We propose a method for real-time motion planning with applications in aerial videography. Taking framing objectives, such as position of targets in the image plane as input, our method solves for robot trajectories and gimbal controls automatically and adapts plans in real-time due to changes in the environment. We contribute a real-time receding horizon planner that autonomously records scenes with moving targets, while optimizing for visibility to targets and ensuring collision-free trajectories. A modular cost function, based on the re-projection error of targets is proposed that allows for flexibility and artistic freedom and is well behaved under numerical optimization. We formulate the minimization problem under constraints as a finite horizon optimal control problem that fulfills aesthetic objectives, adheres to non-linear model constraints of the filming robot and collision constraints with static and dynamic obstacles and can be solved in real-time. We demonstrate the robustness and efficiency of the method with a number of challenging shots filmed in dynamic environments including those with moving obstacles and shots with multiple targets to be filmed simultaneously.