This paper is concerned with the collision avoidance for mobile robots with uncertain dynamics in the presence of obstacles that can considerably change their velocities over time. To address this problem, we propose a robust collision-avoidance method based on the continuous-control-obstacles one. The proposed method uses an arbitrary-order overdamped low-pass filter to generate sufficiently smooth position commands for the robot and a high-order sliding mode differentiator to robustly estimate the obstacles’ maximum accelerations. Based on these estimates, we define a set of possible future positions for the obstacles according to how each one is changing its velocity to calculate a robust position command for the robot. The method has been numerically evaluated using a conventional quadcopter flying among moving obstacles and has been shown to be effective in providing collision avoidance and velocity constraints satisfaction.