Slope Terrain Gait Planning and Admittance Control Method for Underwater Quadruped Robots Based on Righting Moment Compensation

Benthic AUVs (underwater quadruped robots) merge the cruising efficiency of submersibles with the bottom-crawling stability of legged robots for unstructured deep-sea exploration. However, the deliberate separation of the center of gravity and buoyancy—essential for static stability—generates a significant righting moment. When climbing steep slopes, this moment resists hull alignment. If the slope exceeds the robot’s maximum hydrostatic pitch limit, conventional inverse kinematics algorithms fail: the hind legs lose ground contact and propulsion is lost. To overcome this, this paper proposes a framework integrating optimal force distribution, adaptive trajectory probing, and admittance control. An analytical multi-point moment balance model derives the terrain-adaptive pitch boundaries. A Quadratic Program (QP) then distributes contact forces, tasking front legs with stabilizing the righting moment while hind legs provide thrust. During the swing phase, adaptive Bezier sequences prevent anterior slope collisions and ensure posterior ground contact. Furthermore, a Cartesian admittance controller provides active compliance to manage the nonlinear friction of dynamic waterproof seals. Validated via a high-fidelity physics-based simulation model calibrated against physical pool trials, the robot achieved robust traversal of ${15}^{\circ }$ and ${33}^{\circ }$ steep slopes. Statistical robustness is substantiated via a 30-trial Monte Carlo study, where postural stability remained remarkably consistent with a mean Pitch RMSE of $2.{88}^{\circ }$ across a $\pm 10\%$ parameter uncertainty envelope. Compared to traditional baseline algorithms, the proposed method successfully suppressed torque chattering by $54.1\%$ in the high-frequency band (2–$50\mathrm{Hz}$) and improved energetic efficiency by up to $43\%$ on steep gradients. These findings offer a validated control architecture for heavy-duty deep-sea platforms navigating complex benthic topographies.