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Topological drone navigation in uncertain environment

Bhumeshwar Patle (Department of Mechanical Engineering, National Chung Cheng University, Minxiong, Taiwan)
Shyh-Leh Chen (Department of Mechanical Engineering, National Chung Cheng University, Minxiong, Taiwan)
Brijesh Patel (Department of Aeronautical Engineering, MATS University, Raipur, India)
Sunil Kumar Kashyap (Department of Mathematics, Pandit Ravishankar Shukla University, Raipur, India)
Sudarshan Sanap (Department of Mechanical Engineering, MIT ADT University, Pune, India)

Industrial Robot

ISSN: 0143-991x

Article publication date: 8 April 2021

Issue publication date: 3 August 2021




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.


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.


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.


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.



The proposed work is not funded by any government or private organization. It is purely self-sponsored work.


Patle, B., Chen, S.-L., Patel, B., Kashyap, S.K. and Sanap, S. (2021), "Topological drone navigation in uncertain environment", Industrial Robot, Vol. 48 No. 3, pp. 423-441.



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