Branislav Borovac

ZERO-MOMENT POINT — THIRTY FIVE YEARS OF ITS LIFE

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.

ZMP: A REVIEW OF SOME BASIC MISUNDERSTANDINGS

One of basic characteristics of the regular bipedal walk of humanoid robots is the maintenance of their dynamic balance during the walk, whereby a decisive role is played by the unpowered degrees of freedom arising at the foot–ground contact. Hence, the role of the Zero-Moment Point (ZMP) as an indicator of dynamic balance is indispensable. This paper gives a detailed discussion of some basic theoretical assumptions related to the ZMP in the light of imprecise, and even incorrect, interpretations that have recently appeared, and which have led to some erroneous conclusions. Examples are given to show some erroneous basic attitudes and the genesis of some of them is indicated. It is also pointed out that in the domain of bipedal walk there are still notions that are not clearly defined and their meanings differentiated in some related branches of science and engineering. One of the examples is dynamic balance and stability, which are often used interchangeably.

Mechanics of Turin Parallel Robot

The Turin parallel robot is a parallel manipulator whose mobile platform has 6 DOF. The platform is connected to three double parallelograms via three spherical joints and prismatic slider guides, whose axes are perpendicular to the mechanism planes. The specific design allows location of servomotors on the robot base enabling minimization of the inertia parameters. In this paper geometry, kinematics and dynamics of the mechanism are analyzed. The complete dynamic model of the robot has been derived and robot behavior simulated.

Towards a unified understanding of basic notions and terms in humanoid robotics

The intention of this paper is to contribute towards a unified understanding of the basic notions and terms in the domain of humanoid robotics, having in mind that the same notions are sometimes interpreted in different ways (some interpretations are contradictory, and some even erroneous). Hence, the first part of the paper is devoted to defining some basic notions, walk and gait being among the first. Then, the paper deals with the notion of dynamic balance and stability, particularly the difference between them, since these essentially different notions are often confused and, rarely, regarded as identical. As dynamic balance is directly related to the notion of zero-moment point (ZMP), it was necessary to touch upon some misunderstandings concerning the ZMP. Gait stability is an especially delicate category, as humanoid locomotion systems have certain specific features that are not possessed by other systems. Namely, because of external disturbances, there may appear unpowered (passive) degrees of freedom that cause loss of dynamic balance. Hence, these unpowered degrees of freedom cannot be overlooked in the stability analysis. As the stability of motion of humanoid robots is inseparably linked with control, it was also necessary to pay due attention to this notion. Finally, the paper ends with a discussion of posture and postural stability with all their specificities. The authors hope that this paper will contribute to a clearer understanding of the basic notions of humanoid robotics, especially concerning robots with high dynamic and control performances.

ON SOME ASPECTS OF HUMANOID ROBOTS GAIT SYNTHESIS AND CONTROL AT SMALL DISTURBANCES

This work considers some aspects of the problem of generating and preserving of two-legged gait bearing in mind the requirements for a higher degree of similarity with human gait (anthropomorphism) and robustness to the constantly present small disturbances during the walk. Reference motion was synthesized by semi-inverse method, varying the mode of ZMP traveling along a path selected in advance on the foot–ground surface. It was found that different ways of ZMP motion along the path has a decisive role in the trunk deflection in the sagittal plane. Also, the problem of classification of disturbances and their compensation during the gait is discussed in detail. The significance of the multi-link trunk in the gait synthesis and its role in the compensation of disturbances is also considered.

Multi-arm robot control system for manipulation of flexible materials in sewing operation

A new automated sewing system is described, consisting of two robots handling the fabric on the table in a similar manner as does a human operator during sewing. To enable user-friendly operation of the system operation, particularly in the phase of preparing new tasks, the original Multi-arm Robot Control (MRC) system has been developed. It incorporates a task-oriented robot language and graphical user interface to enable easy programming of complex motion such as hands coordination during task execution, fabric tension control, and synchronization with the sewing machine speed. To avoid possible collisions, simulation of the already programmed task can be easily performed. The control of hand coordination and the fabric tension has also been developed and implemented. To control seam path and its deviation from the desired trajectory, visual feedback was adopted. Complete system functioning was verified experimentally by sewing.

Dynamic analysis of balanced robot mechanisms

Abstract A comparison of dynamic behaviour of the unbalanced and balanced robot mechanisms is carried out. Two various ways of balancing are considered: balancing by masses (by adding counterweights and by link mass redistribution) and balancing by springs. Dynamic behaviour of the robot is studied on the basis of its motion simulation. A simple open kinematic chain structure (“PUMA” configuration), is used as a basic mechanism. Some comparisons are made with a mechanism of closed loop structure (“ASEA” mechanism).

NOTE ON THE ARTICLE "ZERO-MOMENT POINT — THIRTY FIVE YEARS OF ITS LIFE"

In Vol. 1, No. 1 of Int. J. Humanoid Rubotics, we gave a review of the Zero-Moment Point (ZMP) concept, on the occasion of thirty five years of its use in modeling dynamics of the biped gait. At the time of writing this article, we thought that thirty five years was a long enough period in which all confusions, if they existed, could be cleared up. However, we were not quite right, and we will indicate here some of the most important points concerning the concept. A survey of the literature that appeared in the last several years related to the widely accepted ZMP method reveals a diversity of terms used to describe the state in which the biped system performs “regular” gait, safe from overturning. The terms in use are: stability (stable gait), dynamic balance, and dynamic equilibrium. Stability is a customary term in the theory of automatic control, and in this domain it has its well-defined meaning and usage, so that it is not appropriate to use it in some other instances, straying from its basic meaning. The term dynamic equilibrium is also unsuitable because it is used in the D’Alambert principle to transform dynamic equations into a static form, with a zero on the right-hand side — hence the term equilibrium. Therefore, dynamic balance remains the most appropriate term, as it fully reflects the nature of the related notion, and is not in use in other areas. We ourselves did not make clear this terminological distinction in the aforementioned article, which would have been prudent. Another issue we want to address is the situation illustrated in Fig. 4 in the paper — to make it easier to follow the explanation we repeat it here — concerning the notions of ZMP and fictitious ZMP (FZMP). As is well known, the crucial characteristic of a dynamically balanced gait is that the point at which the conditions ΣMx = 0, ΣMy = 0 are fulfilled is within the support polygon (Fig. 4), whereby

An Approach to Biped Control Synthesis

A novel approach to control synthesis of biped locomotion mechanisms is suggested. The synthesis is carried out in two stages: the stage of nominal regimes (the synthesized control has to ensure the realization of gait in the absence of any disturbance), and the stage of perturbed regimes (the control has to eliminate deviations from the nominals under an additional condition of preserving the stability of the overall System). At the level of perturbed regimes, the proposed control synthesis should ensure the compensating movements such to bring the System ot its nominal during the gait. However, the compensating movements can, as a side–effect, induce the undesirable inertial forces which can influence the mechanism overall stability. To avoid this, it is suggested such a control which ensures that the acceleration of compensating movements does not exceed a value given in advance. In addition, the case is considered when an additional correction of the zero moment point ZMP position is accomplished by different mechanism joints.

Dynamic balance concept and the maintenance of the dynamic balance in humanoid robotics

One of basic characteristics of regular bipedal walk of humanoid robots is the maintenance of their dynamic balance during the walk, whereby a decisive role is played by the unpowered degrees of freedom arising at the foot-ground contact. Hence, the role of Zero-Moment Point (ZMP) as an indicator of dynamic balance is indispensable. The paper gives a very detailed discussion of some basic theoretical assumptions related to the notion of dynamic balance (term stability, is often used as a synonym, which we consider erroneous). Some special cases of gait in which dynamic balance need not be realized are also discussed.