Abstract

A simulation study on whether the six-dimensional physical wrench transmitted through a humanoid’s waist — gravitational, inertial, and interaction loads combined — can be reconstructed from proprioception alone (encoders, torso IMU, leg motor torques), without a dedicated six-axis force/torque sensor. Evaluated on a simulated Unitree G1 in MuJoCo, the main finding is that a correctly source-synchronized reconstruction nearly matches an exact-state reference, while naively mixing differently-staged cached signals produces errors several times larger — a measurement-timing problem, not an algorithm problem.

Method

• Reconstructed the waist wrench via lower-body inverse dynamics: transported leg-torque-derived ground wrenches to a fixed waist point and subtracted the transported upper-body inertial and gravitational wrench
• Separated the target time an estimate represents from its data-availability time, comparing an exact-state reference path against a realistic sensor-input path under same-trajectory and delayed-replay conditions
• Cross-checked the result against an independent, algebraically-reduced 18×18 inverse-dynamics implementation
• Ran 30 simulation trials spanning payload changes, upper-body motion, applied forces/moments, and combined loads, under explicit contact-validity screening

Results

• Source-synchronized (delayed) reconstruction nearly matched the exact-state reference — e.g. 3.718 N vs. 3.717 N force RMSE on one test condition
• Naively using cached, differently-staged signals produced errors roughly 4–8x larger
• The reduced 18×18 implementation agreed with the sequential reconstruction to within machine precision — confirming numerical equivalence rather than independently validating accuracy
• Contribution is the measurement-stage characterization and evaluation protocol, not a new estimator; physical validation on a real G1 remains future work

Skills

MuJoCo Python Inverse Dynamics Sensor Fusion