Performance of parallel shooting method for closed loop guidance of an optimal launch vehicle trajectory

The objective of this paper is to provide a real-time, on-board, closed-loop guidance scheme for a minimum fuel (or, equivalently, minimum time) optimal trajectory of a launch vehicle. This is achieved through parallelization of parallel shooting method in time domain, by breaking the time of flight into number of time zones (divide and conquer). The optimal control vector over each flight time zone are obtained by solving the two point boundary value problem (TPBVP) resulting from the first order necessary condition for optimality of constrained optimization problem, in each time zone, by imposing the continuity condition for optimality between the successive time zones. The solution of the TPBVP is computationally expensive, particularly the simulation of the trajectory and the calculation of the Jacobian. A star connected network is used for implementation of parallel shooting algorithm. The Newton's method is used to generate successively approximate decision variables. The performance of the algorithm with respect to the computation time for star connected network and the solution accuracy is done through the numerical simulation of the launch vehicle problem. A study on parallel computation time, speed-up and utilization is done. The algorithm gave a speed-up of 7 with 16 processors. Realistic data for a PSLV class of launch vehicle are used to simulate the closed-loop guided trajectory using the parallel shooting algorithm. A study on the effectiveness of the various nominal and off-nominal conditions on thrust and the sensor measurements are carried out to validate the closed-loop guidance. We have shown that the closed-loop guidance developed in this paper achieves the desired height and the orbital velocity in presence of disturbances on thrust, and noise in measurements. The computation time details of the closed-loop implementation on RS/6000 machine were carried out and presented.