Collision detection is critical for safe robot operation in the presence of humans. Acoustic information originating from collisions between robots and objects provides opportunities for fast collision detection and localization; however, audio information from microphones on robot manipulators needs to be robustly differentiated from motors and external noise sources. In this paper, we present Panotti, the first system to efficiently detect and localize on-robot collisions using low-cost microphones. We present a novel algorithm that can localize the source of a collision with centimeter level accuracy and is also able to reject false detections using a robust spectral filtering scheme. Our method is scalable, easy to deploy, and enables safe and efficient control for robot manipulator applications. We implement and demonstrate a prototype that consists of 8 miniature microphones on a 7 degree of freedom (DOF) manipulator to validate our design. Extensive experiments show that Panotti realizes near perfect on-robot true positive collision detection rate with almost zero false detections even in high noise environments. In terms of accuracy, it achieves an average localization error of less than 3.8 cm under various experimental settings.