The high degree of nonlinearity and high dimension of the problem, along with all the constraints, make it unreasonable to assume that by specifying the state equations, boundary conditions, and inequality constraints together with a naive initial guess of the solution, the optimization procedure will immediately find an optimal solution. Various simpler problems were first solved such as that of standing in place and then moving only small distances. In fact, an iterated process was undertaken which gradually approximated the actual problem, whereby the solution of each generalization of the problem was made using the previous one as an initialization. As the number of grid points has a large influence on the length of each optimization run, it is preferable to use a coarse grid, then to refine the grid if more exact solutions are needed.
Run times depend on the starting values given to the problem and the problem to be solved.
Run Time 18 min. These runs were conducted on a Sparc Ultra 2 with a 166 MHz processor. For example, a subproblem would be solved without enforcing positivity of the contact constraints, then the complete problem could be solved by initializing it on the solution of the subproblem.