Wukong-Omni: Design, Modeling and Control of a Multi-mode Robot for Air, Land, and Underwater Exploration with All-in-One Propulsion Unit

Yufan Liu; Rixi Yu; Junjie Li; Yishuai Zeng; Zhenting Wen; Cheng Li; Haifei Zhu; Shikang Lian

References	Type	Land ability	Water ability	Propulsion number	Air endurance	Water hover endurance
[ 5 ]	Coaxial tricopter	Active differential	Surface	6	18 mins	None
[ 22 ]	Quadrotor	Passive rolling	Surface	4	None	None
[ 13 ]	Coaxial Quadrotor	Passive rolling	Underwater	8	None	None
Proposed	Tilt Quadrotor	Active ackermann	Underwater vector	4	5 mins	1-2h

Table 1: Comparison of Structure and Performance of Representative prototypes

Figure 1: Several representative cross-domain and motor reuse structure prototypes. A. SHOALBOT wheel-propeller prototype ( [ 16 ] ). B. Coaxial tricopter based prototype ( [ 5 ] ). C. Two-wheeled based prototype ( [ 22 ] ). D. Caged based prototype ( [ 13 ] ). E. Dipper’s motor reuse structure prototype ( [ 18 ] ). F. TJ-FlyingFish’s gearbox structure prototype ( [ 14 ] ).

Figure 2: Cross-Domain Operation Scenarios in Flood Rescue Missions. A . Taking off from the rescue boat. B . Swimming to the operation area. C . Flying to the operation area. D . Searching for accessible entry points at the operation area. E . Performing search and rescue tasks. F . Swimming back to the rescue boat via the water surface. G . Flying back to the rescue boat. H . Diving to access submerged entrances. I . Entering through open entrances via flight or rolling.

Figure 3: A .The prototype of Wukong-Omni. B .The diagram of Wukong-Omni’s various modes and the transitions.

Parameter	Gears	G.width	Shift coff	Quality
(unit)	(z)	(mm)(b)	-(x)	ISO1328:2013(A)
Sun(1)	12	9.6	0.488	Q6
Planetary(1)	30	4.0	-0.488	Q6
Internal gear(2)	78	5.0	-0.195	Q6
Planetary(2)	15	14.4	0.195	Q6

Table 2: All-in-One Propulsion Unit’s Gearbox Param Selection

Figure 4: All-in-One Propulsion Unit operation schematic. A. The Unit structure composition. B. The aerial mode. C. The aquatic and land mode. D. The exploded view of the developed unit. E. The front view and size of the unit. F. The gearbox structure details of the unit. G. The overall structure of the unit.

Parameter	unit	Value
Diameter	mm	180
Pitch ratio	-	0.71
Disk ratio	-	0.3056
Blade-number	-	3
Meanline type	-	NACA a=0.8
Thickness type	-	NACA 66 (DTRC)

Table 3: Wheel-Propeller Initial Param Selection

Figure 5: Performance evaluation of propellers in (160 mm, 180 mm, 200 mm) diameters. A . The Schematic of the test bench and water tank. B . The thrust-rpm curves. C . The efficiency-rpm curves. D . The torque-rpm curves. E . The motor–gearbox efficiency-rpm curves. F . The simulated efficiency-diameters curves using OpenProp.

Equipment	Type
Force sensor	RUILIDE RDF-TM20
Torque sensor	RUILIDE RDN-97B
Encoder	blheli dshot Feedback
Driver	Tmotor velox-V45A-V2
Distribution Board	Holybro PM07
Controller	Pixhawk 4 (custom high rate feedback)

Table 4: Test bench Component Selection

Propeller size	Max thrust	Max efficiency	Max unit efficiency
(mm)	(N)	(N/W)	(Q $\omega$ /UI)
D160mm	41.2	0.337	0.46
D180mm	49.6	0.449	0.488
D200mm	41.5	0.507	0.47

Table 5: Performance Comparison of Different Propeller Sizes in Thrust and Efficiency

Figure 6: The cross-sectional and 3D views of the mesh during simulation.

Figure 7: Performance evaluation of propellers in different structure (D180mm, wheel+propeller, wheel-propeller fusion)

Rotation speed	Simulation results	Experimental results	Error
(RPM)	(N)	(N)	(%)
200	2.53	2.605	2.9
300	7.24	6.4	11.6
400	13.07	11.1	15.07
500	20.33	17.72	12.83
600	28.40	24.1	15.64

Table 6: Comparison of Simulated and Experimental wheel-propeller fusion Thrust Results at Varying Rotation Speeds

Propeller	Max thrust	Max efficiency	Max speed	Max drag
type	(N)	(N/W)	(RPM)	torque(NM)
D180mm	49.6	0.449	734	-
W+P	12.1	0.209	441	0.603
fusion	36.5	0.399	710	0.06

Table 7: Tank test Performance Comparison of Different Propeller shapes in Thrust and Efficiency

Figure 8: The Verification of the simulation results in the water tank.

Figure 9: A-C .Comparison of hydrodynamic characteristics for different wheel–propeller tilt angle sets. D .Tank test results of three wheel–propeller tilt angle.

Figure 10: Simulation results of the thrust and efficiency in five different agnle at different rotate-speed and five different width at different speed.

Figure 11: Simulation results of the thrust produced by the five different agnle at different rotate-speed.

Propeller	Max	Test 600r	Simulation	Error	Efficiency
type	thrust(N)	thrust(N)	thrust(N)	(%)	(N/W)
D180mm	49.6	24.98	29.39	15.01	0.449
30deg	38.0	24.10	28.40	15.14	0.399
0deg	28.6	18.12	21.21	14.56	0.338
-30deg	20.3	15.87	18.82	15.67	0.310

Table 8: Tank test Performance Comparison of Different wheel angles in Thrust and Efficiency

Figure 12: Performance evaluation of air-propellers in different diameter and blades number. A . The thrust-rpm curves. B . The efficiency-rpm curves. C . The torque-rpm curves.

Width	Max	Max	300r	500r	700r
(mm)	thrust(N)	torque(NM)	Eff(N/W)	Eff(N/W)	Eff(N/W)
12	45.6	1.18	1.16	0.72	0.52
20	44.4	1.19	1.13	0.69	0.50
28	37.0	0.90	1.21	0.76	0.56
36	40.4	1.16	1.042	0.65	0.48
44	40.8	1.27	0.96	0.60	0.44

Table 9: Simulation Performance Comparison of Different width in Thrust and Efficiency

Propeller	Max thrust	Max efficiency	Valid efficiency(6000 r/min)
type	(N)	(N/W)	(N/W)
T9045-3	14.8	0.1674	0.0869
T9045-2	12.9	0.0849	0.0791
T1050-3	18.2	0.1599	0.0882
T1070-2	13.9	0.1519	0.0786

Table 10: Performance Comparison of Different Propeller size in Thrust and Efficiency

Figure 13: All-in-one propulsion unit performance evaluation experiments. A . Evaluation of aerial propeller interference on underwater mode. B . Evaluation of one-Way bearing impact on aerial mode. C . Evaluation of wheel–propeller interference with aerial inflow.

Name	Weight	Aquatic Unit Efficiency	Aerial Unit Efficiency	Aerial Efficiency(N/W)	Aquatic Efficiency(N/W)	Max Aquatic Thrust/Weight Ratio	Air	Land	Water
[ 14 ]	122g	52.5%	63.3%	0.073	0.265	32N/122g = 0.262	✓	✗	✓
[ 24 ]	28g	46.0%	50.0%	0.031	0.172	9.5N/28g = 0.339	✓	✗	✓
[ 23 ]	19.3g	NA	12.3%(simu)	NA	0.4(simu)	4.8N/19.3g = 0.249(simu)	✓	✗	✓
[ 16 ]	$\geq$ 500g	NA	NA	NA	NA	55N/500g = 0.11	✗	✓	✓
[ 1 ]	130.4g	NA	NA	NA	0.18	12N/130.4g = 0.092	✓	✗	✓
[ 3 ]	83.4g	NA	NA	NA	0.27	15N/83.4g = 0.180	✗	✗	✓

Table 11: Comparison of the Performance of Representative Drive Unit

Figure 14: The prototype of Wukong-Omni and the labels of its main components.

Exp	Max thrust	Proportion	Max efficiency	Proportion
type	loss(N)	(%)	loss(N/W)	(%)
Test1	2.7	7.397	0.02	9.09
Test2	2.0	1.098	0.0126	9.77
Test3	1.5	8.33	0.0074	11.2

Table 12: Comparison of interference between air propeller and wheel-propeller in Thrust and Efficiency

Component	Type
Motor	T-MOTOR AT2321-KV950
Aerial propeller	GEMFAN1050X3
Aerial ESCs	velox-V45A-V2
Battery	Geshi LiPo 4S 5300mAh
Flight Controller	Pixhawk6C
Onboard Computer	Orin Nx-16Gb

Table 13: Prototype Component Selection

Figure 15: Model of Wukong-Omni with the labels on the coordinate systems and thrusters arrangement in air, land, water surface mode.

Figure 16: Electronic and hardware framework of Wukong-Omni.

Figure 17: Wukong-Omni’s integrated control framework structure.

Figure 18: Air-to-Ground Mode Transition Sequence of Wukong-Omni.

Figure 19: A . Multi-constraint analysis of wheel–propeller configuration and tilt angle. B . Illustration of main-arm rotation during the air-to-ground transition.

Symbol	Value
$[I_{xx},I_{yy},I_{zz}]$	$[1.44,1.48,2.13]\times 10^{-1}\ \text{kg}\cdot\text{m}^{2}$
$[m_{a},V]$	$[4.4$ kg $,3.21\times 10^{-3}\ \text{m}^{3}]$
$[L_{a},W_{a},H_{a}]$	$[44,22,20]$ cm
$[\rho_{a},\rho_{w}]$	$[1.29,1000]\ \text{kg/m}^{3}$
$\boldsymbol{K}_{d},C_{d}$	$diag$ $([0.9,0.5,0.8]),0.9$
g	$9.81\ \text{m/s}^{2}$

Table 14: Model Parameters

Figure 20: A . Complete water-air cross-domain motion loop. B . Experimental results showing attitude and power data during the transition. C . The robot hovers underwater after submerging. D . Trajectory of the water-to-air transition loop. E . Underwater depth-hold performance results.

Performance	Value	Performance	Value
Roll RMSE(deg)	1.54	Roll $\bar{e}$ (deg)	1.50
Pitch RMSE(deg)	1.86	Pitch $\bar{e}$ (deg)	1.37
Depth RMSE(m)	0.11	Depth $\bar{e}$ (m)	0.07
Max Surface Power(W)	220	Stable Flight Power(W)	860

Table 15: Evaluation of robot Performance in water-air Transition

Performance	Value	Performance	Value
Roll RMSE(deg)	1.78	Roll $\bar{e}$ (deg)	1.45
Pitch RMSE(deg)	2.19	Pitch $\bar{e}$ (deg)	1.77
Yaw RMSE(deg)	7.40	Yaw $\bar{e}$ (deg)	4.54
Max Land Power(W)	74.2	Max Flight Power(W)	1010

Table 16: Evaluation of robot Performance in land-air Transition

Figure 21: A . Complete air-land cross-domain motion loop. B . Experimental results showing attitude and power data during the transition. C . The robot mission path in field test. D . Trajectory of the air-land transition loop.

Figure 22: A . Wukong-Omni tracking a designated path in land mode. B . Wukong-Omni performing manual circling in land mode. C . Experimental results showing the trajectory, velocity, and yaw during tracking. D . Experimental results showing the trajectory, velocity, and yaw during the circling test.

Cruise Performance	Value	Manual Performance	Value
Yaw $\bar{e}$ (deg)	0.08	Yaw $\bar{e}$ (deg)	8.71
Yaw RMSE(deg)	0.53	Yaw RMSE(deg)	10.5
Speed(m/s)	1.0	Max Speed(m/s)	3.3
Stop Radius(m)	2.5	Max Power(W)	152
Average Power(W)	27.36	Average Power(W)	76

Table 17: Evaluation of Robot Performance In Land Mode

Figure 23: A . Schematic illustration of underwater lateral motion. B . Underwater roll attitude response and corresponding motor speed. C . Schematic illustration of underwater yaw maneuver. D . Underwater yaw rate response and tilt servo actuation data.

Figure 24: A . Schematic illustration of trajectory tracking in aerial mode. B . Experimental results of trajectory tracking. C . Experimental results of body velocity and motor rotational speed.

Figure 25: A . The Obstacles on the water surface and the coordinate system which they are traversed. B . Experimental results of the attitude and position during the traversed. C . Underwater crossing process pictures.

Air Performance	value	Water Performance	value
Trajectory $\bar{e}$ (m)	0.31	Roll $\bar{e}$ (deg)	3.33
Trajectory RMSE(m)	0.35	Roll RMSE(deg)	6.56
Max Speed(m/s)	4.86	Max Speed(m/s)	1.2
Average Power(W)	942	Average Power(W)	128

Table 18: Evaluation of Robot Performance In Air And Water Mode

Figure 26: A . Illustration of the field mission execution. B–E . Wukong-Omni successfully performing outdoor tasks at an artificial lake, including water surface moving, underwater operation, ground locomotion, and air–water transitions.

Figure 27: A . Illustration of the mission execution. B . Outdoor experiment trajectory.

Wukong-Omni: Design, Modeling and Control of a Multi-mode Robot for Air, Land, and Underwater Exploration with All-in-One Propulsion Unit

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