Y. Li, H. Yu, and D.J. Braun, Algorithmic Resolution of Multiple Impacts in Non-smooth Mechanical Systems with Switching Constraints, IEEE International Conference on Robotics and Automation, Montreal, CA, pp. 7639-7645, May 2019.

This paper presents a differential–algebraic formulation for modeling non-smooth robot dynamics involving switching constraints and multiple impacts. The method integrates a unified governing equation, switching kinematic constraints, and the plastic impact law. Its key contribution is a new algorithmic approach that explicitly resolves multiple simultaneous impacts, replacing traditional iterative complementarity-based methods. The approach is validated through simulations of biped locomotion.

Why it matters: Robots frequently interact with their environment through impacts, which are difficult to model and simulate efficiently. This work provides a simple and explicit framework for resolving multiple impacts, improving the accuracy and computational efficiency of simulations in locomotion and contact-rich robotics.