This thesis describes a predictive sampling-based algorithm for real-time robot motion planning to reach dynamic goals. The planner utilizes all available information about future obstacle and goal positions over a time window to select a path that approximately minimizes the time to reach this goal. Then, we integrate the proposed method with an online learning algorithm that predicts future goal and obstacle positions. Because future states are predicted by propagation, an incorrect model would result into a greater prediction error for large horizons. Thus, using a pool of candidate models, we utilize a Multiple Model Adaptive Estimation~(MMAE) method with online parameter estimation to learn an appropriate model that keeps this error bounded. Several simulations show the efficacy of the proposed algorithms.