Robot control
Geometric fabric
Definition
A geometric fabric is a structured second-order dynamical system used to shape a robot's motion geometry while allowing task objectives to be supplied separately as potential functions. It is designed so modular behaviours can be combined with stated stability and path-consistency properties.
Also known as: Geometric fabrics
Updated
Separate motion style from the task goal
A geometric fabric encodes nominal second-order motion, such as how trajectories bend around obstacles or respect velocity-dependent priorities. A separate potential supplies the task objective. The fabric shapes the path followed as the forced system moves toward a minimum of that potential.
Ratliff and colleagues develop geometric fabrics within a broader theory of optimisation fabrics. Their construction uses Finsler geometry to define a priority metric while allowing the policy geometry to be designed separately. The paper states conditions for convergence and geometric path consistency within its mathematical model.
Build behaviour in multiple task spaces
Humanoid control often combines end-effector tracking, posture, joint-limit avoidance, collision avoidance, and balance. A fabric can be designed in a task space and transformed back through robot kinematics, allowing several components to contribute to one configuration-space policy.
This resembles a Riemannian motion policy, and the fabric work grows from RMP and RMPflow research. The distinction is the fabric framework's separation of an unbiased motion geometry from the forcing task potential and its associated stability construction. It is also different from trajectory optimization: a fabric defines a continuous-time policy field rather than solving one finite trajectory for a fixed initial condition.
Formal structure does not supply a robot model
The foundational paper is theory-led and includes a simple planar-arm demonstration. It does not by itself validate high-speed whole-body humanoid control, contact switching, actuator saturation, perception error, or delay. Those elements require a compatible implementation and separate evaluation.
Poorly chosen component metrics or transformations can create ill-conditioning or unexpected priorities. A stable continuous-time formulation can also lose its intended behaviour after discrete integration, clipping, or low-rate execution. Geometric fabrics provide tools for composing motion policies; they do not choose safe goals, guarantee collision-free sensing, or replace contact and hardware constraints.
Sources
Related terms
Riemannian motion policy
A Riemannian motion policy is a reactive robot motion rule expressed in a task space together with a state-dependent metric that represents the rule's directional importance. RMPflow combines several such policies and maps them through a robot's kinematic structure.
Operational-space control
Operational-space control formulates a robot’s motion and force behavior in task coordinates, such as the position and orientation of its hand, while accounting for the robot’s dynamics. Secondary joint objectives can be coordinated with the primary task.
Whole-body control
Whole-body control coordinates a robot’s joints and contacts to satisfy several motion and force objectives together. In humanoids, it commonly combines balance, foot motion, hand tasks, and posture subject to physical constraints.
Null space
The null space of a matrix is the set of vectors it maps to zero. For a robot task Jacobian, it contains joint velocities that produce no instantaneous motion in the specified task coordinates.