Momentum observer

Turn a dynamics mismatch into an external-force estimate#

Robot dynamics predict how generalized momentum should change under commanded actuation, gravity, and modeled internal forces. A momentum observer integrates that relationship and forms a residual between expected and observed behaviour. An unexpected residual can be interpreted as external joint torque and, with the robot Jacobian, related to a contact wrench.

This offers a way to detect contact without installing a force-torque sensor at every possible contact. The MOB-Net paper describes momentum observers as sensorless external joint-torque estimators and applies a learned correction to a high-dimensional floating-base humanoid.

Useful for contact, collision, and locomotion#

A sufficiently fast residual can trigger collision detection or a safety reaction. Estimated external torques can also support contact-wrench feedback, manipulation, and legged state estimation. Lim and colleagues report external-torque and contact-wrench estimation from encoders and an inertial measurement unit, then use the estimate in zero-moment-point feedback during humanoid walking.

A momentum observer is not a physical force sensor. It infers the part of the motion that the internal model and measured actuation do not explain. It also differs from a general state estimator, although both may share encoder and inertial data.

Model error appears as apparent contact#

Friction, gearbox elasticity, inaccurate inertial parameters, current-to-torque error, and unmodelled actuator dynamics can all enter the observer residual. A threshold high enough to reject these effects can miss a weak contact; a low threshold can generate false detections. Differentiation, filtering, and delay further affect when an impact is recognised.

Learned correction methods can reduce repeatable model error, as the cited humanoid studies report, but they introduce training coverage and distribution-shift limits. Sensorless estimation therefore complements rather than automatically replaces calibrated force sensing, especially where the direction and magnitude of contact are safety-critical.