<![CDATA[Near-ground unexploded ordnance (UXO) sensing requires a mobile carrier that maintains a controlled detector air gap over uneven terrain. This paper develops a static-slope rigid-body baseline for a Bobcat E20-class mini excavator carrying a 15 kg VMF4-class payload on a self-leveling gimbal. The research contribution is a body-frame, parked-base formulation that separates arm-level Cartesian positioning from payload-level attitude stabilization and identifies which rigid-body terms change on a static slope. The four-DOF attachment is reduced to a planar three-DOF boom-stick-tool subsystem for line sweeping. A kinetic-energy argument and potential-energy differentiation show that, with parked chassis and body-fixed coordinates, the inertia and Coriolis/centrifugal terms retain their level-ground form, while only the gravity torque is recomputed from the rotated gravity vector and center-of-mass Jacobians. Evaluation combines static torque analysis, Monte Carlo propagation, computed-torque tracking, and runtime timing. At 10° pitch, the 95th-percentile end-effector uncertainty is 2.63-3.65 cm; at 15° pitch, the tested gravity-torque change reaches 322.66 Nm. In the Python reproducibility environment, gravity-only update takes 24.0 microseconds per sample, compared with 38.9 microseconds for full rigid-body term recomputation. The 5.7°-6.3° trigger is a heuristic gravity-bias indicator, not a stability or clearance guarantee. Results support lightweight slope-aware gravity recomputation, while hydraulic dynamics, friction, soil interaction, moving-base effects, embedded timing, and hardware validation remain future work.]]>
