When a legged robot stands or walks, gravity and its own accelerations add up to a single ground reaction force. The zero moment point (ZMP) is where that force would have to act for the robot not to rotate about the edge of its foot.
If the ZMP stays inside the support polygon, the area covered by the foot or feet in contact with the ground, the robot is dynamically stable. If it reaches the edge, the foot starts to tip. Classic humanoid walking controllers plan footsteps and body sway so the ZMP follows a safe path through the support polygon.
ZMP-based control produces the careful, slightly bent-knee gait familiar from early biped demonstrations. Newer humanoids often use whole-body optimisation or learned controllers instead, which allow more athletic motion, but ZMP remains a standard way to measure and explain balance.
