Two low-cost drones flying in formation
How much of a drone formation's error comes from control, how much from localization and how much from the network? This project separated them experimentally with two Tello drones costing under 130 US dollars each, with no motion capture system and no dedicated radios. The least obvious result is that, in a leader-follower scheme, communication delay does not destabilize the formation. The error comes almost entirely from noise in position estimation.
Context
Cooperation between aerial vehicles couples three problems: control of each vehicle, relative localization and communication between them. On high-cost research platforms, motion capture and dedicated radio links take care of the last two. With educational hardware they have to be characterized.
Architecture
Each drone is controlled by an independent computer over its own WiFi network. The two computers talk over a direct Ethernet link, which acts as the cooperation network. Each drone's position is estimated with its camera from a grid of six fixed ArUco markers.
The work was organized into 16 tests grouped under five objectives: dynamic model, cooperative control, network, simulation and integration.
Dynamic model
The Tello's response to displacement commands fits a critically damped second-order system with a natural frequency of 1.9 rad/s and a fit error of 2.8 cm.
Step response and second-order model fit
Characterization also exposed the platform's limits: a variability of 10 to 25% in the execution of discrete commands, a median latency of about one second between command and action, and a hover drift of about 5 cm/s without external control.
Drone drift in hover over 60 s
Control
Individual closed loop. With feedback of the ArUco position estimate, tracking error has a bias under 1 cm per axis and a three-dimensional error of 8.1 cm in steady state. The drone recovers from physical disturbances of 30 to 46 cm in about two seconds.
Closed-loop tracking error, with five disturbances
Leader-follower formation. The follower computes its reference as the leader's position plus a fixed offset. In static formation the error was 12.9 cm, and in dynamic formation over a square path 0.6 m on a side it was 23 cm.
Static formation error, with and without moving-average filter
Distributed consensus. The classical consensus law drives the agents to a single point, which is not viable with multirotors: one ends up above the other and the wake of the upper rotor destabilizes the lower one. It was modified to converge with a minimum lateral separation.
Position convergence in distributed consensus with a safety separation
Where the error comes from
Formation error grows 59% when going from one drone to two in static formation, and 184% in dynamic formation. The work breaks it down into three factors:
- Position noise. The follower's reference inherits the uncertainty of the leader's position, about 6 cm per axis, which adds to its own.
- Filtering. An eight-sample moving average reduces steady-state error from 27.4 to 12.9 cm, but introduces a 0.6 s delay that turns into error when the leader moves.
- Network latency. It is 5.6 ms, negligible against the 73 ms period of the control loop.
Network
The link is not the bottleneck, with about 2 ms latency and 93 Mbps. A custom 41-byte binary protocol with CRC-16 checking kept integrity over more than 50,000 messages, even with 20% injected packet loss.
Formation error under injected delay and packet loss
Replicating the experiments in a simulation based on the identified model made it possible to isolate the effect of delay. In an architecture where the follower has its own position feedback, delay affects only the setpoint and not the loop, which is why it does not destabilize the system. The degradation seen in the physical experiment with a degraded network is due to other factors occurring at the same time.
Full mission
The integrated mission, comprising takeoff, formation, trajectory and landing, succeeded in seven of eight repetitions. The failure was caused by an inertial unit error on one of the drones.
Error per repetition and repeatability metrics of the cooperative mission
What is missing
The system only works in front of the marker grid. The camera was used with approximate intrinsic parameters. It was only validated with two agents, and the current architecture needs one computer per drone. The simulation underestimates transients, with a 19% gap against the experiment in steady state.
The thesis also devotes a chapter to the methods that were discarded, which is useful for anyone continuing the work on the same platform.
How it fits in Robiolab
Collective behavior is a recurring theme in bioinspired robotics, and the group had approached it before from the robots' bodies, with the vehicle of cooperating spherical units. This work approaches it from the information side: what each agent needs to know about the others, and with what quality. The conclusion that the limiting factor is perception rather than communication applies to other systems in the lab that rely on vision to close the loop, such as the camera-controlled continuum robot.