Construction of mathematical model for the controlled dynamics of connected bodies system in robotics

Abstract

Differential-algebraic equations for describing the motion of connected bodies sys-tem are considered. The dynamic model includes geometric and nonholonomic connections. The connections equations contain second-order derivatives of the system coordinates. The in-fluence of connections by the system is taken into account using Lagrange multipliers. Pro-posed equations of controlled motion can be used in the development of algorithms for model-ing the motion of mechanical systems, in particular, in the construction of control systems for cyclic motions in robotics. To construction, solve a mathematical model using software pack-ages, it is necessary to obtain the equations of motion for all components of connected bodies system. The presence of many numbers of walking robots mobility degrees makes the task of their creation and control more difficult. The synthesis of control systems for such devices is reduced to stabilizing the motion of the robot body. Algorithm for setting the trajectory de-pends on the relative motion of a point on the body from the point of the foot. The body makes uniform rectilinear motion while the foot makes periodic motions.