Abstract: In the event of rocket failures, navigation errors, model parameter deviations and fault identification biases jointly constitute significant sources of uncertainty in rocket guidance. Conventional trajectory planning methods largely rely on the tracking control loop to compensate for such uncertainties, which substantially increases the design complexity and burden of the control system, making it difficult to achieve a proper balance between robust guidance and optimal guidance performance. To further ensure orbital insertion safety and improve mission success probability under failure conditions, this paper investigates a stochastic trajectory optimization method for rocket trajectory reconstruction. The effects of random disturbances on system states are characterized through the evolution of system covariance, based on which orbital safety constraints under uncertainty are formulated using terminal state covariance. Two stochastic trajectory reconstruction problems are established to enhance robustness against random disturbances: one employing a combined feedforward–feedback closed-loop control law, and the other based on a purely feedforward control strategy. To enhance the solution performance of fault-triggered re-planning, appropriate convexification techniques are introduced to handle nonlinear terms, and a sequential convexification approach is proposed to solve the resulting optimization problems. Simulation results demonstrate that the proposed method guarantees orbital safety altitude under uncertain disturbances. Moreover, the feedforward–feedback control strategy effectively suppresses the impact of random disturbances on system states, whereas deterministic methods may lead to rocket crash in the presence of large deviations.

Key words: rocket failure, trajectory reconstruction, stochastic disturbances, trajectory planning, covariance dynamics, convex optimization