Trajectory Optimization for Real-Time Guidance: Part 1, Time-Varying LQR on a Parallel Processor

A key algorithmic element of a real-time trajectory optimization hardware/software implementation is presented, the QP solver element. The purpose of the effort is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aero-maneuvering orbiter. Many methods of nonlinear programming require the solution of a quadratic program (QP) at each iteration. In the trajectory optimization case the QP has a special Dynamic Programming structure, a LQR-like structure. QP algorithm speed is increased by taking advantage of this special structure and by parallel implementation.