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Bimanual robotic assembly is modeled at the task-level using contact states of workpieces and their transitions. Task-compatibility-based motion planning is developed to derive the lower-level velocity commands from the task-level symbolic transitions of the bimanual assembly model. The cost-function based on the manipulability and compatibility is designed to determine the assembly motions of the two manipulators. The assembly motions are executed along the direction of maximizing the sum of the performance indices to improve the control performance of the two manipulators. The problem is formulated as a constrained optimization considering the assembly constraints, position of the workpieces, and the kinematics and redundancy of the bimanual robot. The proposed approach is evaluated with 2D simulation of a peg-in-hole assembly with an L-shaped peg and two 3-dof manipulators.