Several methods and subsystems are provided for aligning a workpiece as it is being loaded into a die space of a bending apparatus, and for performing sensor-based control of a robot as it moves a workpiece from one location to another within a bending apparatus environment. A backgaging mechanism is provided with finger gaging mechanisms having force sensors for sensing forces in directions perpendicular to and parallel to a die. In addition, a robot gripper sensor is provided for sensing either or both of shear forces and normal forces created by movement of a workpiece being held by the gripper. Several sensor-based control modules are disclosed, including a bend-following control module, a speed control module, a module for actively damping vibrations in a workpiece, a module for controlling active compliance/contact between a workpiece and an obstacle, a module for performing a guarded move to intentionally bring a workpiece into contact with an obstacle, and a module for detecting unintentional impacts between a workpiece and an obstacle. Several droop sensing methods and systems are also provided, including methods for performing droop sensing and compensation with the use of a vision-based droop sensor, a compound break-beam droop sensor, and a single break-beam droop sensor. In addition, an angle sensor is provided, along with a springback control method utilizing the disclosed angle sensor.