TimetoCollision

TimetoCollision, often written as Time-to-Collision (TTC), is a metric used in robotics, computer vision, and automated systems to estimate the time remaining before two moving objects would collide if their current velocities continue unchanged.

Calculation typically relies on relative position and velocity. Let r be the relative position vector from one object to the other, and v the relative velocity of the second object with respect to the first. If v · v is not zero, TTC is defined as TTC = - (r · v) / (v · v). When TTC is positive, a collision would occur in approximately TTC seconds under constant velocity and linear motion. In a simplified two-dimensional case with distance D and a direct approach at relative speed s, TTC ≈ D / s; if s ≤ 0, there is no collision.

Interpretation of TTC hinges on its assumptions. It reflects instantaneous motion and assumes velocity and direction do not change, and it does not account for braking, steering, or evasive maneuvers. As such, TTC is commonly used for collision avoidance, alerting systems, and risk assessment, often together with other metrics like minimum separation or time-to-react.

Applications and limitations include widespread use in autonomous driving, aviation collision avoidance, robotics, and surveillance. Limitations arise from reliance on accurate state estimation and motion models, potential nonlinearity in real trajectories, and the possibility of misinterpreting trajectories that are not co-linear or involve maneuvering objects. See also Time to closest approach and Time-to-Contact.