Theoretical Investigations of the Control Movement of the CLAWAR at Statically Unstable Regimes

Abstract

Dynamic control of constrained spatial mechanical systems, such as manipulators, CLAWAR, multifingered robotic hands and etc have been classic problem in robotics research. The theory of control based on fundamental idea of dynamic inverse. One of the best control schemes is hybrid position/force (Mayorga R. V., Wong A. K, . .). Ones works has been exploited the hybrid control to manipulators with open constraints. The theory of the control of robotics with closured constraints (Vukobratovic M., Kircanski M.) assumed that the rectangular matrix of the coefficients of constraints is the matrix of full rank, and not include redundant constraints. The problem of the redundant constraint raised in walking machines and systems with redundantly drive parallel mechanisms too (Jongwon K., Frank C. P. ). The mentions methods are references at two classes of mechanical systems. First it is spatial system with unmovable body and seconds is a spatial system without unmovable body. The dynamics of the systems first class is described by equations, expressed at explicit form at relative or absolute coordinates. That form of equation is permitted simple using classical method of stability analysis. The method of this type well compliance to control and stability analysis of the manipulators with end effectors constrained, parallel manipulators and multifingered robotic hands with closured constrained. Walking machines (CLAWAR) have not unmovable body. So the dynamics equations can not be expressed in generalized coordinates. At any case to equations in this form it is difficult to apply the classical methods of stability analysis. To avoid it constrain researcher used linearization equations of motion (Jong H. P.). Linearization equations made possible to provide stable analysis only at small domain of the point of linearization. To create robust CLAWAR it is necessary to accomplish stability analysis of nonlinear equation of motion at large neighborhood of current position. At present work describes the mathematical formulation of control dynamic of a class of spatial mechanical system. The proposed mathematical formulation is realized at computer software of simulation dynamic linked multibody systems. For CLAWAR applications are investigated strong instability locomotion regimes at four foots and two fingers simulation model.