Optimization of Δvega trajectory based on analytical gradients

In deep space exploration missions, total ΔV is a very important performance index. Δ VEGA and optimization are two important technique to reduce the total Δ V in deep space missions. The earth swingby increase the sensitivity of the trajectory greatly, so the optimization of Δ VEGA trajectory is one of the most sophisticated problem currently investigated in the region. In this paper, the whole Δ VEGA trajectory is divided into several trajectory segments. Each trajectory segment connecting consecutive maneuver points is found by solving an N-body analog to Lambert´s problem. We can also obtain state transition matrix of each trajectory segments. The analytical gradients of total Δ V with respect to adjustable variables such as launch time, arrival time, swingby time and the periapsis position relative to the gravitating body are derived based on the transition matrix and calculus of variation. The performance index could be reduced by utilizing quasi-Newton algorithm. At the end of this paper, the Δ VEGA trajectory of Chinese deep space exploration mission to the near earth asteroid Ivar is optimized by this method.