This paper presents a compliant control method for insertion of complex objects with concavities. Most work on robot assembly using compliant motion control focuses on overcoming jamming conditions for simple peg-in-hole problems, and cannot be used for complex shapes frequently encountered in assembly applications. When an object is being inserted into a hole or slot with a small clearance, a contact path issued to compensate for uncertainties. When the object shape is complex, however, the contact state changes several times and severely, making compliant control difficult. Our algorithm is capable of controlling compliant motion in spite of changing contact states. During the execution of a nominal motion plan, it computes the actual position of the contact point from the force/torque sensor reading using a contact localization algorithm. It then dynamically updates the center of compliance to the computed contact point, and minimizes the chance of jamming and unwanted collisions. The control scheme has been implemented on hardware and tested on the task of inserting a T-shape into a C-shape involving a very tight tolerance. The insertion motion was accomplished by a sequence of 2 translational and 1 rotational compliant motions, and successfully executed by the proposed compliant motion controller.