Object State Complexity
OSC breaks down what makes a manipulation Action difficult into six independent axes. Each axis represents one condition that makes the object's state hard to handle.
The same insertion can be easy at a ±2 mm tolerance and an open problem at ±0.2 mm. The same pour can be easy into a clear glass and fail when filling an opaque container to a set level. Action names alone do not reveal these differences. OSC does.
- Why does a task fail?
- A 70% success rate, for example, does not reveal why the other 30% fail.
- When is advanced Dexterity required?
- The same task requires different capabilities depending on the object's geometry, friction, and occlusion.
- How should sensors, control, and learning be designed?
- Task names alone are not enough to make engineering design decisions.
OSC Vector
The OSC Vector
Every task in DexBench is characterized by a six-dimensional OSC vector that captures independent sources of difficulty.
OSC =C_geom,C_force,C_contact,C_obs,C_deform,C_dyn
Whether each axis applies is judged separately for every task. Some axes may apply to a task while others do not, and that pattern shows which capabilities the task tests.
Axes
The Six Axes
C_geomGeometric ComplexityGeometric
Does the task allow only a narrow range of valid poses and contact configurations?
This axis covers shape complexity, tolerance requirements, and alignment sensitivity. It applies when the object's shape, symmetry, or tolerance requirements constrain the space of valid configurations for successful manipulation.
C_forceForce Control ComplexityForce
Does the task require precise regulation of force and torque to avoid failure?
This axis applies to tasks whose success or failure depends on force and torque thresholds. These tasks leave a narrow margin between too little force, which causes the task to fail, and too much force, which damages the object.
C_contactContact Mode ComplexityContact
Does the task pass through multiple contact states, with contact changing frequently?
This axis is judged by the diversity of contact points, contact surfaces, and friction states, and by how often the contact mode changes. It applies to tasks that require several sequential contact reconfigurations.
C_obsObservation IncompletenessObservation
Is task-critical state invisible to the sensors?
This axis covers occlusion, internal contact states, motion blur, and any case where sensors cannot directly observe the information needed for control. When it applies, the task must rely on inference, memory, and tactile feedback.
C_deformDeformation ComplexityDeformation
Does the object have a shape with many degrees of freedom and a configuration that depends on its history?
This axis covers the high-dimensional deformation states found in cloth, film, cable, and other deformable objects. Deformation greatly expands the state space, adds history dependence, and introduces material uncertainty that rigid-body assumptions cannot handle.
C_dynDynamic / Temporal ComplexityDynamic
Does the task's state change quickly enough that timing decides success?
This axis is judged by the rate of state change, the presence of discontinuous events such as impacts and releases, and whether control latency directly decides success or failure. It applies to moving objects, pouring, and catching.
Key Principle
Sensitivity to Error
Not every axis applies to every task. The OSC axes that apply to a given task define its primary difficulty profile and determine which Dexterity Regimes it calls for. For example, C_geom and C_force may apply to a precision insertion task while C_deform and C_dyn do not. This indicates that geometric precision and force control are the main challenges, and that deformation and timing are not at issue.
This sensitivity profile informs hardware selection, sensor strategy, and control architecture choices for each class of task.