Robot control
Virtual constraint
Definition
A virtual constraint is a relation among a robot's configuration variables that is imposed by feedback instead of by a physical linkage. In legged locomotion, virtual constraints often coordinate joint trajectories around a state-based gait phase.
Also known as: Virtual constraints
Updated
Feedback replaces a mechanical linkage
A physical constraint ties coordinates together through geometry, such as a rigid linkage. A virtual constraint specifies a desired relation and uses actuators plus feedback to enforce it. For a walking robot, an output might be the difference between an actual joint angle and a desired angle indexed by gait phase. Driving that output to zero coordinates several joints without adding hardware.
Grizzle and colleagues define virtual constraints as state-variable relations imposed through time-invariant feedback. A state-based phase variable can make the relation advance with the robot's configuration rather than with a wall clock, which helps coordinate a gait when timing varies.
Use in biped control
Virtual constraints can specify torso posture, swing-foot clearance, leg shape, or other outputs. They are central to one construction of hybrid zero dynamics, where the controlled relations also need to remain consistent through foot impact.
They can be combined with other control layers. Gong and colleagues report a Cassie controller that joins virtual-constraint motion regulation with an angular-momentum pendulum model and model predictive control, including a physical moving-walkway demonstration. This is a particular implementation rather than a universal virtual-constraint architecture.
A desired relation must be feasible
Feedback cannot enforce a trajectory that conflicts with actuator limits, contact forces, joint ranges, or the robot's underactuation. Poor output selection can leave important internal motion weakly controlled even when the measured output error is small.
The phase variable also needs to progress reliably. If it reverses or becomes ambiguous during a disturbance, the desired joint values can become inappropriate. Stability and feasibility therefore depend on the model, chosen outputs, gait construction, and treatment of impacts.
Sources
Related terms
Hybrid zero dynamics
Hybrid zero dynamics is the reduced closed-loop dynamics that remains when a legged robot's controlled outputs are held at zero and that zero set is preserved through impacts. It provides a way to design and analyse periodic gaits in systems with continuous motion and discrete contact events.
Underactuation
Underactuation means that a system’s available control inputs cannot independently command acceleration in every degree of freedom of its model. It often occurs when a mechanism has fewer independent actuators than degrees of freedom.
Bipedal locomotion
Bipedal locomotion is movement using two legs, with body motion coordinated through changing contacts between the feet and the environment. It includes walking and running.
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.