adaptive-control-underactuated

Running the Code

From the repository root, start Julia and activate the project environment:

] activate .
] instantiate

The main entry point is run_simulation.ipynb. Open that notebook, choose the scenario and controller mode in the setup cell, then run the notebook cells from top to bottom.

Useful files:

• run_simulation.ipynb: main simulation, plotting, and comparison workflow.
• vtol.jl: nonlinear VTOL dynamics model.
• high_level_control.jl: reference trajectories and high-level acceleration commands.
• control_allocation.jl: adaptive control allocation and reduced dynamics model.
• simulation.jl: simulation callbacks, adaptive controller integration, and PID benchmark.
• animation.jl: animation helpers.

Animations

Landing Comparison

Takeoff

Vehicle Dynamics

Let $p = [x,z]^\top$, $v = [\dot{x},\dot{z}]^\top$, $V = \lVert v\rVert$, $\gamma$ be the flight-path angle, $\alpha = \theta-\gamma$, and $\omega = \dot{\theta}$. The control input is $u = [u_f,u_r,u_p,u_e]^\top$, where $u_f$ and $u_r$ are the normalized front and rear vertical propeller speeds, $u_p$ is the normalized pusher propeller speed, and $u_e$ is the elevator deflection.

Define the body-axis propulsive force components and wind-axis aerodynamic force components as

$$ F_p = T_{\mathrm{max},p}u_p^2,\qquad F_v = T_{\mathrm{max},v}\left(u_f^2 + C_{pr}(V,u_p)u_r^2\right). $$

$$ D = \frac{1}{2}\rho S V^2 C_D. $$

$$ L = \frac{1}{2}\rho S V^2 C_L + \frac{1}{4}\rho S\bar{c}V C_{L_\omega}\omega. $$

The full nonlinear translational dynamics are

$$ \ddot{x} = \frac{1}{m}\left(F_p\cos\theta - F_v\sin\theta - D\cos\gamma - L\sin\gamma\right). $$

$$ \ddot{z} = \frac{1}{m}\left(F_p\sin\theta + F_v\cos\theta - D\sin\gamma + L\cos\gamma\right) - g_z. $$

The full nonlinear pitch dynamics are

$$ \ddot{\theta} = \frac{1}{J}\left(\frac{1}{2}\rho S\bar{c}V^2 C_M + \frac{1}{4}\rho S\bar{c}^2 V C_{M_\omega}\omega + l_vT_{\mathrm{max},v}\left(u_f^2 - C_{pr}(V,u_p)u_r^2\right)\right). $$

The aerodynamic coefficients are

$$ C_D = C_{D_0} + C_{D_\alpha}\alpha^2 + C_{D_e}u_e + C_{D_t}(u_f+u_r). $$

$$ C_L = C_{L_e}u_e + (1-\sigma(\alpha))(C_{L_0}+C_{L_\alpha}\alpha) + \sigma(\alpha)2,\mathrm{sgn}(\alpha)\sin^2(\alpha)\cos(\alpha). $$

$$ C_M = C_{M_e}u_e + (1-\sigma(\alpha))(C_{M_0}+C_{M_\alpha}\alpha) - \sigma(\alpha)2,\mathrm{sgn}(\alpha)\sin^2(\alpha)\cos(\alpha). $$

The stall blending function is

$$ \sigma(\alpha) = \frac{1 + e^{-M(\alpha-\alpha_{\mathrm{stall}})} + e^{M(\alpha+\alpha_{\mathrm{stall}})}}{\left(1 + e^{-M(\alpha-\alpha_{\mathrm{stall}})}\right)\left(1 + e^{M(\alpha+\alpha_{\mathrm{stall}})}\right)}. $$

The rear propeller effectiveness is

$$ C_{pr}(V,u_p) = 1 - \kappa_{pr}u_p^2\left(1+\frac{V}{V_{pr}}\right). $$

Model Parameters

The model parameters are listed below.

Parameter	Value	Units	Description
$g_z$	9.81	m/s^2	Gravitational acceleration magnitude
$m$	10.0	kg	Vehicle mass
$J$	1.0	kg m^2	Pitch-axis moment of inertia
$l_v$	0.5	m	Distance from center of mass to each vertical propeller
$T_{\mathrm{max},v}$	100.0	N	Maximum vertical propeller thrust scale
$T_{\mathrm{max},p}$	50.0	N	Maximum pusher propeller thrust scale
$\rho$	1.225	kg/m^3	Air density
$S$	0.5	m^2	Reference wing area
$\bar{c}$	0.2	m	Reference chord
$C_{D_0}$	0.043	-	Zero-lift drag coefficient
$C_{D_\alpha}$	0.03	1/rad^2	Angle-of-attack drag coefficient
$C_{D_e}$	0.0135	1/rad	Elevator drag coefficient
$C_{D_\omega}$	0.1	-	Rotational drag coefficient
$C_{D_t}$	0.8	-	Drag coefficient contribution from vertical propeller throttle
$C_{L_0}$	0.23	-	Zero-angle lift coefficient
$C_{L_\alpha}$	5.61	1/rad	Lift slope
$C_{L_e}$	0.13	1/rad	Elevator lift coefficient
$C_{L_\omega}$	7.95	-	Pitch-rate lift coefficient
$C_{M_0}$	0.0135	-	Zero-angle pitching moment coefficient
$C_{M_\alpha}$	-2.74	1/rad	Pitching moment slope
$C_{M_e}$	-0.99	1/rad	Elevator pitching moment coefficient
$C_{M_\omega}$	-38.21	-	Pitch-rate moment coefficient
$\alpha_{\mathrm{stall}}$	15.0	deg	Stall blending angle
$M$	50.0	-	Stall blending sharpness
$\kappa_{pr}$	0.5	-	Rear propeller interaction coefficient
$V_{pr}$	80.0	m/s	Rear propeller interaction velocity scale