系统控制。导航遵循基于黎曼度量的最佳路径，角轨迹范围为 0° 到 360°。静态和动态环境中的避障分别由度量张量和曲率张量控制。内部无人机是使用 C++ 开发和编码的。为了比较静态和动态环境下的实时结果和仿真结果，使用MATLAB软件进行了仿真研究。所提出的控制器遵循由基于流形的目标函数和黎曼度量构成的拓扑规划，

发现

这项拟议的研究证明了为无人机导航开发新的基于拓扑的高效路径规划方法的可能性，并提供了一种独特的方法来开发具有静态和动态避障和在不确定环境中追逐移动目标的特征的创新系统。从在仿真和实时环境中获得的结果来看，在导航参数方面已经看到了令人满意的协议，其误差最小，证明了所提出的控制器的重要工作是合理的。此外，所提出的导航控制器与其他人工智能控制器的比较揭示了性能的改进。

原创性/价值

在这项研究中，提出了一种用于无人机导航的新拓扑控制器。拓扑无人机导航包括分别对应于黎曼度量上的 Ricci 流方程和 Ricci 曲率的有效速度控制和无碰撞决策。