Trajectory Optimization Techniques

Abstract

This chapter discusses the algorithms to solve trajectory optimization problems. It reviews the basic variational concepts and discusses indirect methods for the solution of optimization problems. The chapter also provides an overview on gradient methods, the second variation method, and the generalized Newton–Raphson method. It presents the comparison of the different methods and discusses the application of the latter three methods to a specific example. The mathematical rigor of theorem-proof has been compromised for a more heuristic development so that the over-all presentation is more informative to the practicing engineer. The chapter discusses singular subarcs, the Jacobi condition, corners of transversal surfaces, mixed control and state constraints, state constraints, and relaxed variational problems. It also discusses the advantages and disadvantages of indirect methods, gradient methods, second variation methods, and generalized Newton-Raphson methods.