COMPUTER SYNTHESIS AND OPTIMIZATION OF JUMPING MOTIONS VIA NONSTATIONARY CONSTRAINTS

Introduction: This report considers the results of the authors’ research on the goal-oriented computer synthesis of human motions in support and non-support phases. The main attention is paid to the synthesis of the pushing phases. In particular, an analysis is made of the results of a sequential optimization of running long jumps and acrobatic jumps. The computer modeling of complex coordination motions is based on the development of an adequate anthropomorphic model. Methods and Results: Most effective in the developed modeling system proved to be the employment of differentiated non-stationary holonomic and nonholonomic constraints equations in order to model goal-oriented motions [1]. For descriptions of additional non-stationary items in constraints equations we used parametrically controlled smooth approximation functions which allowed us to synthesize the desired motion trajectories, ground reaction force and kinetic moment increment. Due to the non-stationary nature of constraints equations, any experimental data on kinematics and/or the dynamics of real motion can fulfill their function. For the analysis of modeling results we consider estimates of interelement control motions distribution in the support phase of jumping motion. A number of anthropomorphic model (AM) elements can change with respect to the level of AM adequacy to real human motion. For example, we used a 15-element AM for modeling the support and flying phases of the running long jump. Analysis of synthesized inter-element control moments values showed that the most significant influence on the value of the ground reaction and, therefore, on the pushingoff velocity was the motion of the swinging nonsupport leg. Variation of the parameters values of ground reaction and the resulting value of the kinetic moment allowed us to synthesize the AM motion in the support phase so that it would ensure the desired trajectory of the AM motion in the flying phase of acrobatic motions. Conclusions: Research showed the necessity of employment of non-stationary constraint equations in the synthesis of complex coordination human motions. Such an approach to motion control synthesis minimizes the number of parameters to be varied and gives a relatively stable solution with respect to small variations of AM structure. REFERENCES: 1. Zinkovsky, A.V., Sholuha, V.A., Ivanov, A.A. (1997). Mathematical Modeling and Computer Simulation of Biomechanical Systems, WSP, Singapore, 216

PRINCIPLES OF ADEQUACY CRITERIA FORMULATION IN HUMAN MOTION ANALYSIS

Introduction. Number of parameters of an anthropomorphic model (AM), which simulates real human motion, can achieve the value of one hundred and even more than that. This makes obvious the necessity of adequacy criteria formulation. Optimal value of such criteria should indicate structural and parametric adjustment of AM to certain real human motion. Modelling of human motion with employment of mechanical-mathematical apparatus of system of body motion equations implies a significant number of problem parameters [1] required for description of the structure, and components and kinematics of motion as well. Choice of these parameters values seriously depends on what experimental data is available. METHODS AND RESULTS: The base of computer model consists in a system of differential-algebraic equations of motion of a ramified kinematics chain with nonstationary constraints. In particular, as constraint equations there can serve generalized coordinates behaviour functions, obtained through video-registration data processing. Such approach allows to determine main dynamic values, including generalized forces. However, measurement errors lead to significant errors in assessed values of inter-element forces and moments and especially values of external with respect to AM ground reaction and total moment of external forces in support phase of motion. Variation of AM elements parameters, positions of joints, parameters of trajectories smoothing allows to obtain an averaged assessment of external forces values. In the report there is suggested a new approach to structural an parametrical adjustment of AM. Presence of non-stationary constraint equations allows to use some of experimental data for such constraints. For example, ground reaction force and/or external moment can be available or equal to zero during the flight phase. One of investigation result is that there have been analyzed grand circles on the horizontal bar with a following jump off the bar and four backward somersaults performed in a grouped position. The number of AM elements is widely varied. There has been investigated influence of possible errors in determination of visco-elastic properties of the bar on the analysis results for different processing procedures. CONCLUSION: The suggested approach to iterational parametric adjustment of AM on the basis of employing of constraint equations allows for complete matching of model motion characteristics with most important experimental data. Less important data are estimated in average, which corresponds to traditional structural- parametric adjustment of AM. REFERENCES: 1. Zinkovsky A.V., Sholuha V.A., Ivanov A.A. Mathematical Modelling and Computer Simulation of Biomechanical Systems, WSP, Singapore, 1997. 216p

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