VMC explorer

VMC (Virtual Model Control) is a simple idea: pretend you have virtual springs and dampers in task space (between body parts and targets), compute the resulting forces, then convert those forces into joint torques.

// Core VMC pattern (task-space PD + Jacobian transpose) F = k * (x* - x) + b * (v* - v) τ = J(q)^T F

Tip: drag the target dots in each canvas. Try low damping (b) to see overshoot, then increase b to calm it down.

0) Point mass (pure virtual spring + damper)

Spring k (N/m)30

Damping b (N·s/m)9

Mass m (kg)1.0

Force limit |F| (N)25

Presets:

0b) Ground contact (spring + penalty contact)

Drag the target into the ground to see normal force + friction. Tune contact stiffness/damping to get soft vs stiff ground.

Spring k (N/m)35

Damping b (N·s/m)10

Mass m (kg)1.0

Gravity g (m/s²)9.8

Force limit |F_vmc| (N)40

Contact stiffness k_n (N/m)2500

Contact damping b_n (N·s/m)45

Friction μ0.7

Friction damping b_t (N·s/m)18

Presets:

1) Single joint (virtual torsional spring)

Angle spring kθ (N·m/rad)10

Angle damping bθ (N·m·s/rad)2.5

Torque limit |τ| (N·m)6

Presets:

2) 2-link arm (end-effector spring → joint torques)

Spring k (N/m)120

Damping b (N·s/m)18

Joint damping (N·m·s/rad)1.2

Torque limit (N·m)35

Presets:

2b) 2-link arm + ground contact

Same VMC mapping (τ = JᵀF), but now the end-effector has a simple ground contact model (normal + friction). Drag the target below the ground, or toggle the auto step cycle.

VMC spring k (N/m)170

VMC damping b (N·s/m)20

Joint damping (N·m·s/rad)1.2

Torque limit |τ| (N·m)45

Contact stiffness k_n (N/m)6000

Contact damping b_n (N·s/m)80

Friction μ0.8

Friction damping b_t (N·s/m)25

Auto step cycleoff

Step frequency (Hz)1.20

Stride length (m)0.28

Step height (m)0.12

Stance press (m)0.010

Presets:

3) Quadruped (walk cycle + ground contact)

Drag the green foot targets, or toggle auto walk to see a simple trot gait generate contacts (normal + friction) automatically.

Spring k (N/m)220

Damping b (N·s/m)26

Joint damping (N·m·s/rad)1.5

Torque limit (N·m)24

Contact stiffness k_n (N/m)9000

Contact damping b_n (N·s/m)120

Friction μ0.8

Friction damping b_t (N·s/m)30

Auto walk (trot)off

Step frequency (Hz)1.40

Stride length (m)0.22

Step height (m)0.08

Stance press (m)0.010

Presets:

4) Drone (spring to target → thrust + moment)

Position k (N/m)12

Position b (N·s/m)7

Attitude k (N·m/rad)14

Attitude b (N·m·s/rad)4

Max thrust / rotor (N)12

Presets: