A Propagative Model of Simultaneous Impact: Existence, Uniqueness, and Design Consequences

TL;DR

This paper introduces a propagative impact model ensuring energy and momentum conservation, with algorithms and simulations demonstrating its application to billiards and legged robots, including impact optimization.

Contribution

It provides new existence and uniqueness results for impact modeling, along with a novel energy-conserving time-stepping algorithm applicable to elastic, plastic, and inelastic impacts.

Findings

Model guarantees energy and momentum conservation.

Algorithm successfully simulates impacts in various scenarios.

Optimized robot impact behavior through model application.

Abstract

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.