An adaptive mesh refinement method for numerically solving optimal control problems is described. The method employs collocation at the Legendre-Gauss- Radau points. Within each mesh interval, a relative error estimate is derived based on the difference between the Lagrange polynomial approximation of the state and an adaptive forward-backward explicit integration of the state dynamics. Accuracy in the method is achieved by adjusting the number of mesh intervals and degree of the approximating polynomial in each mesh interval. The method is demonstrated on time-optimal transfers from an $\mathbf{L}_{1}$ halo orbit to an $\mathbf{L}_{2}$ halo orbit in the Earth-Moon system, and performance is compared against previously developed mesh refinement methods.