Spacecraft Attitude Motion Planning Using Gradient-Based Optimization

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

“…A different group of methods is based on trajectory optimization algorithms in which the constrained attitude motion planning problem is formulated as an optimal control problem. The obtained optimization problems are nonconvex, and their solution is determined either by indirect methods [16], or by gradient-based techniques [9], or by global optimizers [4,21,29,30,32], or by employing a convexification method [13]. This second group of methods might have a high computational cost, too.…”

“…However, using those methods makes the attitude representation quite complex. In some works, including this one, attitude is represented on the special orthogonal group SO(3) [2,9,11,15,16,31,33] which is a global, unique, nonsingular, but nonminimal parametrization. However, nonminimality does not represent an issue when open-loop control torques are designed as in the present research.…”

“…In practice, derivative-free techniques do not even need the analytical expression of objective function or constraints; they only need to compute them in a number of points by using simulations. Thus, the method presented in this work represents an improvement of the one in [9] for the following aspects. In [9] a gradient-based optimization was employed to find the weights.…”

“…Thus, the method presented in this work represents an improvement of the one in [9] for the following aspects. In [9] a gradient-based optimization was employed to find the weights. However, since it was not possible to determine expressions for the gradients of the objective and of the constraints, both the objective and the constraints were replaced by approximations for which it was possible to compute the corresponding gradients.…”

“…The basic idea is to temporarily modify the objective function until the local minimum is escaped, or to slightly change it so to have less local minima. In our case, we have both the original objective (maneuvering time) and the approximating differentiable objective proposed in [9] (sum of the squared weights). Hence, we can think of temporarily switching from the first objective to the second one to escape the local minima, still within the framework of the same derivative-free algorithm.…”