A multibody UAV joins several small aircraft wingtip-to-wingtip through hinges, forming a single high-aspect-ratio wing. It keeps the efficiency of a long, slender span while retaining the strength and redundancy of independent aircraft — if one body fails, the others hold the formation. The catch: connect them and the whole assembly becomes aerodynamically unstable, and it cannot fly without a deliberately designed control system.
A long, jointed span gives a high lift-to-drag ratio and long endurance — inspired by the X-HALE flexible test aircraft.
Wingtip hinges pass roll between bodies but block bending moments — cutting structural weight while adding coupled dynamics.
Each body can hold its own controller, take off and land independently, and reconfigure the wing shape in flight.
The engineering question this work answers: is it possible to keep such an aircraft stable when every added body makes the lateral modes worse — using nothing but classical control fundamentals applied a smarter way? The journey below builds up from the simplest unstable system to the full variable-geometry twin.
Every model here is written in state-space form and stabilised with an optimal regulator. These are the exact tools used throughout the dissertation — and the exact math running in the rigs below.
Fidelity note — the inverted-pendulum rig uses the exact A, B matrices from the dissertation appendix and solves the Riccati equation live. The aircraft rigs use representative lateral-dynamics models tuned to reproduce the report's roll-response and eigenvalue behaviour, since the original state-space .mat matrices are not embedded here.
The classic unstable system: a pole balanced above a cart. Like the aircraft, it senses its own tilt and moves to stay upright. Drag the cart or nudge the pole — the live LQR controller catches it. Tune Q and R and the Riccati equation is re-solved in real time.
Drag the pendulum to disturb it. The gain K is recomputed from the algebraic Riccati equation whenever you move a slider.
A single aircraft with seven inputs (aileron, elevator, rudder, thrust + three gusts) and nine outputs. Left alone, its lateral motion diverges — roll and yaw wander off exactly as in the dissertation's Figure 12. Switch the LQR controller on and the roll snaps back to level.
The horizon shows the aircraft's roll from behind; the trace plots roll angle over time.
Two aircraft joined at a hinge. Now the bodies fight each other: a disturbance on one rolls the other. Standard LQR assumes clean decoupling; structural LQR respects the real cross-coupling between control inputs and outputs — and holds both bodies steady even through a gust.
Watch both bodies. A gust hits body 1 — see how it bleeds into body 2 through the hinge, and how control contains it.
The hinge angle reshapes the aircraft. A raised hinge (+17°) gives the A-configuration; a lowered hinge (−17°) gives the V-configuration — a genuinely non-linear change in dynamics. Sweep the hinge and compare how no control, LQR, and LQG handle each geometry.
Drag the hinge slider between the two configurations. The plot shows roll response under three strategies; the geometry above morphs to match.
Time plots show what happens; frequency plots show why. The Bode curves reveal how strongly each input frequency is amplified and how far it is delayed; the Nyquist trace maps the same response onto the complex plane. Sweep the frequency marker and watch the point travel both plots at once.
Drag the frequency marker; the same ω is highlighted on the Bode curves and the Nyquist locus. Toggle the controller to see how feedback reshapes the response.
LQR assumes you can measure every state perfectly. Real sensors are noisy. The Kalman filter fuses a model prediction with noisy measurements to estimate the true state — and pairing it with LQR gives LQG. Crank the sensor noise and watch the estimate hold its nerve while the raw measurement scatters.
Grey dots are what the sensor sees. The indigo line is the filter's estimate; the white line is the truth it cannot see directly.
Stability lives in the complex plane. Everything left of the vertical axis is stable; anything to the right diverges. Pick a system and drag the control weight — the eigenvalues are recomputed live and slide across the boundary as the controller does its work.
Green poles are stable, red poles are unstable. Raise the control weight to pull the poles into the left half-plane.
The dissertation sits on a web of prior work — wingtip docking, formation flight, aerodynamic interaction, and modern control. Hover a node to trace its links; click to read the reference. Grouped by theme.
A progression from an unstable pole to a stabilised variable-geometry twin — each stage stabilised, analysed, and simulated. The conclusions, chapter by chapter:
The exact appendix routine — build A and B, solve the LQR, verify the closed-loop eigenvalues. This is the code the rig above reproduces in JavaScript.