It specifies the point with respect to which reaction forces at the contacts between the feet and the ground do not produce any moment in the horizontal direction, i.e., the point where the sum of horizontal inertia and gravity forces is zero.
The concept assumes the contact area is planar and has sufficiently high friction to keep the feet from sliding.
This concept was introduced to the legged locomotion community in January 1968 by Miomir Vukobratović and Davor Juričić at The Third All-Union Congress of Theoretical and Applied Mechanics in Moscow.
[examples needed] The zero moment point is an important concept in the motion planning for biped robots.
The trajectory of a walking robot is planned using the angular momentum equation to ensure that the generated joint trajectories guarantee the dynamical postural stability of the robot, which usually is quantified by the distance of the zero moment point in the boundaries of a predefined stability region.
The position of the zero moment point is affected by the referred mass and inertia of the robot's torso, since its motion generally requires large angle torques to maintain a satisfactory dynamical postural stability.
One approach to solve this problem consists of using small trunk motions to stabilize the posture of the robot.
However, some new planning methods are being developed to define the trajectories of the legs' links in such a way that the torso of the robot is naturally steered in order to reduce the ankle torque needed to compensate its motion.
If the trajectory planning for the leg links is well-formed, then the zero moment point won't move out of the predefined stability region and the motion of the robot will become smoother, mimicking a natural trajectory.
The Newton–Euler equations can be rewritten as: so it's easier to see that we have: These equations show that the biped robot is dynamically balanced if the contact forces and the inertia and gravity forces are strictly opposite.
is a point on the contact plane, e.g. the normal projection of the center of mass.
Zero moment point has been proposed as a metric that can be used to assess stability against tipping over of robots like the iRobot PackBot when navigating ramps and obstacles.