https://github.com/zju-fast-lab/ground-effect-controller
Ground-Effect-Aware Modeling and Control for Multicopters
https://github.com/zju-fast-lab/ground-effect-controller
Last synced: 6 months ago
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Ground-Effect-Aware Modeling and Control for Multicopters
- Host: GitHub
- URL: https://github.com/zju-fast-lab/ground-effect-controller
- Owner: ZJU-FAST-Lab
- License: gpl-3.0
- Created: 2024-10-07T11:37:50.000Z (almost 2 years ago)
- Default Branch: main
- Last Pushed: 2024-10-17T14:13:45.000Z (almost 2 years ago)
- Last Synced: 2025-01-08T15:37:44.848Z (over 1 year ago)
- Size: 71.4 MB
- Stars: 11
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Ground-effect-controller
**Supplementary material** for the paper: Ground-Effect-Aware Modeling and Control for Multicopters.
The detailed [***data***](./figs/traj_rmse_plot.pdf) of the above video is in the Part.5. Control algorithm.
## 1. The quadrotor
### 1.1. Firmware for the flight controller
This firmware is included in a [***VMware***](https://www.vmware.com/) virtual machine environment.
Downlink: [***Fireware with virtual environment***](http://zjufast.tpddns.cn:9110/share.cgi?ssid=cfde8ecbb0b8432fb59c241b98ab59a9)
Downlink: [***Fireware***](http://zjufast.tpddns.cn:9110/share.cgi?ssid=d6dd0e1a97cf43f7a9f5feb82fca04d5)
Password: fastlab@2024
### 1.2. Devices
Flight controller: [***CUAV V5***](https://doc.cuav.net/flight-controller/v5-autopilot/en/v5+.html)
Lattice laser sensor: [***Laser***](https://www.nooploop.com/tofsense-m/)
Onboard computer: [***Intel NUC***](https://www.intel.com/content/www/us/en/products/sku/205603/intel-nuc-11-pro-kit-nuc11tnki5/specifications.html)
Motion capture system: [***NOKOV***](https://en.nokov.com/products/motion-capture-cameras/Mars.html)
### 1.3. CAD model
The [***CAD model***](./CAD/quadrotor.STEP) of the quadrotor in this paper.
### 1.4. BOM list
| **Type** | **Name** | **Mass (g)** | **Quantity** | **Gross Mass (g)** |
| -------------------------------- | ------------------------------------------ | ------------ | ------------ | ------------------ |
| **Rack** | Upper center plate | 112.80 | 1 | 112.80 |
| | Lower center plate | 150.00 | 1 | 150.00 |
| | Flight controller base PCB | 14.00 | 1 | 14.00 |
| | Flight controller core PCB | 10.50 | 1 | 10.50 |
| | Flight controller | 41.30 | 1 | 41.30 |
| **Rack mounting** | M3 Lockout nuts | 0.40 | 20 | 8.00 |
| | M3 Isolation column (6mm) | 0.18 | 20 | 3.56 |
| | M3 screw (16mm) | 1.04 | 20 | 20.80 |
| **Undercarriage** | Landing gear carbon clamp | 4.90 | 4 | 19.60 |
| | Landing gear carbon tube spacer | 4.23 | 4 | 16.93 |
| | Landing gear carbon tube | 2.50 | 4 | 10.00 |
| | Landing gear carbon tube sponge cylinder | 3.25 | 4 | 13.00 |
| | Landing gear carbon tube sponge round pad | 0.40 | 4 | 1.59 |
| | Motor | 45.00 | 4 | 180.00 |
| | Paddle (7 inches) | 7.50 | 4 | 30.00 |
| | M3 screw (20mm) | 1.23 | 16 | 19.68 |
| **Onboard computer and battery** | 3D printed parts (on-board computer fixed) | 56.50 | 1 | 56.50 |
| | Intel NUC | 494.20 | 1 | 494.20 |
| | SSD | 8.80 | 1 | 8.80 |
| | RAM | 8.20 | 2 | 16.40 |
| | Battery 22.2V 1400mAh | 233.80 | 1 | 233.80 |
| | Reflector bracket | 31.50 | 1 | 31.50 |
| | Reflective (25mm) | 6.52 | 5 | 32.60 |
| **Laser sensor and fixation** | M3 screw (10mm) | 0.77 | 8 | 6.16 |
| | M3 Lockout nuts | 0.40 | 8 | 3.20 |
| | M3 screw (16mm) | 1.04 | 4 | 4.16 |
| | M3 Isolation column (6mm) | 0.18 | 4 | 0.71 |
| | M3 single pass aluminum column (12mm) | 0.60 | 4 | 2.40 |
| | M3 Lockout nuts | 0.40 | 4 | 1.60 |
| | Laser sensors fix carbon plates | 10.60 | 1 | 10.60 |
| | Laser sensor | 8.30 | 1 | 8.30 |
| **Total** | | | | **1562.70** |
## 2. The quadrotor platform for model validation
### 2.1. CAD model
The [***CAD model***](./CAD/platform.step) of the force measurement platform in this paper.
### 2.2. Platform data: The leveling torque
The following [***figure***](./figs/getorque_all_rpmmodel.pdf) shows the data in the leveling torque experiment. The figure shows the relationship between leveling torque **${{\bf{\tau }}_G}$** and average rotor speed **$\left\| {{n_i}} \right\|$**. The black points are sensor data and the blue lines are model-fitting results.
### 2.3. Platform data: ROS bags and processing
To be uploaded.
## 3. Motor calibration and rotor speed control
### 3.1. Motor model
To control the rotors to the desired speeds, the rotors need to be modeled and calibrated.
The thrust **$T_i$** and torque **$M_i$** generated by a single rotor are:
**$$T_i = k_T n_i^2,$$**
**$${M_i} = {k_I}{n^2} + {J_R}{{\dot n}_i}.$$**
- **$k_T$** is the thrust coefficient,
- **$k_I$** is the torque coefficient,
- **$J_R$** is the moment of inertia of the rotor,
- **$i$** is the rotor number.
The following [***figure***](./figs/sigle_motor_platform.pdf) is the calibration of the (a)thrust and (b)torque model with the single motor platform in the paper. The static/dynamic modelmeans: without/with a differential term of rotor speed **$\dot{n}$**.
### 3.2. Throttol model of the flight controller
The rotor speeds are controlled through the throttle input (**$t_i^{des} \in \left[ {0,1} \right]$**), and the rotational speeds are fed back through [***BDhot***](https://ardupilot.org/copter/docs/common-dshot-escs.html).
When the flight controller receives a throttle control signal (**${t_c} \in [0,1]$**), the rotor speed will be maintained at a roughly determined value. The relationship between the rotor speed and the throttle, after eliminating the influence of battery voltage, is usually a quadratic function:
**$$n_{esc}(t_c) = c_2 t_c^2 + c_1 t_c + c_0.$$**
We collect rotor speed and throttle data on the single-motor platform and calibrate the model. The data is illustrated in the following [***figure***](./figs/id_single_motor.pdf).
- (a) The relationship between rotor speed $n$ and throttle $t_c$.
- (b) The time series of motor speed, with the blue line representing the speed predicted using the throttle model.
It can be seen that the data demonstrates a strong alignment with the model.
### 3.3. Rotor speed control
The rotor speeds require closed-loop control; however, we do not implement this control for each motor individually. Instead, we apply closed-loop control to the combined acceleration generated by all rotors along **${\bf{z}}_B$**. The control method for rotor speed is:
**$$
t_i^{des} = t_i^{ref} + t_E,
$$**
**$$
t_i^{ref} = n_{esc}^{ - 1}(n_i),
$$**
**$$
t_E = K_P^T T_a^E + K_I^T \sum T_a^E,
$$**
**$$
T_a^E = \left( {\sum\limits_i {{k_T}n{{_i^{des}}^2}} - \sum\limits_i {{k_T}{n_i}^2} } \right)/m
$$**
- **$t_i^{ref}$** is the feedforward throttle obtained by **$n_{esc}^{ - 1}$**, the inverse function of throttol model,
- **$t_E$** is the throttle from rotor speed error,
- **$T_a^E$** is the acceleration error by all rotors,
- **$K_P^T$**, **$K_I^T$** are the parameters of the Proportional-Integral controller.
## 4. Parameters
### 4.1. Model and Control Gain Parameters
The results of parameter identification in the paper are shown in following table:
| **Symbol** | **Value** | **Name** | **Method** |
| ------------ | ------------------------------------------------------------ | ------------------------------------ | ----------------------- |
| **$k_T$** | $4.0083 \times 10^{-8} \, \text{N/rpm}^2$ | Thrust coefficient | Single-rotor platform |
| | $3.7840 \times 10^{-8} \, \text{N/rpm}^2$ | | Quadrotor platform |
| | $4.2958 \times 10^{-8} \, \text{N/rpm}^2$ | | Real flight by hovering |
| **$k_{TX}$** | $4.678 \times 10^{-8} \, \text{N/rpm}^2$ | Torque by thrust coefficient (roll) | Quadrotor platform |
| **$k_{TY}$** | $3.588 \times 10^{-8} \, \text{N/rpm}^2$ | Torque by thrust coefficient (pitch) | |
| **$k_I$** | $6.3859 \times 10^{-10} \, \left( \text{N} \cdot \text{m} \right) / \text{rpm}^2$ | Rotor torque coefficient | Single-rotor platform |
| **$J_R$** | $1.0556 \times 10^{-4} \, \text{kg/m}^2$ | Rotor inertia | Single-rotor platform |
| **$g_1$** | $1.804 \times 10^{-2}$ | Ground effect coefficient | Quadrotor platform |
| **$g_2$** | $7.339 \times 10^{-3}$ | | |
| **$g_3$** | $-3.365 \times 10^{-1}$ | | |
| **$g_4$** | $4.126 \times 10^{-2}$ | | |
| **$g_5$** | $6.494 \times 10^{-2}$ | | |
| **$c_2$** | $-1.448471 \times 10^8$ | Throttle curve parameter | Quadrotor platform |
| **$c_1$** | $5.228928 \times 10^8$ | | |
| **$c_0$** | $1.033111 \times 10^8$ | | |
| **$d_x$** | $0.3970 \, \text{N/(m/s)}$ | Rotor drag coefficient | Real flight |
| **$d_y$** | $0.3300 \, \text{N/(m/s)}$ | | |
| **$m$** | $1.696 \, \text{kg}$ | Mass of the quadrotor | Electronic scale |
| | $1.562 \, \text{kg}$ | | Mechanical model |
| **$I_x$** | $0.00745220 \, \text{kg/m}^2$ | Inertia of the quadrotor | Mechanical model |
| **$I_y$** | $0.00792752 \, \text{kg/m}^2$ | | |
| **$I_z$** | $0.01249522 \, \text{kg/m}^2$ | | |
The control gain parameters in the paper are shown in following table:
| Symbol | Name | Value |
|-------------------------|-------------------------|--------------------------------------------------|
| **$$\mathbf{K}^P$$** | Position control gain | **$$(3.0, 3.0, 3.0)$$** |
| **$$\mathbf{K}^V$$** | Velocity control gain | **$$(2.5, 2.5, 2.5)$$** |
| **$$\mathbf{K}^{\xi}$$** | Angle control gain | **$$(6.0, 6.0, 2.0)$$** |
| **$$\mathbf{K}^{\omega}$$** | Body rate control gain | **$$(15.0, 15.0, 16.0)$$** |
### 4.2. Spearman's rank correlation
The following table shows the Spearman's rank correlation coefficient between variables.
- **$\uparrow $** : Strong correlation;
- **$\downarrow$** : Weak correlation.
| **Spearman coefficient** | ${{\bf{x}}_W}^ \top {{\bf{\tau }}_B}$ | ${{\bf{z}}_W}^ \top {{\bf{\tau }}_B}$ | ${{\bf{y}}_W}^ \top {{\bf{\tau }}_G}$ | ${{\bf{y}}_W}^ \top {{\bf{\tau }}_G}/\sin \delta$ | ${{\bf{f}}_{\bf{G}}}$ |
| --------------------------------- | ------------------------------------- | ------------------------------------- | ------------------------------------- | ------------------------------------------------- | --------------------- |
| ${\bf{N}_{base}}\left( 1 \right)$ | - | - | $\uparrow -0.6640$ | - | $\uparrow +0.4703$ |
| ${\bf{N}_{base}}\left( 2 \right)$ | $\uparrow +0.8245$ | - | - | - | - |
| ${\bf{N}_{base}}\left( 3 \right)$ | - | - | - | - | - |
| ${\bf{N}_{base}}\left( 4 \right)$ | - | $\uparrow +0.9251$ | - | - | - |
| $h$ | $\downarrow +0.0284$ | $\downarrow +0.1781$ | $\uparrow +0.3384$ | - | $\uparrow -0.5465$ |
| $\delta$ | - | - | - | $\downarrow +0.0930$ | $\downarrow +0.0054$ |
## 5. Control algorithm
The following [***figure***](./figs/traj_rmse_plot.pdf) shows the curves of Exp.~7($3m/s$, near-ground) in the paper. Every loop is well-controlled, including the rotor speed, thrust acceleration, body torque, etc.
## 6. Future work
The fluid simulation work is in progress.