Force Control Compensation Method with Variable Load Stiffness and Damping of the Hydraulic Drive Unit Force Control System

Each joint of hydraulic drive quadruped robot is driven by the hydraulic drive unit（HDU）, and the contacting between the robot foot end and the ground is complex and variable, which increases the difficulty of force control inevitably. In the recent years, although many scholars researched some control methods such as disturbance rejection control, parameter self-adaptive control, impedance control and so on, to improve the force control performance of HDU, the robustness of the force control still needs improving. Therefore, how to simulate the complex and variable load characteristics of the environment structure and how to ensure HDU having excellent force control performance with the complex and variable load characteristics are key issues to be solved in this paper. The force control system mathematic model of HDU is established by the mechanism modeling method, and the theoretical models of a novel force control compensation method and a load characteristics simulation method under different environment structures are derived, considering the dynamic characteristics of the load stiffness and the load damping under different environment structures. Then, simulation effects of the variable load stiffness and load damping under the step and sinusoidal load force are analyzed experimentally on the HDU force control performance test platform, which provides the foundation for the force control compensation experiment research. In addition, the optimized PID control parameters are designed to make the HDU have better force control performance with suitable load stiffness and load damping, under which the force control compensation method is introduced, and the robustness of the force control system with several constant load characteristics and the variable load characteristics respectively are comparatively analyzed by experiment. The research results indicate that if the load characteristics are known, the force control compensation method presented in this paper has positive compensation effects on the load characteristics variation, i.e., this method decreases the effects of the load characteristics variation on the force control performance and enhances the force control system robustness with the constant PID parameters, thereby, the online PID parameters tuning control method which is complex needs not be adopted. All the above research provides theoretical and experimental foundation for the force control method of the quadruped robot joints with high robustness.

Force Distribution Model of Motor Units of Leg Extensor Muscles

The paper aims to defme the lawfulness （model）, by which one can reliably estimate the distribution of motor units＇ force from the moment when leg extensor muscles start to generate the force until the moment when the maximal level is achieved. The study included 110 participants. To assess the contractile characteristics of leg extensors, standardized equipment and standardized isometric test in sitting position with the angle of the knee joint of 125° were used. The participants were instructed to exert their maximal force as quickly as possible. Using descriptive statistics, cluster analysis and fitting the exponential model of the distribution of force of leg extensor motor units in the whole range of force generation is defined. The model has the following form： y = 0.2051e3.3855x, where y is the motor units force expressed in daN （decanewtons）, x is the time expressed in s （seconds）. It provides an understanding of the control of multivariate motor unit recruitment and distribution of their force during sports movements as well as training programming for the adoption of forms for conlrolling force distribution of motor units, the development of their maximum force and their involvement speed.

STUDY OF ROLLING FORCE DISTRIBUTION ALONG THE ROLLING OF PAIR CROSS MILL

The theory of three-dimensional deformation is used.Based on rigid plastic assumption, the theory of stick friction and the sheet crown curve at the entry and the exit are used. The mathematical analytical formula of the rolling force in lateral distribution is deriven.

The Gravitational Force Quantum and its Value

Gravitation is one of the basic phenomena of the world. Tremendous number of theoretical works on origin, nature, essentials, consequences, etc. of the gravitation and related phenomena were published so far. The most prominent ones are based on the Albert Einstein＇s general theory of relativity. The author of this communication based his approach to the gravitation on Isaac Newton＇s law of the universal gravitation and related quantities, i.e. gravitational forces of matter objects, distance and motion. Namely on the fact, that the gravitation force is - as well as the inertia, mass, space ＂occupied＂ and other properties are - principal features/attributes/properties of matter objects. Gravitation is an additive property of matter objects. Taking into account other positivistic quantities like mass of the Earth, standard acceleration of gravity, and the value of the atomic unit of mass, the author defined a gravitational force of atomic unit （or ＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of Earth＇s mass on 1 kilogram of a mass on Earth＇s surface, and he calculated its value： GFO = 1.4958 × 10^-54 N. This quantity can be useful for further development of the ＂quantum mechanical＂ approach to the description and general notion about the world.

RESEARCH ON WAVE FORCES ACTING ON THE UNIT LENGTH OF A VERITICAL BREAKWATER BY TESTS AND A NUMERICAL MODEL

Comprehensive 3D model tests and numerical simulation were performed to study the effects of wave obliquity and multidirectionality on the wave forces acting on vertical breakwaters. The variation of wave forces acting on the unit length of a breakwater was analyzed, and the results were compared with Goda＇s formula. A numerical model based on a short-crest wave system was used to model regular wave forces for practical use, which showed good results for those waves with small incident angles.

The Elementary Gravitational Charge and Its Value

In the article ＂The Gravitational Force Quantum and its Value＂ [1 ], the author defined a gravitational force of the atomic unit （＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of the Earth＇s mass on l kilogram of a mass on the Earth＇s surface, and he calculated its value as： GFQEarth = 1.4958 × 10.54 N. In the present contribution, he extended the Gravitational Force Quantum concept to further Objects of the Solar Planetary System and for the Pluto. He calculated values of the GFQo on the analogous basis, i.e. of the mass and the standard acceleration of the gravity of individual objects and of the atomic unit of the mass. He received GFQo values for the Mercury 102.1427 × 1055N, the Venus 16,60012 × 10-55N, the Earth 14.97839 × l0-55 N, the Mars 52.91869 × 10-55N, the Jupiter 0.124391×1055 N, the Saturn 0.17929 ×1055N, the Uranus 0.945178 ×1055N, the Neptune 1.002845 × 10-55N, for the Pluto 458.9124 × 10-55N, and for the Sun 0.001257 × 10-55N, respectively. He multiplied the GFQo values by second power of the radii of the individual objects （O）, receiving values denoted as the ＂Elementary Gravitational Charge＂ （Go）. The Elementary Gravitational Charge represents a gravitational force of one atomic unit of mass in the （radius） distance of 1 meter. They were found of the same value： GMe= Gv = GE= GMa= Gj= Gs = Gp= GSun= 6.079675463 × 10-41N. The values were the same as the calculated one on the basis of the ＂classical＂ Newton＇s formula： FG = И × M × m / R2, for the gravitational force between the atomic unit mass and a mass of 1 kg at a distance of 1 meter, which value was calculated as G = 6.079675463 ×1041 N. The quantity of the Elementary Gravitational Charge can be supposed to be analogous to the Elementary （Electric） Charge （e =1.6021766208（98） × 10-19 C） quantity.