A system includes at least one common support configured to span at least a width of a web of material in a manufacturing or processing system. The system also includes multiple sensor heads each configured to move independently along at least part of the at least one common support. The sensor heads can be configured to move simultaneously along the at least one common support, and at least one controller can be configured to control movement of the sensor heads so that the sensor heads do not contact one another. Each sensor head could include one or more sensors configured to measure one or more characteristics of the web. Different sensor heads could include different types of sensors. The sensor heads can be configured to move in non-overlapping patterns over or under the web. Different sensor heads can be configured to move at different speeds.