Struct ArticulatedBodyInertia 

pub struct ArticulatedBodyInertia {
    pub top_left: SymmetricMat3,
    pub h: SMatrix<3, 3>,
    pub mass: SymmetricMat3,
}

Articulated body spatial inertia matrix for complex multi-body systems.

This represents the effective inertia of an articulated body, which accounts for the inertia of all bodies in the subtree beyond a given joint. Unlike rigid body inertia, articulated body inertia captures the dynamic coupling between joints in a kinematic chain.

Matrix Structure

The articulated body inertia has the form:

     | I   H |
I_A = |      |
     | Hᵀ  M |

where:

• I: 3×3 matrix representing rotational inertia effects
• H: 3×3 matrix representing coupling between rotation and translation
• M: 3×3 matrix representing translational inertia effects

Physical Meaning

Articulated body inertia represents the effective inertia seen at a joint when all bodies beyond that joint move together. It accounts for:

1. Propagated inertia: Inertia of all bodies in the subtree
2. Dynamic coupling: How motion at one joint affects other joints
3. Constraint forces: Forces transmitted through the kinematic chain

Use in Dynamics

This is a key component in Featherstone’s Articulated Body Algorithm:

• Used in forward dynamics to compute joint accelerations
• Captures the influence of the entire subtree on each joint
• Enables O(n) complexity dynamics for tree-structured mechanisms

Storage

The matrix stores 21 independent elements (6 for I, 9 for H, 6 for M), optimized for the symmetric structure of the top-left and bottom-right blocks.

Fields

top_left: SymmetricMat3

Top-left 3×3 block (I) of the articulated body inertia matrix.

This symmetric matrix represents rotational inertia effects and couples angular accelerations to resulting moments.

h: SMatrix<3, 3>

Top-right 3×3 block (H) of the articulated body inertia matrix.

This general (non-symmetric) matrix represents cross-coupling between rotational and translational motion in the articulated system.

mass: SymmetricMat3

Bottom-right 3×3 block (M) of the articulated body inertia matrix.

This symmetric matrix represents translational inertia effects and couples linear accelerations to resulting forces.

Implementations

impl ArticulatedBodyInertia

pub fn add_arti_inertia(&self, rhs: &Self) -> Self

pub fn sub_arti_inertia(&self, rhs: &Self) -> Self

pub fn add_spat_inertia(&self, rhs: &RigidBodyInertia) -> Self

Add a rigid body inertia to this articulated body inertia.

This operation is used in the articulated body algorithm when propagating inertia from child bodies to parent bodies. It combines the effective articulated body inertia of the subtree with the rigid body inertia of the current body.

Physical Meaning

This represents adding the inertia of a rigid body to an existing articulated body, effectively extending the articulated system by one body. The operation accounts for:

• Adding the rigid body’s mass to the translational inertia
• Including cross-coupling effects from the rigid body’s first moment
• Adding the rigid body’s rotational inertia to the system

Algorithm Context

This is a crucial step in Featherstone’s articulated body algorithm for computing the effective inertia at each joint in a kinematic tree.

pub fn mul_motion_vec( &self, motion_vec: SpatialMotionVector, ) -> SpatialForceVector

pub fn from_symmertic_matrix(matrix: SMatrix<6, 6>) -> Self

take the lower triangle part.

pub fn matrix(&self) -> SMatrix<6, 6>

Trait Implementations

impl Add<RigidBodyInertia> for ArticulatedBodyInertia

type Output = ArticulatedBodyInertia

The resulting type after applying the + operator.

fn add(self, rhs: RigidBodyInertia) -> Self::Output

Performs the + operation.

impl Add for &ArticulatedBodyInertia

type Output = ArticulatedBodyInertia

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> ArticulatedBodyInertia

Performs the + operation.

impl Add for ArticulatedBodyInertia

type Output = ArticulatedBodyInertia

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl AddAssign<&ArticulatedBodyInertia> for ArticulatedBodyInertia

fn add_assign(&mut self, rhs: &ArticulatedBodyInertia)

Performs the += operation.

impl Clone for ArticulatedBodyInertia

fn clone(&self) -> ArticulatedBodyInertia

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ArticulatedBodyInertia

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for ArticulatedBodyInertia

fn default() -> ArticulatedBodyInertia

Returns the “default value” for a type.

impl From<RigidBodyInertia> for ArticulatedBodyInertia

fn from(value: RigidBodyInertia) -> Self

Converts to this type from the input type.

impl Mul<&ArticulatedBodyInertia> for PluckerTransform

type Output = ArticulatedBodyInertia

The resulting type after applying the * operator.

fn mul(self, rhs: &ArticulatedBodyInertia) -> ArticulatedBodyInertia

Performs the * operation.

impl Mul<SpatialVector<Motion>> for &ArticulatedBodyInertia

type Output = SpatialVector<Force>

The resulting type after applying the * operator.

fn mul(self, rhs: SpatialMotionVector) -> Self::Output

Performs the * operation.

impl Mul<SpatialVector<Motion>> for ArticulatedBodyInertia

type Output = SpatialVector<Force>

The resulting type after applying the * operator.

fn mul(self, rhs: SpatialMotionVector) -> Self::Output

Performs the * operation.

impl Sub<ArticulatedBodyInertia> for &ArticulatedBodyInertia

type Output = ArticulatedBodyInertia

The resulting type after applying the - operator.

fn sub(self, rhs: ArticulatedBodyInertia) -> Self::Output

Performs the - operation.

impl Sub for ArticulatedBodyInertia

type Output = ArticulatedBodyInertia

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.