Enhancing Drone Light Shows Performances: Optimal Allocation and Trajectories for Swarm Drone Formations

Yunes Alqudsi

cs.ROMar 25, 2026

Enhancing Drone Light Shows Performances: Optimal Allocation and Trajectories for Swarm Drone Formations

Authors: Yunes Alqudsi

Abstract

Drone light shows (DLShows) represent a rapidly growing application of swarm robotics, creating captivating aerial displays through the synchronized flight of hundreds or thousands of unmanned aerial vehicles (UAVs) as environmentally friendly and reusable alternatives to traditional pyrotechnics. This domain presents unique challenges in optimally assigning drones to visual waypoints and generating smooth, collision-free trajectories at a very large scale. This article introduces the Unified Assignment and Trajectory Generation (UATG) framework. The proposed approach concurrently solves two core problems: the optimal assignment of drones to designated goal locations and the generation of dynamically feasible, collision-free, time-parameterized trajectories. The UATG framework is specifically designed for DLShows, ensuring minimal transition times between formations and guaranteeing inter-drone collision avoidance. A key innovation is its exceptional computational efficiency, enabling the coordination of large-scale in real-time; for instance, it computes the optimal assignment and trajectories for 1008 drones in approximately one second on a standard laptop. Extensive simulations in realistic environments validate the framework's performance, demonstrating its capability to orchestrate complex formations, from alphanumeric characters to intricate 3D shapes, with precision and visual smoothness. This work provides a critical advancement for the DLShow industry, offering a practical and scalable solution for generating complex aerial choreography and establishing a valuable benchmark for ground control station software designed for the efficient coordination of multiple UAVs. A supplemental animated simulation of this work is available at https://youtu.be/-Fjrhw03594.

Figures & tables

Fig. 1: Drone light show system architecture illustrating the integrated components: centralized control software, drone fleet with positioning and illumination systems, communication infrastructure, GCS, and redundancy mechanisms for reliable operation.

Fig. 2: Workflow of a DLShow performance illustrating the sequential phases. The sequence begins with synchronized takeoff and formation initialization, followed by smooth transitions between formations at $t=\{t_{1},t_{2},t_{3},t_{4}\}$ with LED illumination patterns. Pre-programmed trajectory guidance ensures formation dynamics, concluding with a controlled landing.

Fig. 3: UATG Problem Visualization showing initial drone positions ( $r_{i}$ ), target goal locations ( $G_{i}$ ), and generated 3D trajectories. The illustration highlights collision-free path planning and optimal assignment in obstacle-free environments.

\min_{\mathbf{c}_{i,s,m}}\sum_{s=1}^{W-1}\int_{t_{s}}^{t_{s+1}}\left\|\frac{d^{4}\mathbf{p}_{i}(t)}{dt^{4}}\right\|^{2}dt

Algorithm 1 A Pseudocode of the UATG Framework

Parameter	Value/Unit
Quadrotor total mass	1.79 kg
Motor to c.g. distance ( $R$ )	0.18 m
Roll and pitch inertia	$1.335\times 10^{-2}$ kg $\cdot$ m 2
Yaw inertia	$2.465\times 10^{-2}$ kg $\cdot$ m 2
Aerodynamic coefficient	$8.82\times 10^{-6}$ N/(rad/sec) 2
Drag coefficient	$1.09\times 10^{-7}$ N $\cdot$ m/(rad/sec) 2

TABLE I: Quadrotor Model Parameters for Experimental Simulations

Fig. 4: Sequential numerical formations demonstrating the UATG algorithm’s capability to transform a 16-drone swarm through digits 1, 2, and 3. The sequence illustrates smooth transitions between formations while maintaining optimal assignments and collision-free trajectories.

Fig. 5: Alphabetical character formations (T, S, A, G) generated by a 16-drone swarm, showcasing the algorithm’s flexibility in creating complex letter-based patterns with efficient task allocation and synchronized movements.

Fig. 6: Geometric shape transformations featuring a 43-drone swarm transitioning between crescent moon and star formations. The results demonstrate scalable coordination for medium-sized swarms executing precise 2D shape patterns.

Fig. 7: Complex organic pattern formation showing a 66-drone swarm configured as a butterfly, highlighting the algorithm’s capacity to orchestrate intricate biological shapes with smooth, visually appealing transitions.

Fig. 8: Validation of the UATG framework on large-scale 3D structures. The upper panel shows a World Cup trophy formed by 389 drones, while the lower panel shows a TOGG car formed by 1008 drones, collectively demonstrating the algorithm’s capability for high-density swarm coordination.

Simulation Scenario	Drones #	Formation Transitions #	AnimatedSim Time (sec.)		Algorithm Execution Time (sec.)
		Formation Transitions #	DynamicSim.	KinematicSim	Algorithm Execution Time (sec.)
Numbers	16	3	33.85	3.75	0.3885
Letters	16	4	45.15	4.41	0.3440
Shapes	43	2	65.02	3.37	0.4913
Butterfly	66	1	67.11	2.58	0.1373
World Cup	389	1	395.48	3.91	0.1896

TABLE II: Performance Metrics for Various Scenarios

Comparative Aspect	CAPT Approach [ 23 ]	Proposed UATG Framework
Target System Dynamics	Robots with first-order kinematics	Multirotor drones with higher-order, nonlinear dynamics
Trajectory Profile	Straight-line paths	Dynamically feasible trajectories with minimum derivatives (jerk/snap)
Framework Scope	Focuses on assignment and straight-line trajectory planning	Comprehensive coverage from optimal assignment to dynamically feasible trajectory generation and validation
Collision Avoidance	Provides basic geometric avoidance	Robust, multi-layered avoidance with safety margins for dense swarms
Real-World Considerations	Not designed for rotorcraft-specific effects	Accounts for aerodynamic interference and actuator limits
Scalability (Empirical)	Effective for small-to-moderate swarms	Designed to handle up to thousands of drones with real-time performance

TABLE III: Comparative Analysis of the CAPT Approach and the Proposed UATG Framework

AA	Auction Algorithm
ACO	Ant Colony Optimization
AI	Artificial Intelligence
B&B	Branch and Bound
CO	Combinatorial Optimization
D2D	Drone-to-Drone
DLShows	Drone Light Shows

Table 13

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