pydrake.multibody.cenic

class pydrake.multibody.cenic.CenicIntegrator

Bases: pydrake.systems.analysis.IntegratorBase

Convex Error-controlled Numerical Integration for Contact (CENIC) is a specialized error-controlled implicit integrator for contact-rich robotics simulations [Kurtz and Castro, 2025].

CENIC provides variable-step error-controlled integration for multibody systems with stiff contact interactions, while maintaining the high speeds characteristic of discrete-time solvers required for modern robotics workflows.

Benefits of CENIC include:

Guaranteed convergence. Unlike traditional implicit integrators that rely

on non-convex Newton-Raphson solves, CENIC’s convex formulation eliminates step rejections due to convergence failures.

Guaranteed accuracy. CENIC inherits the well-studied accuracy guarantees

associated with error-controlled integration [Hairer and Wanner, 1996], avoiding discretization artifacts common in fixed-step discrete-time methods.

Automatic time step selection. Users specify a desired accuracy rather

than a fixed time step, eliminating a common pain point in authoring multibody simulations.

Implicit treatment of external systems. This means that users can connect

arbitrary stiff controllers (e.g., a custom LeafSystem) to the MultibodyPlant and have them treated implicitly in CENIC’s convex formulation. This allows for larger time steps, leading to faster and more stable simulations.

Principled static/dynamic friction modeling. Unlike discrete solvers,

CENIC can simulate frictional contact with different static and dynamic friction coefficients.

Speed. CENIC consistently outperforms general-purpose integrators by

orders of magnitude on contact-rich problems. Error-controlled CENIC is often (but not always) faster than discrete-time simulation, depending on the simulation in question and the requested accuracy.

CENIC works by solving a convex Irrotational Contact Fields (ICF) optimization problem [Castro et al., 2023] to advance the system state at each time step. A simple half-stepping strategy provides a second-order error estimate for automatic step-size selection.

Because CENIC is specific to multibody systems, this integrator requires a system diagram with a MultibodyPlant subsystem named "plant".

Running CENIC in fixed-step mode (with error-control disabled) recovers the “Lagged” variant of discrete-time ICF simulation from [Castro et al., 2023].

References:

[Castro et al., 2023] Castro A., Han X., and Masterjohn J., 2023. Irrotational Contact Fields. https://arxiv.org/abs/2312.03908.

[Hairer and Wanner, 1996] Hairer E. and Wanner G., 1996. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics, Vol. 14. Springer-Verlag, Berlin, 2nd edition.

[Kurtz and Castro, 2025] Kurtz V. and Castro A., 2025. CENIC: Convex Error-controlled Numerical Integration for Contact. https://arxiv.org/abs/2511.08771.

Note

This class is templated; see CenicIntegrator_ for the list of instantiations.

__init__(self: pydrake.multibody.cenic.CenicIntegrator, system: pydrake.systems.framework.System, context: pydrake.systems.framework.Context = None) → None

Constructs the integrator.

Parameter system:: The overall system diagram to simulate. Must include a MultibodyPlant and associated SceneGraph, with the plant found as a direct child of the system diagram using the subsystem name "plant". The plant must be a continuous-time plant. This system is aliased by this object so must remain alive longer than the integrator.
Parameter context:: context for the overall system.

get_solver_parameters(self: pydrake.multibody.cenic.CenicIntegrator) → pydrake.multibody.contact_solvers.IcfSolverParameters: Gets the current convex solver tolerances and iteration limits.

SetSolverParameters(self: pydrake.multibody.cenic.CenicIntegrator, parameters: pydrake.multibody.contact_solvers.IcfSolverParameters) → None: Sets the convex solver tolerances and iteration limits.

template pydrake.multibody.cenic.CenicIntegrator_: Instantiations: CenicIntegrator_[float], CenicIntegrator_[AutoDiffXd]

class pydrake.multibody.cenic.CenicIntegrator_[AutoDiffXd]

Bases: pydrake.systems.analysis.IntegratorBase_[AutoDiffXd]