Trajectory Optimization Using Collocation And Evolutionary Programming For Constrained Nonlinear Dynamical Systems

Abstract

Trajectory design and optimization has a broad variety of applications in fields such as aerospace and electrical engineering. The solution of a trajectory that minimizes a cost function subject to nonlinear differential equations of motion and various types of constraints may be obtained by the methods of optimal control theory. 
\nA framework is presented for numerical solution of the optimal control problem. The solution is converted to that of a constrained discrete parameter optimization problem. Direct collocation and nonlinear programming are used to perform a local gradient-based search for the optimal solution. A genetic algorithm combined with a shooting method conducts a global search of the solution space to provide a near-optimal, near-feasible initialization for the nonlinear program.
\nThe framework is applied to three minimum-time case studies: i) a path planning problem for two mobile robots with obstacle avoidance; ii) an aircraft turning maneuver; iii) a low-thrust interplanetary transfer.