Virtual Model Control

Imagining virtual springs and dampers attached to the robot, then converting the forces they'd produce into joint torques.

Virtual model control was proposed by Jerry Pratt and colleagues at the MIT Leg Lab, published in IJRR in 2001, and first used on planar biped walking. The method imagines springs, dampers, and other ‘virtual components’ hung between the robot's body and some reference point — for instance, a spring pulling the torso up toward a target height. It computes a virtual force F from the spring-damper equation, then converts it into support-leg joint torques via the Jacobian transpose: τ = Jᵀ F, where J is the matrix mapping joint velocity to body velocity. It needs no full dynamics model and no inverse kinematics, and its parameters have an intuitive physical meaning — tuning it feels like adjusting how stiff a spring is. The robot in the original paper relied only on foot contact detection and walked over slopes and uneven ground without knowing the grade in advance. It ignores the legs' own inertia, making it a quasi-static approximation whose error grows with more aggressive motion. It's since also commonly used for leg force control on quadrupeds and wheel-legged robots.

ExampleA biped in stance phase: a vertical virtual spring-damper on the torso maintains body height, a torsional spring keeps the torso upright, and a horizontal damper controls forward speed. The three virtual forces are converted via τ = Jᵀ F into hip, knee, and ankle torques.

Also called

VMC, Virtual Spring-Damper Control

Related

Jacobian Transpose Method · Impedance Control · Torque Control · Bipedal Locomotion · Whole-Body Control · Raibert Heuristic

Sources

Pratt, Chew, Torres, Dilworth, Pratt: Virtual Model Control: An Intuitive Approach for Bipedal Locomotion (IJRR 2001)