Module robotics 

Robotics kinematics: DH parameters, forward kinematics, rotations. Robotics kinematics helpers: DH parameters, forward kinematics, Jacobian, and algebraic inverse kinematics.

Denavit-Hartenberg Convention

Each joint in a serial robot arm is described by four parameters:

• θ (theta): joint angle (variable for revolute joints)
• d: link offset along z-axis
• a: link length along x-axis
• α (alpha): link twist angle

These produce a 4×4 homogeneous transformation matrix per joint. Chaining these matrices gives the forward kinematics.

Enums

EulerConvention

Euler angle convention for rotation composition.

Functions

dh_matrix

Build the standard Denavit-Hartenberg transformation matrix for one joint.

fk_chain

Chain-multiply a sequence of DH transformation matrices to compute the total forward-kinematics transformation.

fk_chain_typed

Compute the full 4×4 FK transformation matrix from typed DH parameters.

fk_position

Extract the end-effector position (x, y, z) from the forward-kinematics chain.

fk_position_typed

Compute end-effector position from typed DH parameters.

fk_rotation

Extract the 3×3 rotation submatrix from the forward-kinematics result.

fk_rotation_typed

Compute the 3×3 rotation matrix from typed DH parameters.

homogeneous

Build a 4×4 homogeneous transformation matrix from a 3×3 rotation matrix and a 3-element position vector.

inverse_kinematics_2dof

Solve 2-DOF planar inverse kinematics algebraically.

rot_euler

Rotation matrix from Euler angles with specified convention.

rot_x

Rotation matrix about the x-axis by angle θ.

rot_y

Rotation matrix about the y-axis by angle θ.

rot_z

Rotation matrix about the z-axis by angle θ.

skew3

Skew-symmetric matrix from a 3-vector [a, b, c].

translation

Pure translation as a 4×4 homogeneous transformation matrix.

Type Aliases

DhParams

Typed DH parameter tuple: (joint_angle, link_offset, link_length, link_twist).