Rigid Body Dynamics Algorithms

Rigid Body Dynamics Algorithms#

This module provides a set of algorithms for rigid body dynamics.

aba(model, *, base_position, ...[, ...])

Compute forward dynamics using the Articulated Body Algorithm (ABA).

collidable_points

contacts.soft

crba(model, *, joint_positions)

Compute the free-floating mass matrix using the Composite Rigid-Body Algorithm (CRBA).

forward_kinematics(model, link_index, ...)

Compute the forward kinematics of a specific link.

jacobian(model, *, link_index, joint_positions)

Compute the free-floating Jacobian of a link.

utils

Collision Detection#

jaxsim.rbda.collidable_points.collidable_points_pos_vel(model, *, base_position, base_quaternion, joint_positions, base_linear_velocity, base_angular_velocity, joint_velocities)[source]

Compute the position and linear velocity of collidable points in the world frame.

Parameters:

  • model (JaxSimModel) – The model to consider.

  • base_position (Array) – The position of the base link.

  • base_quaternion (Array) – The quaternion of the base link.

  • joint_positions (Array) – The positions of the joints.

  • base_linear_velocity (Array) – The linear velocity of the base link in inertial-fixed representation.

  • base_angular_velocity (Array) – The angular velocity of the base link in inertial-fixed representation.

  • joint_velocities (Array) – The velocities of the joints.

Return type:

tuple[Array, Array]

Returns:

A tuple containing the position and linear velocity of collidable points.

Contact Models#

class jaxsim.rbda.contacts.soft.SoftContacts(parameters=<factory>, terrain=<factory>)[source]

Soft contacts model.

Parameters:

  • parameters (SoftContactsParams)

  • terrain (Annotated[Terrain, '__jax_dataclasses_static_field__'])

compute_contact_forces(position, velocity, tangential_deformation)[source]

Compute the contact forces and material deformation rate.

Parameters:

  • position (Array) – The position of the collidable point.

  • velocity (Array) – The linear velocity of the collidable point.

  • tangential_deformation (Array) – The tangential deformation.

Return type:

tuple[Array, tuple[Array]]

Returns:

A tuple containing the contact force and material deformation rate.

class jaxsim.rbda.contacts.soft.SoftContactsParams(K=<factory>, D=<factory>, mu=<factory>)[source]

Parameters of the soft contacts model.

Parameters:

  • K (Array)

  • D (Array)

  • mu (Array)

static build(K=1000000.0, D=2000, mu=0.5)[source]

Create a SoftContactsParams instance with specified parameters.

Parameters:

  • K (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The stiffness parameter.

  • D (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The damping parameter of the soft contacts model.

  • mu (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The static friction coefficient.

Return type:

SoftContactsParams

Returns:

A SoftContactsParams instance with the specified parameters.

static build_default_from_jaxsim_model(model, *, standard_gravity=9.81, static_friction_coefficient=0.5, max_penetration=0.001, number_of_active_collidable_points_steady_state=1, damping_ratio=1.0)[source]

Create a SoftContactsParams instance with good default parameters.

Parameters:

  • model (JaxSimModel) – The target model.

  • standard_gravity (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The standard gravity constant.

  • static_friction_coefficient (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The static friction coefficient between the model and the terrain.

  • max_penetration (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The maximum penetration depth.

  • number_of_active_collidable_points_steady_state (Union[int, Array, ndarray, bool, number, bool, float, complex]) – The number of contacts supporting the weight of the model in steady state.

  • damping_ratio (Union[float, Array, ndarray, bool, number, bool, int, complex]) – The ratio controlling the damping behavior.

Return type:

SoftContactsParams

Returns:

A SoftContactsParams instance with the specified parameters.

Note

The damping_ratio parameter allows to operate on the following conditions: - ξ > 1.0: over-damped - ξ = 1.0: critically damped - ξ < 1.0: under-damped

valid()[source]

Check if the parameters are valid.

Return type:

bool

Returns:

True if the parameters are valid, False otherwise.

class jaxsim.rbda.contacts.soft.SoftContactsState(tangential_deformation)[source]

Class storing the state of the soft contacts model.

Parameters:

tangential_deformation (Array)

tangential_deformation

The matrix of 3D tangential material deformations corresponding to each collidable point.

static build(tangential_deformation=None, number_of_collidable_points=None)[source]

Create a SoftContactsState.

Parameters:

  • tangential_deformation (Array | None) – The matrix of 3D tangential material deformations corresponding to each collidable point.

  • number_of_collidable_points (int | None) – The number of collidable points.

Return type:

SoftContactsState

Returns:

A SoftContactsState instance.

static build_from_jaxsim_model(model=None, tangential_deformation=None)[source]

Build a SoftContactsState from a JaxSimModel.

Parameters:

  • model (JaxSimModel | None) – The JaxSimModel associated with the soft contacts state.

  • tangential_deformation (Array | None) – The matrix of 3D tangential material deformations.

Return type:

SoftContactsState

Returns:

The SoftContactsState built from the JaxSimModel.

Note

If any of the state components are not provided, they are built from the JaxSimModel and initialized to zero.

valid(model)[source]

Check if the SoftContactsState is valid for a given JaxSimModel.

Parameters:

model (JaxSimModel) – The JaxSimModel to validate the SoftContactsState against.

Return type:

bool

Returns:

True if the soft contacts state is valid for the given JaxSimModel, False otherwise.

static zero(model)[source]

Build a zero SoftContactsState from a JaxSimModel.

Parameters:

model (JaxSimModel) – The JaxSimModel associated with the soft contacts state.

Return type:

SoftContactsState

Returns:

A zero SoftContactsState instance.

Utilities#

jaxsim.rbda.utils.process_inputs(model, *, base_position=None, base_quaternion=None, joint_positions=None, base_linear_velocity=None, base_angular_velocity=None, joint_velocities=None, base_linear_acceleration=None, base_angular_acceleration=None, joint_accelerations=None, joint_forces=None, link_forces=None, standard_gravity=None)[source]

Adjust the inputs to rigid-body dynamics algorithms.

Parameters:

  • model (JaxSimModel) – The model to consider.

  • base_position (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The position of the base link.

  • base_quaternion (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The quaternion of the base link.

  • joint_positions (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The positions of the joints.

  • base_linear_velocity (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The linear velocity of the base link.

  • base_angular_velocity (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The angular velocity of the base link.

  • joint_velocities (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The velocities of the joints.

  • base_linear_acceleration (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The linear acceleration of the base link.

  • base_angular_acceleration (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The angular acceleration of the base link.

  • joint_accelerations (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The accelerations of the joints.

  • joint_forces (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The forces applied to the joints.

  • link_forces (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The forces applied to the links.

  • standard_gravity (Union[Array, ndarray, bool, number, bool, int, float, complex, tuple, None]) – The standard gravity constant.

Return type:

tuple[Array, Array, Array, Array, Array, Array, Array, Array, Array, Array]

Returns:

The adjusted inputs.

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