Kinematics/dynamics algorithms · RigidBodyDynamics.jl

RigidBodyDynamics.DynamicsResult — Type.

type DynamicsResult{T, M}

Stores variables related to the dynamics of a Mechanism, e.g. the Mechanism's mass matrix and joint acceleration vector.

Type parameters:

T: the scalar type of the dynamics-related variables.
M: the scalar type of the Mechanism.

source

RigidBodyDynamics.Spatial.center_of_mass — Method.

center_of_mass(state, itr)

Compute the center of mass of an iterable subset of a Mechanism's bodies in the given state. Ignores the root body of the mechanism.

source

RigidBodyDynamics.Spatial.center_of_mass — Method.

center_of_mass(state)

Compute the center of mass of the whole Mechanism in the given state.

source

RigidBodyDynamics.dynamics! — Method.

dynamics!(result, state)
dynamics!(result, state, torques)
dynamics!(result, state, torques, externalwrenches)

Compute the joint acceleration vector $\dot{v}$ and Lagrange multipliers $\lambda$ that satisfy the joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau - K(q)^{T} \lambda\]

and the constraint equations

\[K(q) \dot{v} = -k\]

given joint configuration vector $q$, joint velocity vector $v$, and (optionally) joint torques $\tau$ and external wrenches $w_\text{ext}$.

The externalwrenches argument can be used to specify additional wrenches that act on the Mechanism's bodies.

source

RigidBodyDynamics.dynamics! — Method.

dynamics!(ẋ, result, state, state_vec)
dynamics!(ẋ, result, state, state_vec, torques)
dynamics!(ẋ, result, state, state_vec, torques, externalwrenches)

Convenience function for use with standard ODE integrators that takes a Vector argument

\[x = \left(\begin{array}{c} q\\ v \end{array}\right)\]

and returns a Vector $\dot{x}$.

source

RigidBodyDynamics.dynamics_bias! — Method.

dynamics_bias!(torques, biasaccelerations, wrenches, state)
dynamics_bias!(torques, biasaccelerations, wrenches, state, externalwrenches)

Compute the 'dynamics bias term', i.e. the term

\[c(q, v, w_\text{ext})\]

in the unconstrained joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau\]

given joint configuration vector $q$, joint velocity vector $v$, joint acceleration vector $\dot{v}$ and (optionally) external wrenches $w_\text{ext}$.

The externalwrenches argument can be used to specify additional wrenches that act on the Mechanism's bodies.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.dynamics_bias — Method.

dynamics_bias(state)
dynamics_bias(state, externalwrenches)

Compute the 'dynamics bias term', i.e. the term

\[c(q, v, w_\text{ext})\]

in the unconstrained joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau\]

given joint configuration vector $q$, joint velocity vector $v$, joint acceleration vector $\dot{v}$ and (optionally) external wrenches $w_\text{ext}$.

The externalwrenches argument can be used to specify additional wrenches that act on the Mechanism's bodies.

source

RigidBodyDynamics.geometric_jacobian! — Method.

geometric_jacobian!(jac, state, path, transformfun)

Compute a geometric Jacobian (also known as a basic, or spatial Jacobian) associated with a directed path in the Mechanism's spanning tree, (a collection of Joints and traversal directions) in the given state.

A geometric Jacobian maps the Mechanism's joint velocity vector $v$ to the twist of the target of the joint path (the body succeeding the last joint in the path) with respect to the source of the joint path (the body preceding the first joint in the path).

See also path, GeometricJacobian, Twist.

transformfun is a callable that may be used to transform the individual motion subspaces of each of the joints to the frame in which out is expressed.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.geometric_jacobian! — Method.

geometric_jacobian!(out, state, path, root_to_desired)

Compute a geometric Jacobian (also known as a basic, or spatial Jacobian) associated with a directed path in the Mechanism's spanning tree, (a collection of Joints and traversal directions) in the given state.

A geometric Jacobian maps the Mechanism's joint velocity vector $v$ to the twist of the target of the joint path (the body succeeding the last joint in the path) with respect to the source of the joint path (the body preceding the first joint in the path).

See also path, GeometricJacobian, Twist.

root_to_desired is the transform from the Mechanism's root frame to the frame in which out is expressed.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.geometric_jacobian! — Method.

geometric_jacobian!(out, state, path)

Compute a geometric Jacobian (also known as a basic, or spatial Jacobian) associated with a directed path in the Mechanism's spanning tree, (a collection of Joints and traversal directions) in the given state.

A geometric Jacobian maps the Mechanism's joint velocity vector $v$ to the twist of the target of the joint path (the body succeeding the last joint in the path) with respect to the source of the joint path (the body preceding the first joint in the path).

See also path, GeometricJacobian, Twist.

See geometric_jacobian!(out, state, path, root_to_desired). Uses state to compute the transform from the Mechanism's root frame to the frame in which out is expressed.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.geometric_jacobian — Method.

geometric_jacobian(state, path)

Compute a geometric Jacobian (also known as a basic, or spatial Jacobian) associated with a directed path in the Mechanism's spanning tree, (a collection of Joints and traversal directions) in the given state.

A geometric Jacobian maps the Mechanism's joint velocity vector $v$ to the twist of the target of the joint path (the body succeeding the last joint in the path) with respect to the source of the joint path (the body preceding the first joint in the path).

See also path, GeometricJacobian, Twist.

The Jacobian is computed in the Mechanism's root frame.

See geometric_jacobian!(out, state, path).

source

RigidBodyDynamics.inverse_dynamics! — Method.

inverse_dynamics!(torquesout, jointwrenchesout, accelerations, state, v̇)
inverse_dynamics!(torquesout, jointwrenchesout, accelerations, state, v̇, externalwrenches)

Do inverse dynamics, i.e. compute $\tau$ in the unconstrained joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau\]

given joint configuration vector $q$, joint velocity vector $v$, joint acceleration vector $\dot{v}$ and (optionally) external wrenches $w_\text{ext}$.

The externalwrenches argument can be used to specify additional wrenches that act on the Mechanism's bodies.

This method implements the recursive Newton-Euler algorithm.

Currently doesn't support Mechanisms with cycles.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.inverse_dynamics — Method.

inverse_dynamics(state, v̇)
inverse_dynamics(state, v̇, externalwrenches)

Do inverse dynamics, i.e. compute $\tau$ in the unconstrained joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau\]

given joint configuration vector $q$, joint velocity vector $v$, joint acceleration vector $\dot{v}$ and (optionally) external wrenches $w_\text{ext}$.

The externalwrenches argument can be used to specify additional wrenches that act on the Mechanism's bodies.

This method implements the recursive Newton-Euler algorithm.

Currently doesn't support Mechanisms with cycles.

source

RigidBodyDynamics.mass — Method.

mass(m)

Return the total mass of the Mechanism.

source

RigidBodyDynamics.mass_matrix! — Method.

mass_matrix!(M, state)

Compute the joint-space mass matrix (also known as the inertia matrix) of the Mechanism in the given state, i.e., the matrix $M(q)$ in the unconstrained joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau\]

This method implements the composite rigid body algorithm.

This method does its computation in place, performing no dynamic memory allocation.

The out argument must be an $n_v \times n_v$ lower triangular Symmetric matrix, where $n_v$ is the dimension of the Mechanism's joint velocity vector $v$.

source

RigidBodyDynamics.mass_matrix — Method.

mass_matrix(state)

Compute the joint-space mass matrix (also known as the inertia matrix) of the Mechanism in the given state, i.e., the matrix $M(q)$ in the unconstrained joint-space equations of motion

\[M(q) \dot{v} + c(q, v, w_\text{ext}) = \tau\]

This method implements the composite rigid body algorithm.

source

RigidBodyDynamics.momentum_matrix! — Method.

momentum_matrix!(out, state, transformfun)

Compute the momentum matrix $A(q)$ of the Mechanism in the given state.

The momentum matrix maps the Mechanism's joint velocity vector $v$ to its total momentum.

See also MomentumMatrix.

The out argument must be a mutable MomentumMatrix with as many columns as the dimension of the Mechanism's joint velocity vector $v$.

transformfun is a callable that may be used to transform the individual momentum matrix blocks associated with each of the joints to the frame in which out is expressed.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.momentum_matrix! — Method.

momentum_matrix!(out, state, root_to_desired)

Compute the momentum matrix $A(q)$ of the Mechanism in the given state.

The momentum matrix maps the Mechanism's joint velocity vector $v$ to its total momentum.

See also MomentumMatrix.

The out argument must be a mutable MomentumMatrix with as many columns as the dimension of the Mechanism's joint velocity vector $v$.

root_to_desired is the transform from the Mechanism's root frame to the frame in which out is expressed.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.momentum_matrix! — Method.

momentum_matrix!(out, state)

Compute the momentum matrix $A(q)$ of the Mechanism in the given state.

The momentum matrix maps the Mechanism's joint velocity vector $v$ to its total momentum.

See also MomentumMatrix.

The out argument must be a mutable MomentumMatrix with as many columns as the dimension of the Mechanism's joint velocity vector $v$.

See momentum_matrix!(out, state, root_to_desired). Uses state to compute the transform from the Mechanism's root frame to the frame in which out is expressed.

This method does its computation in place, performing no dynamic memory allocation.

source

RigidBodyDynamics.momentum_matrix — Method.