nonlinear programming

The direct transcription method that employs global collocation at Legendre-Gauss-Radau points is addressed and applied to infinite-dimensional dynamic optimization problems in engineering. The formulation of these latter is considered referring to a Bolza-type performance index. A reduced unconstrained form of it is particularly studied in the pseudospectral domain and the continuous-to-discrete conversion is thoroughly discussed. An equivalent finite-dimension nonlinear programming problem is therefore obtained and hints on its numerical implementation are given. Eventually, a few benchmark historical problems in engineering are revisited, stated, numerically solved and compared to literature.

In this paper, problem of trajectory optimization of flexible space robots is considered and an efficient approach is proposed for solving it. The space robots are considered as mechanical manipulators having rigid and flexible links. The main duty of these robots is to translate a payload mass between two specified points. To derive dynamic model of these manipulators, their flexible links are assumed as a set of rigid links connected together. By adding strain potential energy to Lagrange equations, the flexible behavior of flexible links is modeled with good accuracy. In present paper, the problem of trajectory optimization of space manipulators is defined based on minimum joint torque (minimum control effort) objective function. A new approach, that is a developed form of direct collocation method, is used for solving this problem. This new approach is based on simultaneous using of different flatness to decrease dimensional space of the problem and B-spline curves to approximate trajectories. In this approach, state equations and path constraints are applied at specified time nodes and control points of B-spline curves are considered as optimization variables. In this approach, the problem of trajectory optimization is converted to a nonlinear programming problem and exactly solved by nonlinear programming methods. By using this approach, the numbers of optimization variables and constraints are significantly decreased and the possible of online trajectory optimization is provided.