Discrete Models for Simulation

Discrete Models for Simulation

Currently, this is the preferred modality given its speed and robustness. In this modality, the system is updated through periodic updates of length time_step. This can essentially be seen as a time-stepping strategy with a fixed time_step. The value of time_step is provided at construction of the MultibodyPlant.

Drake simulates the discrete model using SAP, a convex formulation originally developed in [Castro et al., 2022] as an extension to the work in [Anitescu, 2006] and [Todorov, 2014] to resolve physical compliance, providing a performant implementation in primal coordinates.

To choose different approximations of discrete contact refer to DiscreteContactApproximation. Today SAP is our preferred discrete solver for its robustness, speed, and rich feature set of constraints. A novel extension to SAP presented in [Castro et al., 2023], still convex, allows for the introduction of complex models of compliant contact, such as [Hunt and Crossley 1975]. The Hunt & Crossley model is based on physics, it is continuous and has been experimentally validated. Therefore it is the preferred model to capture the physics of contact.

Note

Discrete models, formulated at the velocity level, cannot differentiate between static (μₛ) and dynamic (μₖ) friction; only dynamic friction can be resolved. Therefore the static coefficient of friction is ignored.