The goal of this paper is to solve the problem of dynamic obstacle avoidance for a mobile platform using the stochastic optimal control framework to compute paths that are optimal in terms of safety and energy efficiency under constraints. We propose a three-dimensional extension of the Bayesian Occupancy Filter (BOF) (Coué et al. Int. J. Rob. Res. 2006, 25, 19-30) to deal with the noise in the sensor data, improving the perception stage. We reduce the computational cost of the perception stage by estimating the velocity of each obstacle using optical flow tracking and blob filtering. While several obstacle avoidance systems have been presented in the literature addressing safety and optimality of the robot motion separately, we have applied the approximate inference framework to this problem to combine multiple goals, constraints and priors in a structured way. It is important to remark that the problem involves obstacles that can be moving, therefore classical techniques based on reactive control are not optimal from the point of view of energy consumption. Some experimental results, including comparisons against classical algorithms that highlight the advantages, are presented.