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. A 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. The 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.