Physical / Marine Robotics
2-DOF Azimuth Thruster
Developed an empirical mathematical model for a 2-DOF azimuth thruster to overcome the limitations of analytical modeling in complex hydrodynamic environments. The project aimed to derive a precise transfer function covering the entire frequency range (low to high) using the Signal Compression Method (SCM).
- Role
- Solo builder · architecture, implementation, and operational tooling
- Period
- 2020.08
- Context
- Academic
Developed an empirical mathematical model for a 2-DOF azimuth thruster to overcome the limitations of analytical modeling in complex hydrodynamic environments. The project aimed to derive a precise transfer function covering the entire frequency range (low to high) using the Signal Compression Method (SCM).
What made the system difficult.
Analytical modeling was difficult due to complex hydrodynamics, and traditional frequency response tests failed to capture high-frequency data accurately. Additionally, the gimbal structure caused non-linear overshoot and vibrations due to inertia.
How boundaries and flows answered it.
Implemented a 2-DOF gimbal mechanism with a counter-mass for dynamic balancing. Applied SCM using equivalent impulse signals to separate linear/non-linear components. Optimized the transfer function using MATLAB's fmincon curve fitting, achieving a cross-correlation coefficient of 0.83 for the Z-axis moment.
1. Background & Problem Definition
- Project Name: Empirical Modeling of 2-DOF Azimuth Thruster based on Signal Compression Method
- Research Necessity:
- Existing underwater robots use multiple fixed thrusters, resulting in large volume and weight. To solve this, a 2-DOF Gimbal Mechanism capable of changing direction with a single thruster is needed.
- Underwater propulsion systems have complex hydrodynamic characteristics, making Analytical Modeling extremely difficult.
- Traditional frequency response experiments struggle to obtain high-frequency data, limiting the establishment of precise control models.
- Core Objective: Derive an Empirical Mathematical Model covering the entire frequency range (low to high) through actual hardware experiments.
2. Deep Dive into Technologies
A. Mechatronics Hardware Engineering
- 2-DOF Gimbal Mechanism Design:
- Designed a structure that freely controls the thrust direction using two servo motors (Yaw, Pitch).
- Manufactured and mounted a Counter Mass with the same shape and mass (1.35kg) as the servo motor to resolve center of gravity imbalance.
- Underwater Waterproofing Solution:
- Applied O-rings to all fastening parts and used Rotary Seals on rotating shafts to block fluid ingress.
- Applied Cable Glands to prevent water intrusion into motor wires.
- Electronic Component Configuration:
- Thruster: Maxon MI60 (Max Thrust 7kgf, Rated 24V).
- Controller: NI Compact RIO 9049 (Real-time Controller).
- Sensor: 6-axis F/T sensor (ROBOTUS RFT80-6A01) placed at the top to measure reaction force and moment.
B. System Identification & Signal Processing
- Signal Compression Method (SCM) Application:
- Principle: Based on the theory that applying an impulse signal to a system reveals the entire frequency response, but uses an Equivalent Impulse Signal instead of an actual impulse to avoid damaging the physical system.
- Algorithm Implementation:
- Generate time-domain test signal (Frequency band and time delay parameters set to a=450, b=2100).
- Convert to frequency domain via FFT (Fast Fourier Transform) and apply phase delay filter.
- Compress and restore the system output to time-domain impulse response via IFFT (Inverse Fourier Transform).
- Advantage: Separates linear and non-linear components in a system containing non-linearities, allowing effective estimation of only linear system parameters.
C. Data Analysis & Modeling
- Experimental Data Processing:
- Performed a total of 180 experiments varying thruster output (PWM 55%~95%) and rotation axes (1-axis, 2-axis).
- Performed coordinate transformation and position compensation using Homogeneous Transformation Matrix since Sensor Frame and Moving Frame positions differ.
- Transfer Function Derivation:
- Analyzed the slope of the measured Bode Plot to determine the system Order.
- Calculated coefficients (k, a, b, c, d, e, g) minimizing error between experimental data (Raw Data) and model using MATLAB's fmincon optimization technique via Curve Fitting.
3. Results & Achievements
- Model Accuracy Verification:
- Cross-correlation Coefficient analysis between derived transfer function model and actual experimental data:
- Mz,1 (Z-axis Moment): 0.83 (Very High Accuracy).
- Fy,1 (Y-axis Force): 0.75.
- Fx,1 (X-axis Force): 0.60.
- Cross-correlation Coefficient analysis between derived transfer function model and actual experimental data:
- Error Analysis & Engineering Insight:
- Gimbal Inertia: The low correlation coefficient for Fx,1 is due to the large inertia of the gimbal structure causing non-linear overshoot and vibration during rotation.
- Gravity & Buoyancy Disturbance: Identified that model tracking performance for Fz dropped slightly due to the combined effects of gravity and buoyancy.
- Conclusion: Confirmed that the proposed 2-axis propulsion system contributes to the Compact Design of underwater robots, and suggested that lightweight gimbal design is essential for future control performance improvement.
4. References & Links
- Research Paper (PDF): [Download/View PDF](/assets/신호압축법을 이용한 2자유도 애지머스 추진기의 실증적 모델.pdf)
- RISS Research Information: View on RISS