Hardware & control
Divergent component of motion
DCM
The divergent component of motion is the unstable part of a simplified legged robot's centre-of-mass dynamics, combining position and velocity into a state that moves away from the available support unless foot placement or contact forces regulate it.
Updated
DCM isolates the unstable motion
Linear inverted-pendulum models split centre-of-mass behaviour into a convergent part and a divergent part. The divergent component combines planar centre-of-mass position with scaled velocity. If support does not regulate it, this state moves away from the centre of pressure rather than naturally decaying towards it.
Englsberger, Ott, and Albu-Schäffer use that structure to plan and control three-dimensional biped walking. Controllers can shape the DCM trajectory through contact-force distribution and future foot placement while a lower layer tracks the corresponding whole-body motion.
Planar DCM can equal the capture point
For a constant-height linear inverted pendulum without the additional angular-momentum terms needed by richer models, the planar DCM and instantaneous capture point have the same expression. “Capture point” highlights the support location that arrests motion; “DCM” highlights the unstable state being controlled.
This does not make every quantity labelled DCM directly comparable. A source may use three-dimensional extensions, a virtual repellent point, external-force compensation, planned footholds, or different support envelopes. The state definition and reference frame must accompany the number.
A DCM margin inherits its benchmark
HULK shifts the planar DCM to account for an external wrench, then measures it against a tolerance-expanded union of current sole contacts and predicted touchdown regions. Its reported “DCM excursion” is the distance beyond that chosen allowance. A negative signed margin means the state left the benchmark envelope; it does not by itself prove the robot fell.
The model omits some joint-level feasibility, contact, friction, and state-estimation effects. A DCM controller can therefore request a dynamically sensible centroidal response that the full robot cannot execute. Hardware evaluation still needs falls, slips, actuator limits, protective stops, and task outcomes.
For logged training or evaluation data, store the DCM formula, natural frequency or height assumption, centre-of-mass source, velocity filter, external-wrench correction, active and predicted contacts, support-region geometry, and controller timing. Reporting only the minimum margin hides which model and recovery options produced it.
Sources
Related terms
Hardware & control
Capture point
The capture point is the location on a support surface where a simplified legged robot would need to place or regulate support to bring its horizontal centre-of-mass motion to rest without changing its assumed height or angular-momentum model.
Hardware & control
Centre of mass
The centre of mass is the mass-weighted average position of a body or multibody system. For a humanoid, the whole-robot centre of mass changes as its joints move or its payload changes, and its position and acceleration are central variables in balance, locomotion and whole-body control.
Hardware & control
Support polygon
The support polygon is the convex hull of a robot’s contact areas on a declared support surface. For a biped on level ground it is formed by the loaded parts of one or both feet; it changes when contacts are added, removed or reduced to an edge or toe.
Hardware & control
Zero moment point
The zero moment point is a support-surface point used in legged-robot dynamics at which the tipping moment vanishes. ISO defines it from the resultant support forces, while classical biped literature uses the corresponding gravity-and-inertia formulation; for dynamically balanced planar contact, these formulations coincide with the centre of pressure.
Hardware & control
Model predictive control
Model predictive control is a feedback-control method that uses a dynamics model to optimise a sequence of future actions, applies the first action or short part of that sequence, and replans from an updated state estimate. In receding-horizon MPC, the planning window moves forward at each update.