Abstract: A physics-based control system that tracks a single motion trajectory produces high-quality animations, but does not recover from large disturbances that require deviating from this tracked trajectory. In order to enhance the responsiveness of physically simulated characters, we introduce algorithms that construct composite controllers that track multiple trajectories in parallel instead of sequentially switching from one control to the other. The composite controllers can blend or transition between different path controllers at arbitrary times according to the current system state. As a result, a composite control system generates both high-quality animations and natural responses to certain disturbances. We demonstrate its potential for improving robustness in performing several locomotion tasks. Then we consolidate these controllers into graphs that allow us to direct the character in real time.