A virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain, and analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes.
Abstract:
In the area of biped robot research, much progress has been made in the past few years. However, some difficulties remain to be dealt with, particularly about the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits, especially on uneven terrain. In this perspective, both concepts of center of pressure (CoP) and zero moment point (ZMP) are obviously useful. In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. Finally, a virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain. This paper is a theoretical study. Experimental results are presented in a companion paper, analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes.
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Q1. What are the contributions mentioned in the paper "Forces acting on a biped robot. center of pressure—zero moment point" ?
In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. This paper is a theoretical study.
Q2. What is the field of pressure forces normal to the sole?
The field of pressure forces (normal to the sole) is equivalent to a single resultant force, exerted at the point where the resultant moment is zero.
Q3. What are the forces acting on a walker?
The forces acting on a walker can be separated in two categories: 1) forces exerted by contact and 2) forces transmitted without contact (gravity and, by extension, inertia forces).
Q4. What is the advantage of the CoP-ZMP concept?
The major advantage of the CoP-ZMP concept is that this point can be measured: measuring the contact pressure forcemoment allows the CoP to be reconstructed, and the ZMP by coincidence, and therefore the corresponding part of the gravityinertia forces.
Q5. What is the resultant of the gravity plus friction forces?
The resultant of the gravity plus inertia forces (superscript ) may be expressed as(8)and the moment about any point as(9)where is the total mass, is the acceleration of the gravity, is the center of mass (CoM) of the biped, is the acceleration of , and is the rate of angular momentum at .
Q6. What is the difference between the virtual and the cop?
According to the authors, the virtual ZMP is a weighting function of the local ZMP’s and , such that(23)where is a function varying continuously from 0 to 1.