Modeling and Analysis of Non-unique Behaviors in Multiple Frictional Impacts
This work addresses a fundamental challenge in robotics for manipulation and locomotion, providing a novel guarantee for set-valued outcomes in simultaneous frictional impacts.
The paper tackles the problem of multiple possible outcomes in simultaneous frictional impacts in robotics by proposing a differential inclusion model that captures the set of potential post-impact velocities, and proves that solutions to this model must terminate.
Many fundamental challenges in robotics, based in manipulation or locomotion, require making and breaking contact with the environment. To represent the complexity of frictional contact events, impulsive impact models are especially popular, as they often lead to mathematically and computationally tractable approaches. However, when two or more impacts occur simultaneously, the precise sequencing of impact forces is generally unknown, leading to the potential for multiple possible outcomes. This simultaneity is far from pathological, and occurs in many common robotics applications. In this work, we propose an approach for resolving simultaneous frictional impacts, represented as a differential inclusion. Solutions to our model, an extension to multiple contacts of Routh's method, naturally capture the set of potential post-impact velocities.We prove that solutions to the presented model must terminate. This is, to the best of our knowledge, the first such guarantee for set-valued outcomes to simultaneous frictional impacts.