Hardware & control
Underactuation
Underactuation is the condition in which a system’s available control inputs cannot independently produce every possible acceleration of its modelled degrees of freedom. It often arises because there are fewer independent actuators than degrees of freedom, but contact, actuator limits and the chosen model also determine whether a system is underactuated.
Also known as: underactuated system, underactuated robot
Updated
Actuator count is a useful shortcut, not the full definition
A mechanism with fewer independent actuators than modelled degrees of freedom is underactuated. The formal MIT definition asks whether the controls can produce every desired generalized acceleration at a particular state and time.
That distinction matters because underactuation depends on the model and constraints. A rigid two-joint arm with two motors may be fully actuated in joint space, while a model that also includes unactuated link flexibility is not. Torque limits can prevent accelerations that an unconstrained model would consider available.
Humanoid base motion is not directly actuated
A floating-base humanoid adds six coordinates for root translation and rotation, but it has no motor attached between its pelvis and the world. Joint torques influence that base only through inertia and external contacts. Walking is additionally constrained because a foot can push against the ground but cannot pull on it, and friction limits horizontal force.
Contacts can temporarily constrain otherwise free motion, yet those constraints change as feet lift, land or slip. Whole-body control therefore reasons about actuation and feasible contact forces together.
Underactuated does not mean uncontrollable
An underactuated robot cannot track every arbitrary state trajectory, but it may still reach and stabilise useful states by exploiting dynamics. Swinging up a pendulum, balancing a biped and redirecting momentum before a footstep are standard examples.
Data and models should state which coordinates are actuated, actuator and transmission limits, passive joints, contact assumptions and any external support. Treating simulator-only forces at a floating base as ordinary robot actions can make a policy appear feasible while bypassing the real underactuation.
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Related terms
Hardware & control
Degree of freedom
A degree of freedom (DoF) is one independent parameter needed to specify a robot’s configuration; equivalently, a robot’s DoF is the dimension of its configuration space. It describes possible motion, not the number of motors. Joint constraints, closed kinematic chains and environmental contacts can make joint count, actuator count and controllable motion differ.
Hardware & control
Actuator
An actuator is a robot’s power mechanism that converts electrical, hydraulic, pneumatic or other supplied energy into controlled mechanical force, torque or motion. In a humanoid, actuators drive joints, often through transmissions; they are distinct from the joints and sensors, and their arrangement need not correspond one-to-one with the robot’s degrees of freedom.
Hardware & control
Floating base
A floating-base model represents a robot’s root body with six unconstrained spatial degrees of freedom—three for translation and three for rotation—instead of fixing it to the world. Those base coordinates are not directly actuated; a legged robot changes them through joint motion and external contact forces.
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.