On Transient Release Dynamics in Robot Throwing: A Sliding Pivot Model

Humans regularly throw projectiles with high speed and accuracy; some animals, including chimpanzees and elephants, also throw objects occasionally. In comparison, robots are currently lagging behind, despite having lower communication latency and more accurate motor control. To understand this paradox and ultimately achieve ubiquitous throwing robots, one of the major obstacles is the lack of high-fidelity and tractable physical models of the transient release dynamics, where the momentum exchange between the hand and the object occurs within tens of milliseconds via the frictional interface. In this work, we try to establish a physical model for the release dynamics. We first demonstrate that the conventional model, which combines rigidbody dynamics and patch friction (limit surface, LS), struggles to capture the release dynamics and exhibits pathological behaviors, such as Zeno-like oscillations, leading to poor accuracy in predicting throwing outcomes. To mitigate this, we formulate a viscous-smoothed variant of the limit surface model solved via implicit integration (ILS), which achieves high predictive fidelity but incurs significant computational cost. On the other hand, motivated by the dominant effect of in-hand pivoting in release dynamics, we propose a Sliding Pivot (SP) model that simplifies the contact dynamics by capturing the sticking-pivoting-sliding behavior emerging under vanishing normal force. This model achieves accuracy comparable to ILS, with only 10% higher error while offering over 20× faster computation. Compared to conventional LS models, our method reduces horizontal velocity prediction error by 40% and angular velocity prediction error by 63%, achieving 2.4 cm mean absolute error (MAE) for landing position and 15.4 degrees MAE for landing orientation. These results provide a robust, physically grounded foundation for future scalable robot throwing systems.