A robotic system includes an end-effector, an input device, and a controller. The input device is operable for collecting data defining a position and a velocity of a dynamic obstacle in an environment of the end-effector. The dynamic obstacle has an arbitrary shape. The controller is in communication with the end-effector and is programmed to execute a method and thereby receive a set of inputs via the input device, including the position and velocity of the dynamic obstacle. The controller computes a contour function defining the closest allowed distance and direction between the end-effector and the dynamic obstacle using the Gilbert-Johnson-Keerthi algorithm, and controls the end-effector via an output command to thereby avoid contact between the end-effector and the dynamic obstacle.