1982 Volume 18 Issue 4 Pages 371-376
In this paper dynamic systems with certain holonomic constraints are precisely modeled by introducing the penalty function and identifying it with potential energy. In this method the constraints are given as a manifold in a configuration space and actual motion is given as a smooth curve on the manifold.
Application to 7-freedoms biped model shows that this method is sufficiently applicable to multi-freedom dynamic systems imposed certain nonlinear constraints. Still more, it is shown that numerical solutions obtained by the application of this method contain high frequency components. Therefore stability considerations of the numerical solutions and its error analysis become very important. But if step size of integration in Runge-Kutta method is suitably selected for some N (i.e. weight of penalty), errors of solutions can be reduced to small. And by precise analysis of linearized system it is shown that the high frequency parts of the solutions correspond to constrained variables whose amplitudes decrease in proportion to order (N-1/2) or more rapidly, as N→∞.
