Articulations

Articulations are a way to represent a collection of rigid bodies that are connected by joints.

Joint types

Joint Type	Description	DOFs in joint_q	DOFs in joint_qd	DOFs in joint_axis
JOINT_PRISMATIC	Prismatic (slider) joint with 1 linear degree of freedom	1	1	1
JOINT_REVOLUTE	Revolute (hinge) joint with 1 angular degree of freedom	1	1	1
JOINT_BALL	Ball (spherical) joint with quaternion state representation	4	3	3
JOINT_FIXED	Fixed (static) joint with no degrees of freedom	0	0	0
JOINT_FREE	Free (floating) joint with 6 degrees of freedom in velocity space	7 (3D position + 4D quaternion)	6 (see Twist conventions in Newton)	0
JOINT_COMPOUND	Compound joint with 3 rotational degrees of freedom	3	3	3
JOINT_UNIVERSAL	Universal joint with 2 rotational degrees of freedom	2	2	2
JOINT_DISTANCE	Distance joint that keeps two bodies at a distance within its joint limits	7	6	1
JOINT_D6	Generic D6 joint with up to 3 translational and 3 rotational degrees of freedom	up to 6	up to 6	up to 6

D6 joints are the most general joint type in Newton and can be used to represent any combination of translational and rotational degrees of freedom. Prismatic, revolute, planar, universal, and compound joints can be seen as special cases of the D6 joint.

Definition of joint_q

The newton.Model.joint_q array stores the generalized joint positions for all joints in the model. The positional dofs for each joint can be queried as follows:

q_start = Model.joint_q_start[joint_id]
q_end = Model.joint_q_start[joint_id + 1]
# now the positional dofs can be queried as follows:
q0 = State.joint_q[q_start]
q1 = State.joint_q[q_start + 1]
...

Definition of joint_qd

The newton.Model.joint_qd array stores the generalized joint velocities for all joints in the model. The generalized joint forces at newton.Control.joint_f are stored in the same order.

The velocity dofs for each joint can be queried as follows:

qd_start = Model.joint_qd_start[joint_id]
qd_end = Model.joint_qd_start[joint_id + 1]
# now the velocity dofs can be queried as follows:
qd0 = State.joint_qd[qd_start]
qd1 = State.joint_qd[qd_start + 1]
...
# the generalized joint forces can be queried as follows:
f0 = Control.joint_f[qd_start]
f1 = Control.joint_f[qd_start + 1]
...

Axis-related quantities

Axis-related quantities include the definition of the joint axis in newton.Model.joint_axis and other properties defined via newton.ModelBuilder.JointDofConfig. The joint targets in newton.Control.joint_target are also stored in the same per-axis order.

The newton.Model.joint_axis_dim and newton.Model.joint_axis_start arrays can be used to query the number of linear and angular dofs. All axis-related quantities are stored in consecutive order for every joint. First, the linear dofs are stored, followed by the angular dofs. The indexing of the linear and angular degrees of freedom for a joint at a given joint_index is as follows:

num_linear_dofs = Model.joint_axis_dim[joint_index, 0]
num_angular_dofs = Model.joint_axis_dim[joint_index, 1]
# the joint axes for each joint start at this index:
axis_start = Model.joint_axis_start[joint_id]
# the first linear 3D axis
first_lin_axis = Model.joint_axis[axis_start]
# the joint target for this linear dof
first_lin_target = Control.joint_target[axis_start]
# the joint limit of this linear dof
first_lin_limit = Model.joint_limit_lower[axis_start]
# the first angular 3D axis is therefore
first_ang_axis = Model.joint_axis[axis_start + num_linear_dofs]
# the joint target for this angular dof
first_ang_target = Control.joint_target[axis_start + num_linear_dofs]
# the joint limit of this angular dof
first_ang_limit = Model.joint_limit_lower[axis_start + num_linear_dofs]

Forward / Inverse Kinematics

Articulated rigid-body mechanisms are kinematically described by the joints that connect the bodies as well as the relative transform from the parent and child body to the respective anchor frames of the joint in the parent and child body:

Variable names in the kernels from newton.core.articulation

Symbol	Description
x_wp	World transform of the parent body (stored at State.body_q)
x_wc	World transform of the child body (stored at State.body_q)
x_pj	Transform from the parent body to the joint parent anchor frame (defined by Model.joint_X_p)
x_cj	Transform from the child body to the joint child anchor frame (defined by Model.joint_X_c)
x_j	Joint transform from the joint parent anchor frame to the joint child anchor frame

In the forward kinematics, the joint transform is determined by the joint coordinates (generalized joint positions State.joint_q and velocities State.joint_qd). Given the parent body’s world transform \(x_{wp}\) and the joint transform \(x_{j}\), the child body’s world transform \(x_{wc}\) is computed as:

\[x_{wc} = x_{wp} \cdot x_{pj} \cdot x_{j} \cdot x_{cj}^{-1}.\]

newton.eval_fk(model, joint_q, joint_qd, state, mask=None)

Evaluates the model’s forward kinematics given the joint coordinates and updates the state’s body information (State.body_q and State.body_qd).

Parameters:

• model (Model) – The model to evaluate.

• joint_q (array) – Generalized joint position coordinates, shape [joint_coord_count], float

• joint_qd (array) – Generalized joint velocity coordinates, shape [joint_dof_count], float

• mask (array) – The mask to use to enable / disable FK for an articulation. If None then treat all as enabled, shape [articulation_count], int/bool

• state (State) – The state to update.

newton.eval_ik(model, state, joint_q, joint_qd)

Evaluates the model’s inverse kinematics given the state’s body information (State.body_q and State.body_qd) and updates the generalized joint coordinates joint_q and joint_qd.

Parameters:

• model (Model) – The model to evaluate.

• state (State) – The state with the body’s maximal coordinates (positions State.body_q and velocities State.body_qd) to use.

• joint_q (array) – Generalized joint position coordinates, shape [joint_coord_count], float

• joint_qd (array) – Generalized joint velocity coordinates, shape [joint_dof_count], float