Clothoid-Based Path Planning for a Formation of Fixed-Wing UAVs

Abstract

Unmanned aerial vehicles (UAVs) are playing an increasingly crucial role in many applications such as search and rescue, delivery services, and military operations. However, one of the significant challenges in this area is to plan efficient and safe trajectories for UAV formations. This paper presents an optimization procedure for trajectory planning for fixed-wing UAV formations using graph theory and clothoid curves. The proposed planning strategy consists of two main steps. Firstly, the geometric optimization of paths is carried out using graphs for each UAV, providing piece-wise linear paths whose smooth connections are made with clothoids. Secondly, the geometric paths are transformed into time-dependent trajectories, optimizing the assigned aircraft speeds to avoid collisions by solving a mixed-integer optimal control problem for each UAV of the flight formation. The proposed method is effective in achieving suboptimal paths while ensuring collision avoidance between aircraft. A sensitivity analysis of the main parameters of the algorithm was conducted in ideal conditions, highlighting the possibility of decreasing the length of the optimal path by about 4.19%, increasing the number of points used in the discretization and showing a maximum path length reduction of about 10% compared with the average solution obtained with a similar algorithm using a graph based on random directions. Furthermore, the use of clothoids, whose parameters depend on the UAV performance constraints, provides smoother connections, giving a significant improvement over traditional straight-line or circular trajectories in terms of flight dynamics compliance and trajectory tracking capabilities. The method can be applied to various UAV formation scenarios, making it a versatile and practical tool for mission planning.

Path Planning for Fixed-Wing Unmanned Aerial Vehicles: An Integrated Approach with Theta* and Clothoids

“…To highlight the effectiveness of the proposed methodology in terms of the ability to find the minimum-length path and avoid collisions with environmental obstacles, this section presents a comparison with three algorithms with the same objectives: the Essential Visibility Graph (EVG) with Dubins-based smoothing [56,61], a custom graph-based solution with clothoids [17], and an RRT-based algorithm, named the Stack-RRT* algorithm [62].…”

“…The comparison with another clothoid-based approach [17] is faced using the scenario of the test case #3 (see Section 4.3). The parameters are summarized in Table 7.…”

“…Several publications [12,13] introduced purely geometrical approaches, describing paths as sequences of segments, arcs, or template curves. Examples include solutions to Dubins' car problem [14,15] or clothoid curves [16,17]. However, such solutions often require combining other algorithms to account for obstacles and no-fly zones.…”

Fixed-Wing UAV Formation Path Planning Based on Formation Control: Theory and Application

“…Recently, the integer programming has also been introduced into formation path planning problems. Luciano et al [18] presented an optimization method for fixed-wing UAV formation trajectory planning based on graph theory and clothoid curves, while solving the mixed integer optimal control problem of the formation to avoid collisions between UAVs. With the rapid development of machine learning technology, numerous researchers have adopted machine learning methods for path planning.…”

A Fusion Approach for UAV Onboard Flight Trajectory Management and Decision Making Based on the Combination of Enhanced A* Algorithm and Quadratic Programming

“…The other approach concerns the optimization of a local dynamic flight trajectory within the local sensing range of onboard sensors, while performing dynamic obstacle avoidance by using the localization of UAV positions and sensing information of the dynamic environment with an optimization strategy or certain resolution rules. In this case, the smoothness of the trajectory and successfully collision avoidance are two key objectives, which possibly lead to trajectory deviation from the UAV's original planned path [20][21][22][23][24][25][26].…”