Design and Attitude Control of an Underwater Quadruped Robot

Davide Molinaroli; Mohit Singh; Kostas Alexis

cs.ROSep 6, 2026

Design and Attitude Control of an Underwater Quadruped Robot

Authors: Davide Molinaroli, Mohit Singh, Kostas Alexis

Organizations: Norwegian University of Science and Technology, Trondheim 7034, Norway

Abstract

Legged robots are versatile on land, but their use in underwater environments remains limited. Extending quadruped locomotion to water enables amphibious mobility with applications in inspection, environmental monitoring and disaster response. This paper presents the design, modeling, and experimental validation of a reproducible underwater quadruped robot. The robot is built around custom waterproof motor housings machined from polyoxymethylene plastic, which use off-the-shelf O-rings and dynamic shaft seals. A simplified model is derived to describe the dynamics of this underwater legged system, capturing how drag forces on spherical end effectors transmit torque to the floating base. Building on this model, a closed-loop attitude controller is developed using an error formulation defined on the special orthogonal group SO(3). The controller is evaluated both in simulation and experimentally in a water tank, where the robot tracks desired orientation setpoints in roll, pitch and yaw.

Figures & tables

Figure 1: The underwater quadruped robot performing pitch and roll maneuvers.

Figure 4: Main electronics enclosure. The bottom part (left) contains the Jetson Orin NX and A603 board, I2C Mux, PWM driver and 12 ADCs. The top part (right) contains power lines, tether communication boards and cables, IMU, pressure vent for vacuum testing, OBC switch and depth sensor.

Panel of Figure 5 — Figure 5: (a) Reference frames include world ( $\mathcal{F}_{W}$ ), body ( $\mathcal{F}_{B}$ ), and leg-specific ( $\mathcal{F}_{L,i}$ ) systems. (b) The five-bar linkage uses actuated angles $\theta_{1},\theta_{2}$ and passive angles $\theta_{4},\theta_{5},\phi$ , with frame $\mathcal{F}_{P}$ at center of the innermost lateral motor. (c) Leg geometry shows hip motor angle $\theta_{3}$ and offsets $l_{y},l_{z}$ from the origin of $\mathcal{F}_{P}$ to that of $\mathcal{F}_{L,i}$ .

Figure 6: Simulation results of the closed-loop attitude controller on three trials. Step setpoints of amplitudes from 15 to 75 degrees are applied to all three axes simultaneously with increments of 30 degrees between consecutive trials.

Set	Cmd	$\theta_{\text{init}}$	$t_{r}$	$t_{s}$	$e_{\mathrm{ss}}$	$M_{p}$	$\psi_{\text{init}}$	$t_{r}$	$t_{s}$	$e_{\mathrm{ss}}$	$M_{p}$
	[deg]	[deg]	[s]	[s]	[deg]	[%]	[deg]	[s]	[s]	[deg]	[%]
Roll	15	80.89	23.34	51.64	-0.45	58.0	-78.02	12.41	25.67	0.37	13.9
	30	50.86	15.85	34.06	1.48	26.1	-35.49	5.38	18.16	-1.14	11.5
	45	132.86	39.91	61.20	-0.51	28.3	121.83	21.03	46.36	-0.54	14.8
	60	84.54	35.61	64.94	-0.83	17.9	71.15	10.82	37.15	1.09	15.5
	75	115.21	20.45	–	-2.65	10.9	82.91	17.74	45.88	-3.38	9.3

Table 1: Regulation performance across experiments.

Panel of Figure 7 — Figure 7: Closed-loop attitude regulation experiments. (a) Roll setpoints from 15 to 90 degrees. (b) Pitch setpoints from 15 to 90 degrees. The controller corrects yaw from different initial conditions. At the 90-degree pitch setpoint, roll and yaw traces exhibit apparent jumps due to gimbal lock in the Euler angle representation. The geodesic error is the angle of the axis-angle decomposition of $\mathbf{R}_{d}^{T}\mathbf{R}_{B}^{W}$ , plotted both raw and after a 3 s centered moving average.

Figure 8: Regulation to coupled roll and pitch angles, while correcting yaw from different initial conditions. The geodesic error is the angle of the axis-angle decomposition of $\mathbf{R}_{d}^{T}\mathbf{R}_{B}^{W}$ , plotted both raw and after a 3 s centered moving average.

Underwater Robotics

Underwater robotics develops autonomous and remotely operated machines for navigation, inspection, manipulation, and exploration in aquatic environments.

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Prompt extraction of victims from water is crucial in water surface rescue missions. However, previous research on rescue robots has seldom addressed this issue. This paper presents QuadBoat, a bio-inspired unmanned surface vehicle (USV) designed to track and retrieve victims from water. QuadBoat features a quadrupedal robot configuration, enabling it with highly adaptable and agile maneuverability through its actively adjustable posture. Employing an inverse kinematics-based controller and cascaded model predictive control (MPC)-PID controller for overall movement, QuadBoat can accurately track and retrieve objects on the water surface. Maneuverability demonstrations validate QuadBoat's high agility, while a series of tracking experiments, including leg action tracking and trajectory tracking, confirm its high motion accuracy and system mobility. Finally, visual-based tracking and object pickup experiments further verify QuadBoat's target tracking capabilities and its effectiveness in executing rescues, both indoors and outdoors.

Abstract

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