Primate neurophysiology has provided numerous insights into the neural mechanisms of short and stereotypical movements, such as center-out reaching, which are mainly guided by feedforward control. However, to understand highly interactive and feedback-driven behaviors, experimental paradigms are needed that involve continuous interactions with the world. One example of such paradigms is stick-balancing which requires constant integration of feedback for successful control. Recently, a simplified virtual implementation of the stick-balancing task was developed as the Critical Stability Task (CST), where monkeys and humans learned to balance an unstable system in a virtual environment. However, the control strategies to accomplish the task, as well as its neural underpinnings, remains to be examined. In theory, the task could be performed based on various control policies by prioritizing either the control of position or velocity of the system. This distinction, however, is particularly challenging to identify in the data as the unstable nature of the task leads to unique behavior at each attempt, with potentially different control policies at different trials. These variations render trial-averaging methods unsuitable as they fail to capture trial-specific control strategies. Here, we propose a generative-model approach at the level of behavior that successfully accounts for the behavioral features of monkeys and humans who performed the task under matching conditions. The model makes further predictions about the effect of different control strategies on how the task could be accomplished. These predictions were used to identify, at the single-trial level, the control priorities most likely used by monkeys and humans in each trial. These results provide a critical step towards understanding the neural activity associated with highly interactive sensorimotor behavior, and how such activity might represent different control priorities in the motor system.