A Propagative Model of Simultaneous Impact: Existence, Uniqueness, and Design Consequences
This addresses the challenge of accurately simulating impacts in robotics and physics, though it appears incremental as it builds on existing impact modeling approaches.
The paper tackled the problem of modeling simultaneous impacts in mechanical systems by presenting existence and uniqueness results for a propagative model that conserves energy and momentum, with extensions to plastic and inelastic impacts, and developed a corresponding time-stepping algorithm for simulation.
This paper presents existence and uniqueness results for a propagative model of simultaneous impacts that is guaranteed to conserve energy and momentum in the case of elastic impacts with extensions to perfectly plastic and inelastic impacts. A corresponding time-stepping algorithm that guarantees conservation of continuous energy and discrete momentum is developed, also with extensions to plastic and inelastic impacts. The model is illustrated in simulation using billiard balls and a two-dimensional legged robot as examples; the latter is optimized over geometry and gait parameters to achieve unique simultaneous impacts.