Research on the Methods for Correcting Helicopter Position on Deck Using a Carrier Robot
Abstract
:1. Introduction
2. Mathematical Model and Kinematic Characteristic Analysis
2.1. The Structure and Correction Principle of Helicopter Deck Traction System
2.2. Analysis of Traction Motion Characteristics of SRCR
3. The Stepwise Method of Helicopter Deck Position Correction
3.1. The Principle of Stepwise Correction Method
3.2. The Relationship of Speed Cooperative Control in the Stepwise Correction Method
4. The Continuous Method of Helicopter Deck Position Correction
4.1. The Principle of Continuous Correction Method
4.1.1. Parallel Landing Position
4.1.2. Cross Landing Position
4.2. The Relationship of Speed Cooperative Control in the Continuous Correction Method
5. Simulation Verification of the Correction Method
5.1. Simulation of the Stepwise Correction Method
5.2. Simulation of the Continuous Correction Method
5.3. Comparative Analysis of the Efficiency of the Stepwise Correction Method and the Continuous Correction Method
5.3.1. Efficiency Analysis of the Stepwise Correction Method on the Impact of Initial Yaw Angle and Traction Speed
- (1)
- By comparing serial numbers 1-2-3, 4-5-6, 7-8-9, it can be seen that increasing v2 can effectively improve the efficiency of the correction operation and reduce the total correction time t.
- (2)
- By comparing serial numbers 1-4-7, 2-5-8, 3-6-9, it can be seen that during the translational operation, a larger initial yaw angle |θ0| results in a shorter translation time t1; however, during the rotational operation, a larger initial yaw angle |θ0| results in a longer rotation time t2.
5.3.2. Efficiency Analysis of the Stepwise Correction Method on the Impact of Initial Yaw Angle and Lateral Offsets
- (1)
- By comparing serial numbers 1-2-3-4-5-6, 7-8-9-10-11, 12-13-14-15-16 and referring to Figure 22, it can be seen that when the initial yaw angle |θ0| is fixed, the smaller the lateral offset |d0|, the shorter the translation time t1, with no effect on rotation time t2.
- (2)
- According to Figure 22, in the stepwise correction for the cross landing position, when the lateral offset d0 = −600 mm and −400 mm, the total correction time t is minimized when the initial yaw angle θ0 is −20°. For lateral offset d0 = −200 mm, −150 mm, and −100 mm, the total correction time t is minimized when the initial yaw angle θ0 is −10°.
- (3)
- According to Figure 22 and Table 6, in the correction process for the parallel landing position, when the lateral offset d0 is −1200 mm or −800 mm, the total correction time t is minimized when the fuselage yaw angle θ for the first stepwise rotational correction is −20°. For lateral offsets d0 of −400 mm, −300 mm, and −200 mm, the total correction time t is minimized when the fuselage yaw angle θ for the first stepwise rotational correction is −10°.
- (1)
- In the correction process for the cross landing position, a larger initial yaw angle θ0 results in a longer time t2 required for stepwise rotational correction. However, for the same initial lateral offset d0, the stepwise translational correction time t1 will be shorter. Moreover, with the same initial yaw angle θ0, the variation in stepwise correction time t is solely dependent on the initial lateral offset d0.
- (2)
- In the correction process for the parallel landing position, according to the different lateral offset d0, weighing the translation time t1 and the rotation time t2 and choosing the optimal fuselage yaw angle θ for the first stepwise rotational correction is the key to improving the efficiency of the stepwise correction method.
5.3.3. Efficiency Analysis of the Continuous Correction Method on the Impact of Initial Yaw Angle and Traction Speed
- (1)
- By comparing serial numbers 1-2-3, 4-5-6, 7-8-9, it can be seen that an increase in right traction speed v2 can effectively improve correction efficiency and reduce the total correction time t.
- (2)
- By comparing serial numbers 1-4-7, 2-5-8, it can be seen that the larger the initial yaw angle |θ0|, the larger the helicopter control wheel angle |γ|, and the smaller the helicopter correction radius r in the continuous correction method.
5.3.4. Efficiency Analysis of the Continuous Correction Method on the Impact of Initial Yaw Angle and Lateral Offsets
- (1)
- As the initial yaw angle |θ0| increases and the lateral offset d0 decreases, the length of the helicopter correction radius r also decreases, as indicated by the downward trend of the red line in Figure 24.
- (2)
- Comparing serial numbers 1-2-3-4, 5-6-7, 8-9-10 and Figure 24, it is evident that with a fixed initial yaw angle |θ0|, a larger helicopter control wheel angle |γ| results in a smaller helicopter correction radius r and a shorter correction time t.
- (3)
- According to Figure 24, in the continuous correction for the cross landing position, although the helicopter correction radius r varies from large to small under working conditions from 1 to 10, a comparative analysis of serial numbers 1-5-8, 2-6-9, and 3-7-10 shows that with lateral offsets d0 of −200 mm, −150 mm, and −100 mm, the shortest correction time t occurs with the initial yaw angle θ0 of −20°.
- (4)
- According to Figure 24, in the continuous correction for the parallel landing position, when the lateral offset d0 is −400 mm, −300 mm, and −200 mm, the total correction time t is minimized when the fuselage yaw angle θ for the first trajectory of the continuous correction is −20°.
- (1)
- In the correction process for the cross landing position, the continuous correction time t is negatively correlated with the initial yaw angle |θ0| and positively correlated with the initial lateral offset |d0|.
- (2)
- In the correction process for the parallel landing position, it is crucial to balance the helicopter correction radius r and choose the optimal helicopter control wheel angle γ according to different lateral offset d0 to improve the efficiency of the continuous correction method.
5.3.5. Comparison of Performance between Stepwise and Continuous Correction Methods
6. Conclusions
- (1)
- To address the helicopter deck position correction of SRCR, the actual landing position deviation is decomposed into two components: lateral offset d0 and fuselage yaw angle θ0. This allows for a quantitative evaluation of the landing position deviation.
- (2)
- To correct the helicopter landing deviation, this paper proposes both the stepwise correction method and the continuous correction method, based on the motion characteristic model of the SRCR. The feasibility of these two correction methods is verified through mathematical analysis and simulation research.
- (3)
- The three key factors affecting correction efficiency are lateral offset d0, fuselage yaw angle θ0, and right traction speed v2. The stepwise method and continuous method were simulated and analyzed. Results indicate that in the correction process for the parallel landing position, improving the efficiency of the stepwise correction method hinges on selecting the optimal fuselage yaw angle θ for the first stepwise rotational correction based on the different lateral offsets d0. Similarly, enhancing the efficiency of the continuous correction method requires choosing the optimal helicopter control wheel angle γ according to the varying lateral offsets d0.
- (4)
- Comparing the stepwise method with the continuous method, results show that when the initial yaw angle |θ0| ≤ 20°, the stepwise correction method has a significant advantage. However, when the initial yaw angle |θ0| > 20° and the lateral offset |d0| ≤ 200 mm, the efficiency of continuous correction is superior to the stepwise correction method because the helicopter’s correction arc radius r is smaller.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Symbol | Description |
---|---|
θ | The helicopter fuselage yaw angle |
d | The helicopter lateral offset |
v1 | The traction velocity of the left winch |
v2 | The traction velocity of the right winch |
V1 | The traction speed provided by the left winch |
V2 | The traction speed provided by the right winch |
va | The velocity of the left traction point a of the SRCR |
vb | The velocity of the right traction point b of the SRCR |
ω | The rotational angular velocity of the SRCR |
L | The distance between the left and right traction tracks |
Δva | The traction velocity difference between the left and right winches |
Δva1 | The velocity of the left traction point (shaft a) moving within the sliding groove |
Δva2 | The rotational velocity of the left traction point a on the SRCR when it performs rigid body motion around the right traction point b |
vz | The capturing point velocity of the right robotic arm |
vs | The lateral correction velocity of the right robotic arm |
rz | The distance from the right robotic arm capturing point cR to the right traction point b |
γ | The steering angle of the helicopter steerable nose wheel |
xs | The sliding displacement of the right robotic arm |
L0 | The distance from the initial position of the right robotic arm (i.e., axis y1) to the center of the helicopter’s main wheel |
L1 | The distance between the right traction point of the SRCR (i.e., shaft b) and the initial position of the right robotic arm |
L2 | The distance between the helicopter main wheel shaft and the line connecting the left and right traction points (i.e., line a–b) |
vB | The rotational velocity of the right robotic arm’s capture point around the right traction point of the SRCR (i.e., shaft b) |
δ | The central angle of the continuous correction trajectory |
r | The arc radius of the continuous correction trajectory |
L3 | The distance from the center of the helicopter’s main wheel shaft to the center of the helicopter steerable nose wheel |
s | The length of the continuous correction trajectory |
Helicopter Type | Width | Rear Wheelbase | Weight |
---|---|---|---|
CH-53K | 5.33 m | 3.52 m | 25,000 kg |
Sea hawk (SH-60B) | 2.36 m | 2.8 m | 10,400 kg |
Sea king (SH-3) | 4.98 m | 4.70 m | 9707 kg |
MI-171helicopter | 2.50 m | 4.28 m | 11,000 kg |
SH-90 | 3.8 m | 2.7 m | 10,600 kg |
Parameter | Value |
---|---|
The length of track spacing for left and right traction tracks L | 5000 mm |
The length of capturing point to fuselage center line L0 | 2000 mm |
The distance between the right traction point of the SRCR and the initial position of the right robotic arm L1 | 150 mm |
The distance between the helicopter main wheel shaft and the line connecting the left and right traction points L2 | 300 mm |
Initial helicopter yaw angle θ0 | 10° |
Initial helicopter lateral offset d0 | 200 mm |
Right traction speed v2 | 10 mm/s |
Parameter | Value |
---|---|
The length of track spacing for left and right traction L | 5000 mm |
The length of grab point to fuselage center line L0 | 2000 mm |
The distance between the right traction point of the SRCR and the initial position of the right robotic arm L1 | 150 mm |
The distance between the helicopter main wheel shaft and the line connecting the left and right traction points L2 | 300 mm |
The distance between helicopter control wheel and the main wheel shaft L3 | 8000 mm |
Initial helicopter yaw angle θ0 | −20° |
Initial helicopter lateral offset d0 | −200 mm |
Right traction speed v2 | 30 mm/s |
Helicopter control wheel angle γ | 67.48° |
Serial Number | Initial Fuselage Yaw Angle θ0/deg | Lateral Offset d0/mm | Right Traction Speed v2/mm/s | Translation Time t1/s | Rotation Time t2/s | Total Correction Time t/s |
---|---|---|---|---|---|---|
1 | −10° | −200 | 10 | 108.71 | 43.80 | 152.51 |
2 | −10° | −200 | 20 | 54.56 | 21.80 | 76.36 |
3 | −10° | −200 | 30 | 36.42 | 14.60 | 51.02 |
4 | −20° | −200 | 10 | 78.29 | 91.00 | 169.29 |
5 | −20° | −200 | 20 | 39.18 | 45.60 | 84.78 |
6 | −20° | −200 | 30 | 26.16 | 30.40 | 56.56 |
7 | −30° | −200 | 10 | 95.56 | 149.20 | 244.76 |
8 | −30° | −200 | 20 | 47.82 | 74.60 | 122.42 |
9 | −30° | −200 | 30 | 31.90 | 49.80 | 81.70 |
Serial Number | Initial Fuselage Yaw Angle θ0/deg | Lateral Offset d0/mm | Right Traction Speed v2/mm/s | Translation Time t1/s | Rotation Time t2/s | Total Correction Time t/s |
---|---|---|---|---|---|---|
1 | −10° | −600 | 30 | 109.26 | 14.60 | 123.86 |
2 | −10° | −400 | 30 | 72.84 | 14.60 | 87.44 |
3 | −10° | −200 | 30 | 36.42 | 14.60 | 51.02 |
4 | −10° | −150 | 30 | 27.32 | 14.60 | 41.92 |
5 | −10° | −100 | 30 | 18.21 | 14.60 | 32.81 |
6 | −10° | −50 | 30 | 9.11 | 14.60 | 23.71 |
7 | −20° | −600 | 30 | 78.48 | 30.40 | 108.88 |
8 | −20° | −400 | 30 | 52.32 | 30.40 | 82.72 |
9 | −20° | −200 | 30 | 26.16 | 30.40 | 56.56 |
10 | −20° | −150 | 30 | 19.62 | 30.40 | 50.02 |
11 | −20° | −100 | 30 | 13.08 | 30.40 | 43.48 |
12 | −30° | −600 | 30 | 95.70 | 49.80 | 145.50 |
13 | −30° | −400 | 30 | 63.80 | 49.80 | 113.60 |
14 | −30° | −200 | 30 | 31.90 | 49.80 | 81.70 |
15 | −30° | −150 | 30 | 23.88 | 49.80 | 73.68 |
16 | −30° | −100 | 30 | 15.85 | 49.80 | 65.65 |
Serial Number | Initial Fuselage Yaw Angle θ0/deg | Lateral Offset d0/mm | Right Traction Speed v2/mm/s | Helicopter Control Wheel Angle γ/deg | Helicopter Correction Radius r/mm | Total Correction Time t/s |
---|---|---|---|---|---|---|
1 | −10° | −200 | 10 | 31.29 | 13162.86 | 271.60 |
2 | −10° | −200 | 20 | 31.29 | 13162.86 | 135.80 |
3 | −10° | −200 | 30 | 31.29 | 13162.86 | 90.60 |
4 | −20° | −200 | 10 | 67.48 | 3316.98 | 200.60 |
5 | −20° | −200 | 20 | 67.48 | 3316.98 | 100.40 |
6 | −20° | −200 | 30 | 67.48 | 3316.98 | 67.20 |
7 | −30° | −200 | 10 | 79.43 | 1492.82 | 207.60 |
8 | −30° | −200 | 20 | 79.43 | 1492.82 | 103.80 |
9 | −30° | −200 | 30 | 79.43 | 1492.82 | 69.20 |
Serial Number | Initial Fuselage Yaw Angle θ0/deg | Lateral Offset d0/mm | Right Traction Speed v2/mm/s | Helicopter Control Wheel Angle γ/deg | Helicopter Correction Radius r/mm | Total Correction Time t/s |
---|---|---|---|---|---|---|
1 | −10° | −200 | 30 | 31.29 | 13162.86 | 90.60 |
2 | −10° | −150 | 30 | 39.01 | 9875.65 | 71.60 |
3 | −10° | −100 | 30 | 50.55 | 6582.97 | 52.80 |
4 | −10° | −50 | 30 | 67.63 | 3292.46 | 33.80 |
5 | −20° | −200 | 30 | 67.48 | 3316.98 | 67.00 |
6 | −20° | −150 | 30 | 72.73 | 2487.13 | 57.60 |
7 | −20° | −100 | 30 | 78.29 | 1658.18 | 48.40 |
8 | −30° | −200 | 30 | 79.43 | 1492.82 | 69.20 |
9 | −30° | −150 | 30 | 82.03 | 1120.06 | 63.40 |
10 | −30° | −100 | 30 | 84.67 | 746.36 | 57.40 |
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Zhong, Y.; Zhao, D.; Zhao, X. Research on the Methods for Correcting Helicopter Position on Deck Using a Carrier Robot. Actuators 2024, 13, 342. https://doi.org/10.3390/act13090342
Zhong Y, Zhao D, Zhao X. Research on the Methods for Correcting Helicopter Position on Deck Using a Carrier Robot. Actuators. 2024; 13(9):342. https://doi.org/10.3390/act13090342
Chicago/Turabian StyleZhong, Yuhang, Dingxuan Zhao, and Xiaolong Zhao. 2024. "Research on the Methods for Correcting Helicopter Position on Deck Using a Carrier Robot" Actuators 13, no. 9: 342. https://doi.org/10.3390/act13090342