GALCIT Colloquium

The term trajectory optimization often alienates researchers and analysts that presume they do not work with trajectories so they have little use for such an optimization approach. However, trajectory optimization can be generalized to optimal control, and it is astonishing to think of all of the encounters that are subject to optimization.  There is always a demand to save money, save time, maximize distance traveled, maximize fuel efficiency, minimize the amount of control, or other "cost" of interest.  An introductory list of known applications include robotics, chemical processes, shipping routes, Formula 1 racing, Red Bull helicopter racing, orbital reentry, hypersonic vehicles, and unmanned air vehicle mission planning and cooperative operations.  These challenges translate into multi-point boundary value problems which can be solved using direct or indirect methods.  Recent advances in direct method numerical techniques are facilitating solutions to these challenging problems.

Another important challenge with many of these optimization control problems is adhering to limitations or constraints.  These constraints can be imposed on the states, controls, static control parameters, interior points, or functions of the states throughout the trajectory, e.g. staying on the race course!  The complexity of these problems has crippled typical explicit integration shooting method techniques.  This presentation will show the methods and advantages of using an implicit integration scheme to translate the optimality conditions into a nonlinear programming problem.  Some specific software will be introduced, much of which is freely available or intentionally economical for academia.  This software can be used as a catalyst for advances to the numerical methods, or used directly to solve newly proposed optimization problems.