Nominal trajectory optimization methods are widely employed in aerospace engineering. However, deterministic nominal trajectory optimization lacks robustness against uncertainties (e.g., initial state and parameter uncertainties) inherent in actual physical environments. To address this issue, this paper proposes a robust trajectory optimization framework integrating weighted stochastic response surface method (WSRSM) with pseudo-spectral sequential convex programming. A robust optimization (RO) model under uncertain conditions is established, and an uncertainty quantification (UQ) propagation algorithm is designed based on WSRSM and non-intrusive polynomial chaos (NIPC), thereby transforming the problem into a deterministic trajectory optimization formulation in an extended-dimensional state space. Convex optimization techniques are applied to convexify the problem, and the pseudo-spectral method is utilized for discretization to enable rapid solution of this high-dimensional deterministic problem. Two numerical examples involving Dubins vehicle obstacle avoidance are simulated. Results demonstrate that the proposed uncertainty propagation method achieves accuracy comparable to that of the Monte Carlo Simulation (MCS) while significantly improving computational efficiency. Compared with traditional deterministic optimization (DO) algorithms, the proposed RO method effectively reduces the probability of trajectory constraint violations, enhancing trajectory reliability and robustness.