Mechanics-constrained inverse estimation of equivalent wheel–terrain contact angles from wheel-axis wrenches

Wheel–terrain contact-state characterization is essential for maintaining mobile-robot posture stability on deformable terrain. This work formulates equivalent wheel–terrain contact estimation as a mechanics-constrained inverse problem that maps wheel-axis wrench measurements to a wheel-surface contact point parameterized by horizontal and vertical contact angles. A physics-informed neural network (PINN) is developed by combining supervised learning with a wrench-balance residual for single-resultant moment consistency, hard wheel-surface parameterization, and trial-wise temporal smoothness regularization. Surface-validity filtering is applied to offline wrench-derived reference angles, and the residual magnitude is used as a physics-consistency indicator. Wheel-obstacle traversal experiments were conducted on a testbed using a lugged wheel and Mars regolith simulant, with wrench responses collected across representative obstacle, terrain, speed, and lateral-offset conditions. With supervision from six labeled trials, the developed PINN provided lower held-out root-mean-square and mean absolute errors for the vertical contact angle than Baseline-PINN when evaluated against the offline wrench-derived reference, and a lower wrench-balance residual than DataNN. These results indicate that, under the single-resultant contact assumption, the proposed estimator provides a mechanics-consistent limited-supervision inverse-estimation framework that reproduces the adopted offline wrench-derived reconstruction while improving wrench-balance consistency.