Miomir Vukobratovic

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.

On the stability of anthropomorphic systems

Abstract 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.

Contribution to the Synthesis of Biped Gait

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.

A dynamic approach to nominal trajectory synthesis for redundant manipulators

The solution to the inverse manipulation problem for redundant manipulators has mostly been considered from a geometric-kinematic standpoint. A procedure for the inverse problem solution using the dynamic model of the manipulator and its actuators is developed. Nominal trajectories in the space of joint coordinates are generated so as to be optimal with respect to total energy consumption of the actuators (hydraulic or electric). The treatment of constraints on joint coordinates and rates is also involved in the procedure. The algorithm is illustrated by two industrial robots.

Survey of Intelligent Control Techniques for Humanoid Robots

This paper focusses on the application of intelligent control techniques (neural networks, fuzzy logic and genetic algorithms) and their hybrid forms (neuro-fuzzy networks, neuro-genetic and fuzzy-genetic algorithms) in the area of humanoid robotic systems. It represents an attempt to cover the basic principles and concepts of intelligent control in humanoid robotics, with an outline of a number of recent algorithms used in advanced control of humanoid robots. Overall, this survey covers a broad selection of examples that will serve to demonstrate the advantages and disadvantages of the application of intelligent control techniques.

How to Control Artificial Anthropomorphic Systems

This paper describes, in a polemical way, the possible ways for synthesis of artificial gait, taking into account its application in the rehabilitation of severely disabled paraplegics. The essential relation between the hierarchical control concept of artificial legged locomotion systems and human beings has been treated. The method of prescribed synergy has been described in detail. This method, in the authors opinion, renders wide possibilities in solving delicate problems in the synthesis and control of artificial anthropomorphic gait. The possibility of applying the gait-logic description in the synthesis of finite automata and the possibility of driving system hybridization in the rehabilitation of persons with muscular insufficiency have also been considered.

Contribution to control of redundant robotic manipulators in an environment withobstacles

The redundancy of robot manipulators plays an important role in increasing their flexibility and versatility, especially in an environment with obstacles. In this paper, the redundancy is utilized for enabling collision-free motion for a given tra jectory of a manipulator hand. The calculation of the corre sponding trajectory in the space of joint coordinates is per formed using several performance criteria that take into account the vicinity of the obstacles. The advantages and shortcomings of the proposed algorithms are discussed. The implementation of the algorithms is real-time due to modest computational complexity.

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.

New approach to control of robotic manipulators interacting with dynamic environment

The fundamentals of an approach to solving the control task of robots interaction with a dynamic environment based on the stability of a closed-loop control system are given in this paper. The task is set and solved in its general form. The traditional control concept of compliant robot motion-the hybrid position/force control is discussed. In the paper the proposed control laws ensure simultaneous stabilization of both the desired robot motion and the desired interaction force, as well as their required quality of transient responses. In order to emphasize the fundamental point of this approach in controlling the contact tasks in robotics, the authors have assumed ideal parameters of interacting dynamic systems. The proposed control procedure is demonstrated by one simple example.

A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form

This paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form. The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.