motrixsim.ik#

Classes:

DlsSolver([max_iter, step_size, tolerance, ...])

Use Damped Least Squares (DLS) method to solve inverse kinematics problem.

GaussNewtonSolver([max_iter, step_size, ...])

Use gauss newton iterative method to solve inverse kinematics problem.

IkChain(model, end_link[, start_link, ...])

Represents a kinematic chain for inverse kinematics (IK) solving.
class motrixsim.ik.DlsSolver(max_iter=100, step_size=0.5, tolerance=0.001, damping=0.001)#

基类：object

Use Damped Least Squares (DLS) method to solve inverse kinematics problem.

DLS is a robust optimization method that adds regularization to handle singular configurations and improve numerical stability. It's also known as Levenberg-Marquardt for IK applications.

参数:

  • max_iter (int) -- Maximum number of iterations (default: 100).

  • step_size (float) -- Step size for each iteration (default: 0.5).

  • tolerance (float) -- Tolerance for convergence (default: 1e-3).

  • damping (float) -- Damping parameter for regularization (default: 1e-3). - Small values (1e-6 to 1e-4): Near Gauss-Newton behavior - Medium values (1e-4 to 1e-2): Good balance for most applications - Large values (1e-2 to 1.0): More stable but slower convergence

Methods:

solve(ik_model, data, target_pose)

Solve the IK problem for the given chain and target pose.
solve(ik_model, data, target_pose)#

Solve the IK problem for the given chain and target pose.

参数:

  • ik_model (IkChain) -- The IK model. Currently only IkChain is supported.

  • data (SceneData) -- The scene data containing the current state.

  • target_pose (NDarray[float]) -- The target pose the end effector want to reach. It is a 7-element array with (x, y, z, i, j, k, w) format.

返回:

A numpy array with shape (data.shape, ik_model.num_dof_pos + 2,). For each row, the first element is the number of iterations used, the second element is the final residual, and the remaining elements are the solved DOF positions.

class motrixsim.ik.GaussNewtonSolver(max_iter=100, step_size=0.5, tolerance=0.001)#

基类：object

Use gauss newton iterative method to solve inverse kinematics problem.

参数:

  • max_iter (int) -- Maximum number of iterations (default: 100).

  • step_size (float) -- Step size for each iteration (default: 0.5).

  • tolerance (float) -- Tolerance for convergence (default: 1e-3).

Methods:

solve(ik_model, data, target_pose)

Solve the IK problem for the given chain and target pose.
solve(ik_model, data, target_pose)#

Solve the IK problem for the given chain and target pose.

参数:

  • ik_model (IkChain) -- The IK model. Currently only IkChain is supported.

  • data (SceneData) -- The scene data containing the current state. target_pose (NDarray[float]): The target pose the end effector want to reach. It is a 7-element array with (x, y, z, i, j, k, w) format.

返回:

A numpy array with shape (data.shape, ik_model.num_dof_pos + 2,). For each row, the first element is the number of iterations used, the second element is the final residual, and the remaining elements are the solved DOF positions.

class motrixsim.ik.IkChain(model, end_link, start_link=None, end_effector_offset=None)#

基类：object

Represents a kinematic chain for inverse kinematics (IK) solving.

参数:

  • model (SceneModel) -- The scene model containing the kinematic structure.

  • end_link (str) -- The name of the end link of the IK chain.

  • start_link (Optional[str]) -- The name of the start link of the IK chain. If not provided, the root link will be used.

  • end_effector_offset (Optional[ndarray]) -- A 7-element array representing the end-effector offset as a pose (x, y, z, i, j, k, w) in end link's local space. If not provided, no offset will be applied.

抛出:

RuntimeError -- If the IK chain contains unsupported joint types. (Currently only hinge and slider are supported.)

Methods:

get_bias_force(data)

Get the joint space bias force of the chain.

get_dof_pos(data)

Get the DoF positions of the IK chain from the simulation data.

get_dof_vel(data)

Get the DoF velocities of the IK chain from the simulation data.

get_end_effector_jac(data)

Get the Jacobian matrix of the end effector.

get_end_effector_pose(data)

Get the end effector pose in world coordinates.

get_end_effector_vel(data)

Get the end effector velocity in world coordinates.

get_end_point_jac(data, end_point)

Get the Jacobian matrix of a specific point fixed to the end link.

get_inertial_matrix(data)

Get the joint space inertia matrix of the chain.

get_link(index)

Get the link at the specified index in the IK chain.

Attributes:

num_dof_pos

Get the number of DoF positions in the IK chain.

num_dof_vel

Get the number of DoF velocities in the IK chain.

num_links

Get the number of links in the IK chain.
get_bias_force(data)#

Get the joint space bias force of the chain.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The joint space bias force of the chain. shape = (*data.shape, num_dof_vel).

返回类型:

ndarray

get_dof_pos(data)#

Get the DoF positions of the IK chain from the simulation data.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The DoF positions of the chain. shape = (*data.shape, num_dof_pos).

返回类型:

ndarray

get_dof_vel(data)#

Get the DoF velocities of the IK chain from the simulation data.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The DoF velocities of the chain. shape = (*data.shape, num_dof_vel).

返回类型:

ndarray

get_end_effector_jac(data)#

Get the Jacobian matrix of the end effector.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The Jacobian matrix of the end effector. shape = `(*data.shape, 6,

返回类型:

ndarray

num_dof_vel)`. The first 3 rows are angular velocity, the last 3 rows are linear velocity.

get_end_effector_pose(data)#

Get the end effector pose in world coordinates.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The end effector pose array. shape = (*data.shape, 7). Each pose is a

返回类型:

ndarray

7-element array with [x, y, z, i, j, k, w] format.

get_end_effector_vel(data)#

Get the end effector velocity in world coordinates.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The end effector velocity array. shape = (*data.shape, 6). Each velocity is a

返回类型:

ndarray

6-element array with first 3 elements representing angular velocity and last 3 elements representing linear velocity.

get_end_point_jac(data, end_point)#

Get the Jacobian matrix of a specific point fixed to the end link.

参数:

  • data (SceneData) -- The scene data containing the current state.

  • end_point (ndarray) -- A 3-element array representing the point in the end link's local

frame.

返回:

The Jacobian matrix of the specified point. shape = `(*data.shape, 6,

返回类型:

ndarray

num_dof_vel)`. The first 3 rows are angular velocity, the last 3 rows are linear velocity.

get_inertial_matrix(data)#

Get the joint space inertia matrix of the chain.

参数:

data (SceneData) -- The scene data containing the current state.

返回:

The joint space inertia matrix of the chain. shape = `(*data.shape,

返回类型:

ndarray

num_dof_vel, num_dof_vel)`. A symmetric positive definite matrix.

Get the link at the specified index in the IK chain.

参数:

index (int) -- The index of the link in the chain (0-based).

返回:

The link object at the specified index.

返回类型:

Link

抛出:

IndexError -- If the index is out of bounds.

num_dof_pos#

Get the number of DoF positions in the IK chain.

返回:

The number of degree of freedom positions.

返回类型:

int

num_dof_vel#

Get the number of DoF velocities in the IK chain.

返回:

The number of degree of freedom velocities.

返回类型:

int

Get the number of links in the IK chain.

返回:

The number of links in the chain.

返回类型:

int