A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles

• Published in: Numerical algorithms Vol. 89; no. 4; pp. 1639 - 1661
• Main Authors: De Marinis, Arturo, Iavernaro, Felice, Mazzia, Francesca
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2022; Springer Nature B.V
• Subjects: Algebra; Algorithms; Boundary conditions; Boundary value problems; Computer Science; Computer simulation; Control theory; Dynamical systems; Energy consumption; Flight time; Numeric Computing; Numerical Analysis; Obstacle avoidance; Optimal control; Optimization; Ordinary differential equations; Original Paper; Path planning; Theory of Computation; Unmanned aerial vehicles; Variables; 65L04; Obstacle avoidance; Pontryagin minimum principle; Continuation technique; Minimum-time trajectory; Path planning; UAV; 49M25; 65L10
• ISSN: 1017-1398; 1572-9265; 1572-9265
• DOI: 10.1007/s11075-021-01167-w

In this article, we present a new strategy to determine an unmanned aerial vehicle trajectory that minimizes its flight time in presence of avoidance areas and obstacles. The method combines classical results from optimal control theory, i.e. the Euler-Lagrange Theorem and the Pontryagin Minimum Principle, with a continuation technique that dynamically adapts the solution curve to the presence of obstacles. We initially consider the two-dimensional path planning problem and then move to the three-dimensional one, and include numerical illustrations for both cases to show the efficiency of our approach.