Singularity free universal variables method to solve Lambert transfer

The conventional universal variables method has singularity in solving the velocities at transfer time of Lambert transfer orbit when angle between two position vectors is 180°, and may lose some important universal variables by using Newton method. The singularity free formulas for solving velocities were derived by using formula transformation to expurgate singular terms. And the range of universal variables was divided into several sections according to the loop number of transfer orbit, then artificial immune algorithm(AIA) was used to search universal variables solutions in each section, finally all Lambert transfer orbit were derived and the optimal one can be chosen. Simulation results show that, this modified universal variables method can availably avoid the singularity of conventional universal variables method, derive all Lambert transfer orbit and get the transfer orbit whose fuel penalty is optimal.