A key challenge for SaR robotics is to avoid dynamic obstacles in cluttered environments, with limited and noisy information. In this research, a controller for SaR robots is developed by coupling a local heuristic motion planner with a model predictive control (MPC) based trajectory tracker. Constraint tightening and tube-based control are used to make the MPC robust to model mismatch and additive measurement noise, while the motion planner is integrated with the MPC. The motion planner periodically supplies a reference trajectory to the trajectory tracker, but the MPC can request additional updates in case of a noticeable mismatch between the predicted and measured environment, based on a user-defined threshold. A case study is designed in MATLAB where a single robot needs to reach a goal through a cluttered environment with dynamic obstacles. Results from the case study show that the MPC method outperforms two state-of-the-art control approaches that are based on the rapidly-exploring random tree (RRT) and artificial potential function (APF) methods. In particular, the heuristic and MPC coupled controller showed a higher success rate in reaching the goal without collisions, and displayed a lower path length in cases with both low and high computational budget.