Humanoid Dynamics & Whole-Body Control (WBC) Simulator
An interactive engineering laboratory for bipedal humanoid locomotion: simulate Center of Mass (CoM) momentum, Zero Moment Point (ZMP) stability envelopes, dynamic impulse push recovery, and high-density joint actuator torque constraints.
First-Principles Bipedal Humanoid Balance Dynamics
Dynamic bipedal balance is fundamentally underactuated: a humanoid cannot apply arbitrary torques directly to the world frame, but must modulate ground reaction force (GRF) contact wrenches within the convex support polygon defined by foot geometries.
1. Zero Moment Point (ZMP)
The Zero Moment Point is the exact surface coordinate where horizontal contact moments equal zero. Stable, non-tipping bipedal locomotion requires that the ZMP remains strictly enclosed inside the support polygon convex hull.
2. Linear Inverted Pendulum (LIPM)
By constraining CoM vertical acceleration to zero (constant height Zc), multi-body dynamics simplify into linear second-order equations: d^2 x / dt^2 = (g / Zc) * (x - x_zmp), yielding the characteristic natural frequency omega = sqrt(g / Zc).
3. Whole-Body QP Hierarchy
Quadratic programming resolves redundant kinematic chains at 1,000 Hz, prioritizing contact stability and self-collision avoidance at top priority, with torso posture and end-effector tasks satisfied in the null-space.