Passivity

Passivity is an energy accounting rule#

A passive component can store or dissipate supplied energy, but it cannot generate unlimited net energy on its own. The definition is expressed through input and output variables whose product represents power, such as force and velocity. A spring stores energy, while damping dissipates it.

This view helps when a robot, controller, environment, and person exchange forces. Under the relevant assumptions, connecting passive systems preserves a useful form of stability. MIT's manipulator-control notes use passivity to explain why physical damping can support stable contact and why active feedback must be treated carefully.

Interaction controllers use the property#

Impedance control asks a robot to present a relationship between motion and force. A passivity analysis tests whether the implemented controller can inject energy through that interaction port. This matters for a humanoid that makes contact with uncertain objects or people, where the environment dynamics are not fully known.

Passivity depends on the complete implementation, not only the outer control equation. Ficuciello and colleagues analyse how inner torque and velocity loops, filters, and sample frequency change the range of passive and stable impedance parameters. Their experiments illustrate why a nominal spring-damper setting cannot be assessed separately from the control stack.

Passive does not mean harmless or accurate#

A passive robot can still exert a large force using stored or supplied energy. It can also track poorly, collide, or violate a joint limit. Passivity establishes an energy inequality at defined ports; it does not certify every safety requirement.

Delay, discretisation, saturation, model mismatch, and changing controller gains can also affect the property. Engineers may add physical damping, energy tanks, or passivity observers and controllers, but each method has its own assumptions and performance trade-offs. The relevant claim is that a specified interconnection is passive under stated conditions, not that the whole robot is safe in every task.