This paper is devoted to the permanence of the concept of Zero-Moment Point, widelyknown by the acronym ZMP. Thirty-five years have elapsed since its implicit presentation (actually before being named ZMP) to the scientific community and thirty-three years since it was explicitly introduced and clearly elaborated, initially in the leading journals published in English. Its first practical demonstration took place in Japan in 1984, at Waseda University, Laboratory of Ichiro Kato, in the first dynamically balanced robot WL-10RD of the robotic family WABOT. The paper gives an in-depth discussion of source results concerning ZMP, paying particular attention to some delicate issues that may lead to confusion if this method is applied in a mechanistic manner onto irregular cases of artificial gait, i.e. in the case of loss of dynamic balance of a humanoid robot. After a short survey of the history of the origin of ZMP a very detailed elaboration of ZMP notion is given, with a special review concerning “boundary cases” when the ZMP is close to the edge of the support polygon and “fictious cases” when the ZMP should be outside the support polygon. In addition, the difference between ZMP and the center of pressure is pointed out. Finally, some unresolved or insufficiently treated phenomena that may yield a significant improvement in robot performance are considered.

https://www.techfak.uni-bielefeld.de/~rhaschke/lehre/WS04/humanoids/papers/zmp-review.pdf

Zero-moment point — thirty five years of its life

Biped robots have better mobility than conventional wheeled robots, but they tend to tip over easily. To be able to walk stably in various environments, such as on rough terrain, up and down slopes, or in regions containing obstacles, it is necessary for the robot to adapt to the ground conditions with a foot motion, and maintain its stability with a torso motion. When the ground conditions and stability constraint are satisfied, it is desirable to select a walking pattern that requires small torque and velocity of the joint actuators. We first formulate the constraints of the foot motion parameters. By varying the values of the constraint parameters, we can produce different types of foot motion to adapt to ground conditions. We then propose a method for formulating the problem of the smooth hip motion with the largest stability margin using only two parameters, and derive the hip trajectory by iterative computation. Finally, the correlation between the actuator specifications and the walking patterns is described through simulation studies, and the effectiveness of the proposed methods is confirmed by simulation examples and experimental results.

/pdf/planning-walking-patterns-for-a-biped-robot-18hxylrb20.pdf

Planning walking patterns for a biped robot

This contribution treats definitions, dynamic aspects, and stability concepts of anthropomorphic systems. In addition to general conclusions about the new method of two-legged systems modelling, there are given some characteristic schemes of perturbed steady-gait regime stabilization.

On the stability of anthropomorphic systems

The focus of this paper is the problem of foot rotation in biped robots during the single-support phase. Foot rotation is an indication of postural instability, which should be carefully treated in...

Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point

Pstural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point

The connection between the dynamics of an object and the algorithmic level has been modified in this paper, based on two-level control. The central modification consists in introducing feedbacks, that is, a system of regulators at the level of the formed typed of gait only. Such a modification originates from the assumption that a very narrow class of gait types needs to be taken into account when generating the gait. In the paper the gait has been formed on the basis of a fixed program having a kinematic-dynamic character. The kinematic part concerns the kinematic programnmed connections for activating the lower extremities, while the dynamic part exposes appropriate changes in the characteristic coordinates of the compensation system. Such a connection with a minimum number of coordinates extends the possibility of solving the problem of equilibrium in motion for one type of gait without any particular algorithm that would take into account the motion coordinates and form out of them a stable motion at a higher algebraic level.

Contribution to the Synthesis of Biped Gait

The stability of legged machines in locomotion is considered. The general machine has a rigid body to which legs are attached. Locomotion is performed on level smooth surfaces.

On the Stability of Biped Locomotion

This paper considers the possibility of controlling an artificial upper extremity by a special-purpose computer, where the points that the extremity should reach are given in advance.

Davor Juricic

Papers

Contribution to the Synthesis of Biped Gait

On the Stability of Biped Locomotion

Contribution to the Synthesis of Biped Gait

Note on a Way of Moving the Artificial Upper Extremity