We present an algorithm for safe robot navigation in complex dynamic environments using a variant of model predictive equilibrium point control. We use an optimization formulation to navigate robots gracefully in dynamic environments by optimizing over a trajectory cost function at each timestep. We present a novel trajectory cost formulation that significantly reduces conservative and deadlocking behaviors and generates smooth trajectories. In particular, we propose a new collision probability function that effectively captures the risk associated with a given configuration and the time to avoid collisions based on the velocity direction. Moreover, we propose a terminal state cost based on the expected time-to-goal and time-to-collision values that helps in avoiding trajectories that could result in deadlock. We evaluate our cost formulation in multiple simulated scenarios, including narrow corridors with dynamic obstacles, and observe significantly improved navigation behavior and reduced deadlocks as compared to prior methods.