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We present a new method for local obstacle avoidance by indoor mobile robots that formulates the problem as one of constrained optimization in velocity space. Constraints that stem from physical limitations (velocities and accelerations) and the environment (the configuration of obstacles) are placed on the translational and rotational velocities of the robot. The robot chooses velocity commands that satisfy all the constraints and maximize an objective function that trades off speed, safety and goal-directedness. An efficient, real-time implementation of the method has been extensively tested, demonstrating reliable, smooth and speedy navigation in office environments. The obstacle avoidance method is used as the basis of more sophisticated navigation behaviors, ranging from simple wandering to map-based navigation.