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This paper presents a robotic system for steering under real-time fluoroscopic guidance a flexible needle in soft tissue. Given a target and possible obstacle locations, the computer calculates the flexible needle-tip trajectory that avoids the obstacle and hits the target. Using an inverse kinematics algorithm, the needle base maneuvers required for a tip to follow this trajectory are calculated, enabling a robot to perform controlled needle insertion. Assuming small displacements, the flexible needle is modeled as a linear beam supported by virtual springs, where the stiffness coefficients of the springs can vary along the needle. Using this simplified model, the forward and inverse kinematics of the needle are solved analytically, enabling both path planning and path correction in real time. The needle shape is detected in real time from fluoroscopic images, and the controller commands the needle base motion that minimizes the needle tip error. This approach was verified experimentally using a robot to maneuver the base of a flexible needle inserted into a muscle tissue. Along the 40-mm trajectory that avoids the obstacle and hits the target, the error stayed below the 0.5-mm level. This study demonstrates the ability to perform closed-loop control and steering of a flexible needle by maneuvering the needle base so that its tip achieves a planned trajectory.