This paper describes a method for controlling physically-based models submitted to collisions and contacts with their synthetic environment. The aim is not to make an object follow a predefined trajectory, but to use a physical simulation to find a “correct” motion, close to the user-defined path but consistent with the object mass, inertia tensor, with the path complexity and with the casual events such as collisions occurring during motion. To achieve this, objects are provided with actuators (such as motors or muscles) of limited power, and try, at each animation step, to move towards a target position located on the given path. The successive target positions are computed from the object motion. If an object is deflected by a collision, the target position may remain the same during a few time steps, while it changes quickly along the curve when the object goes fast. Applications of this approach to the production of animations sequences where physical models are used but where objects must perform a predefined script are presented.