Source-linked AI summary
Flocking algorithm for autonomous flying robots
Csaba Virágh, Gábor Vásárhelyi, Norbert Tarcai, Tamás Szörényi, Gergő Somorjai, Tamás Nepusz, Tamás Vicsek
TL;DR
The paper asks how flocking patterns can be reproduced by autonomous flying robots despite realistic sensing, communication, and dynamical imperfections. It develops a realistic decentralized model and two control algorithms, finding that viscous alignment reduces instabilities and works in quadcopter experiments.
Problem
Realistic robotic flocking requires modeling delays, local communication, noisy sensors, inertial effects, and environmental disturbances that can destabilize collective motion.
Method
The paper builds a realistic decentralized flying-robot simulation framework and implements self-propelled flocking and collective target-tracking algorithms using repulsion and viscous friction-like alignment.
Results
Simulations found that optimal viscous friction-like strength reduces instabilities, and real quadcopter experiments demonstrated algorithm applicability and stability under environmental noise.
Takeaways & Limitations
Viscous friction-like alignment is an effective stabilizing component for decentralized collective-robot control in noisy, delayed systems.
Takeaways & Limitations
The model does not explicitly treat synchrony versus asynchrony in its simulation updates, delay model, or communication.
Abstract
from arXiv · showhide
Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with agent-based models. If we want to reproduce these patterns with artificial systems, such as autonomous aerial robots, agent-based models can also be used in the control algorithm of the robots. However, finding the proper algorithms and thus understanding the essential characteristics of the emergent collective behaviour of robots requires the thorough and realistic modeling of the robot and the environment as well. In this paper, first, we present an abstract mathematical model of an autonomous flying robot. The model takes into account several realistic features, such as time delay and locality of the communication, inaccuracy of the on-board sensors and inertial effects. We present two decentralized control algorithms. One is based on a simple self-propelled flocking model of animal collective motion, the other is a collective target tracking algorithm. Both algorithms contain a viscous friction-like term, which aligns the velocities of neighbouring agents parallel to each other. We show that this term can be essential for reducing the inherent instabilities of such a noisy and delayed realistic system. We discuss simulation results about the stability of the control algorithms, and perform real experiments to show the applicability of the algorithms on a group of autonomous quadcopters.
1. Introduction
The paper motivates decentralized flocking control for autonomous flying robots by connecting animal collective-motion principles with realistic robotic constraints. It aims to model these constraints and assess whether viscous alignment can stabilize flocking and target-tracking behaviors.
- Animal collectives exhibit neighboring velocity vectors that tend to become parallel, supporting safe, stable, collision-free motion.
- Flocking models commonly combine short-range repulsion, local velocity alignment, and positional constraints to generate collective motion.
- Locality is central to flocking models because agents align using nearby neighbors, paralleling finite-range robot communication.
- Robotic flocking must address reaction delays, communication delays, noisy sensors, and environmental disturbances that can produce unpredictable instability.
- The paper develops a general flying-robot model with independent parameters for realistic deficiencies and applies it to decentralized control algorithms.
- A viscous friction-like alignment term damps oscillations, while simulations and quadcopter experiments examine self-propelled flocking and collective target tracking.
2. Realistic model of a flying robot
The flying-robot model represents decentralized control with inertia, sensor imperfections, limited refresh rates, communication locality, delays, and environmental noise. Its acceleration dynamics use delayed local interactions and stochastic measurements while constraining parameters to an experimental quadcopter setup.
- The model treats a desired velocity as the input to a low-level controller, with acceleration producing the robot’s realized motion.
- Robot deficiencies include inertial response, bounded acceleration, sensor noise, limited sensor refresh, finite communication range, time delay, and environmental noise.
- Time delay and communication range are identified as difficult-to-measure factors whose effects on stability require investigation across parameter values.
- The acceleration model depends on the agent’s current state and delayed positions and velocities of communicating agents, with noise incorporated into measured states.
- The control function is designed around relative coordinates and local pairwise interactions rather than global positional information.
- Model parameters and velocity limits are selected to represent the authors’ quadcopter experimental setup, with valid ranges summarized in Table 1.
3. Self-propelled flocking model
The self-propelled flocking algorithm combines interaction terms for collision avoidance, velocity alignment, and confinement to produce stable, collision-less collective motion.
- Algorithm overview: The algorithm drives robots toward a stable, collision-less, self-organized correlated flocking state.The desired velocity combines interaction terms with terms governing self-propulsion and bounded-arena interactions.
- Short-range repulsion: Local linear repulsion prevents collisions while remaining robust to noisy position measurements.Linear repulsion is preferred because measurement errors do not create sudden changes or singularities in the output.
- Velocity alignment of neighbours: A viscous friction-like alignment term relaxes velocity differences locally and remains bounded near zero separation.Its inverse-square distance decay makes the interaction negligible at large distances when the velocity and alignment parameters are bounded.
- Boundaries and shill agents: The bounded arena is modeled with virtual shill agents that steer units toward the arena center outside the walls.A sigmoid smoothly reduces the shill-repulsion strength inside the arena, while the arena shape is represented by a square-side-length parameter.
- Algorithm overview: The three terms together provide the minimal prerequisites for stable and collision-free collective motion in simulations and experiments.The parameter summary is given in Table 2.
4. Collective target tracking
The collective target-tracking algorithm combines target attraction with local centre-of-mass tracking, repulsion, and viscous velocity alignment to transition between flocking and hovering. Simulations and quadcopter experiments show stable collective tracking under delays, noise, and local communication constraints, while excessive friction slows target arrival.
- Algorithm: The target-tracking algorithm enables a smooth transition between a flocking state far from the target and collective hovering near it.The preferred velocity magnitude approaches zero near the target while maintaining flock coherence and robustness.
- Algorithm: Local centre-of-mass tracking replaces global centre-of-mass computation because robots communicate only within a finite range.The local centre of mass is calculated from information available inside a sphere-shaped communication environment.
- Simulation: Higher viscous friction reduces delay-induced oscillations and stabilizes both flocking and hovering states when the local centre-of-mass sphere contains all units.This condition requires the sphere to contain all units with at least the repulsive interaction range separating them.
- Trade-offs: Increasing viscous friction reduces instabilities but increases the overall time needed to reach the target, especially when delay is present.At extremely high friction, units with zero initial velocity can practically remain at their initial positions.
- Simulation: When communication range greatly exceeds the repulsion range, correlated flocking with high order parameter can emerge; smaller ranges trade collision avoidance against flock stability.Small communication ranges can permit collisions, while ranges near the repulsion range may prevent stable high-order flocking.
- Experiments: Nine autonomous quadcopters approached a stationary target, transitioned smoothly to hovering, and followed a moving car while maintaining a stable grid-like structure.The experiments tested the algorithms under realistic environmental conditions, including moderate wind with randomly changing direction.
Appendix A: PID Controller
The low-level velocity-based PID controller converts desired and measured velocities into control signals, with proportional, integral, differential, and feed-forward terms governing response dynamics.
- The controller takes desired and measured velocity as inputs and sends a control signal to the quadcopter’s standard main board.
- The error signal is the difference between desired and measured velocity for either the north-south or east-west component.
- The proportional, integral, and differential gains determine the controller’s response, while a feed-forward bias is based on measured velocity versus control signal.
- Logged robot data were analyzed to select controller parameters and characterize how real velocity depends on the control signal.
- In the ideal case, the controller produces exponential convergence with characteristic time τ_CTRL.
Appendix B: GPS device – example for modelling inner noise
The GPS inner-noise model represents sensor uncertainty through stochastic velocity and position errors, calibrated against measurements from real receivers.
- The GPS model captures approximately Gaussian velocity-measurement error and a measured position accuracy of 2.5 m (50% CEP).
- GPS position fluctuations are modeled as Brownian motion in a parabolic potential centered on the robot’s real position.
- The stochastic model uses a second-order Langevin equation with delta-correlated Gaussian noise to reproduce fluctuating position errors.
- Parameters sD and sλ were fitted using positional data from a static ground-based GPS receiver.
- With an optimal setup and Euler-Maruyama integration, simulated GPS position errors matched the characteristics of measured data.
- Figure 6 compares a 20-minute GPS East-West position and velocity record with modeled trajectories and velocity distributions under different parameter settings.