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.
Also known as: center of mass, CoM
Updated
Mass, not shape, determines the point
Modern Robotics defines the centre of mass of a rigid body as the centroid of its mass distribution. It need not coincide with the geometric centre, and it can lie outside the material of a curved or articulated object.
For a multibody robot, the whole-system centre of mass is the weighted average of every link’s centre of mass. The MIT treatment of humanoid dynamics makes that dependence on robot configuration explicit. Moving an arm, bending a knee or picking up an object shifts the combined point even when the feet do not move.
Centre-of-mass projection is a limited balance test
For a stationary robot on a level surface, placing the vertical projection of the centre of mass inside the support polygon is a common contact-level condition against tipping. It establishes a realisable static equilibrium only when the configuration, joint torques, friction and other external loads are also feasible. It is not a general test for dynamic balance.
During walking, momentum and acceleration matter. A moving humanoid can remain feasible while its centre-of-mass projection approaches or passes a static support boundary, and it can fall despite a favourable projection if contact slips or angular momentum is uncontrolled. Dynamic controllers therefore use centre-of-mass position, velocity and acceleration together with contact forces and momentum.
The value depends on the model
A computed centre of mass inherits the link masses, link centre-of-mass offsets, joint configuration and payload assumptions of the robot model. An unmodelled tool, battery change or carried object can shift it enough to affect a balance controller.
Datasets should record the coordinate frame, model version, included bodies and whether each value was measured indirectly, estimated online or calculated later from joint state. “Base position” and “centre of mass” are not interchangeable: the base is a chosen body frame, whereas the centre of mass moves with the mass distribution.
Sources
Related terms
Hardware & control
Centre of pressure
The centre of pressure is the point on a support surface at which the resultant of a distributed contact pressure or ground-reaction force can be represented as acting. In legged robotics it summarises how load is applied through one foot or across coplanar contacts and is commonly estimated from a measured contact wrench.
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
Robot dynamics
Robot dynamics describes the relationship between forces and torques acting on a robot and the motion they produce, accounting for mass, inertia, gravity, velocity-dependent effects and external contact. Forward dynamics predicts acceleration from applied forces; inverse dynamics computes forces or torques for a specified motion.
Hardware & control
Whole-body control
Whole-body control coordinates a humanoid’s full multibody state, actuated joints and environmental contacts to pursue several motion or force objectives while respecting constraints such as balance, joint limits and friction. It is a family of hierarchical or optimisation-based methods, not one algorithm; implementations may output joint positions, accelerations or torques.