Constrained motion problems with applications by nonlinear programming methods
Several methods for solving constrained motion problems are presented and applied for the solution of some test problems. Constraints are treated by penalty and augmented Lagrangian methods. The equations of motion are discretized by an implicit time-integration scheme, which has energy- preserving properties. Both holonomic and nonholonomic constraints are considered. For the penalty method a time-discretization of the penalty term is used. It is seen that the augmented Lagrangian method is superior to the penalty method in terms of accuracy for all test cases. This does not mean that there are no cases where the penalty method is an acceptable choice. For cases when the motion is smooth, in the sense that the constraint forces are small, the penalty method is seen to perform well. This is especially true for the time-discretized penalty method which seems to increase the stability of the penalty method. Examples of this are the inequality-constrained double pendulum and the problem of two colliding strings. The advantage of the penalty method is its simplicity and speed, although in some cases the need for excessively small time steps for acceptable accuracy of the solution made the penalty method much slower than the augmented Lagrangian method. This is the case for the equality-constrained double pendulum. As an example of a real world problem a constrained motion problem for the shuttle remote manipulator system is successfully solved with the described augmented Lagrangian method combined with the implicit time- integration algorithm.
scientific article; zbMATH DE number 808220