Passivity-Based Control

Designing a controller from an energy standpoint, so the closed-loop system only ever dissipates energy, never creates it, and is thereby stable.

Passivity-based control is a family of nonlinear controller-design methods built around energy, a name coined by Ortega and Spong in their 1989 survey on adaptive control of rigid manipulators. A system is ‘passive’ if the energy it stores never increases by more than the energy fed in from outside: there exists a storage function H ≥ 0 such that dH/dt ≤ uᵀy, where u is the input and y the corresponding output (such as force and velocity), so uᵀy is the input power. Two passive systems connected in a power-conserving way remain passive together, which is why it's easier to guarantee stability when a robot contacts a person or an unknown environment. Design typically has two steps: energy shaping, reworking the closed-loop storage function so it's minimized at the target state; and damping injection, adding a dissipative term so energy keeps decreasing and settles at the target. Rather than canceling out all the nonlinearity (as computed torque control does), it tends to be more robust to model error. Teleoperation, impedance control, and human-robot collaboration commonly use an ‘energy tank’ to keep the books balanced, preventing communication delay or changing stiffness from breaking passivity.

ExampleETH's Risiglione et al. (2021) built force-feedback teleoperation for a legged robot with an arm: both the leader and follower sides keep a virtual energy tank tracking the energy exchanged, with the follower's whole-body controller constraining the tank's energy to stay positive, so the whole loop stays passive — and stable — even with network delay.

Also called

PBC

Related

Impedance Control · Lyapunov Stability · Bilateral Teleoperation · Computed Torque Control · Gravity Compensation · Physical Human-Robot Interaction

Sources

Borja & Ortega, Introduction to Passivity-Based Control (arXiv 2608.15222)
Passivity-based control for haptic teleoperation of a legged manipulator in presence of time-delays (arXiv 2108.07658)
Wikipedia: Passivity (engineering)