This paper addresses the unexpected contact handling problem for a free-flying orbital robot.A nonlinear observer is developed to detect, isolate and estimate a collision. Then, a reaction control strategy is proposed, which aims at avoiding the build-up of the contact force and possible instabilities. It is proved that the controlled system is input-to-state stable. The performance of the observer and the controller is assessed through a numerical example featuring a 7 degrees-of-freedom arm mounted on a spacecraft and a realistic measurement model. The spacecraft is equipped with thrusters and variable speed control moment gyros.