Generalized Momentum Observer

Estimating the external torque acting on a robot using only joint position, velocity, and motor torque — no force sensor needed.

Proposed by Alessandro De Luca and colleagues around 2003 (originally for actuator-fault detection), and used for collision detection on the DLR-III lightweight arm in 2006, this is the classic method letting collaborative robots sense collisions without a force sensor. It tracks the generalized momentum p = M(q)q̇ (M the mass matrix, q̇ joint velocity), comparing the momentum change predicted by the dynamics model against what's actually measured to get a residual r, satisfying ṙ = K(τ_ext − r): r is exactly the estimate of external torque τ_ext after first-order low-pass filtering, with a larger gain K responding faster but more sensitive to noise. It needs no joint acceleration measurement and no inversion of the mass matrix. Once the residual exceeds a threshold, a collision is declared and a collision reaction triggered; because modeling errors like friction leak into the residual too, it's commonly paired with friction compensation.

ExampleAn arm in motion is blocked by a person's hand; the momentum residual on the first few joints quickly exceeds the threshold, and the controller declares a collision, halting the original trajectory and switching to a compliant or yielding mode.

Also called

Momentum Observer, GMO

Related

Collision Detection (Robot Safety) · Collision Reaction · Disturbance Observer · Sensorless Force Estimation · Mass Matrix · Friction Compensation

Sources

Haddadin, De Luca, Albu-Schäffer, Robot Collisions: A Survey on Detection, Isolation, and Identification (IEEE T-RO 2017)
Collision detection and external force estimation for robot manipulators using a composite momentum observer (AIMS Electronics and Electrical Engineering, 2024)