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This paper presents a new control framework for virtual humans (VHs) in a physics-based virtual environment. This framework combines multiobjective control with motion capture techniques. Each motion-tracking task is associated with a task wrench. Bounds are imposed on lower priority task wrenches to ensure the controller performance of higher priority tasks. An optimization problem is solved to compute optimal task wrenches that are based on wrench bounds. Finally, joint torques are computed using the optimal task wrenches. The novelty of our wrench-bound method is that it can handle inequality constraints on a higher priority task and maintain passivity as well. This control framework allows an operator to interact with the VH in real time, without the necessity of compromising the VH's balance. It also allows the VH to generate appropriate motions to handle interactions with the virtual environment, rather than to simply emulate captured motions. The effectiveness of our approach is demonstrated by a VH performing reaching and manipulation tasks.