tr2jac

RTSX Help: Jacobean from T, euler, or RPY angles

tr2jac

eul2jac

rpy2jac

Compute Jacobian from homogeneous transform, euler, or RPY angles

Syntax

  • J = tr2jac(T)
  • J = eul2jac(eul)    
  • J = rpy2jac(rpy)    

Input Arguments

  • T — 4×4 homogeneous transformation matrix
  • eul — 1 x 3 vector of euler angles (in radian)
  • rpy — 1 x 3 vector of Roll-Pitch-Yaw angles (in radian)

Output Arguments

  • J — 3 x 1 Jacobian matrix

Description

  • J = tr2jac(T) is a Jacobian matrix (6×6) that maps spatial velocity or differential motion from the world frame to the frame represented by the homogeneous transform T.
  • J = eul2jac(eul) is a Jacobian matrix (3×3) that maps Euler angle rates to angular velocity at the operating point eul =[phi, theta, psi].
  • J = rpy2jac(rpy) is a Jacobian matrix (3×3) that maps roll-pitch-yaw angle rates to angular velocity at the operating point rpy=[R,P,Y].

Examples

-->T = transl([1 0 0])*troty(pi/2);
-->J = tr2jac(T)
 J  =
    0.    0.  - 1.    0.    1.    0.  
    0.    1.    0.    0.    0.    1.  
    1.    0.    0.    0.    0.    0.  
    0.    0.    0.    0.    0.  - 1.  
    0.    0.    0.    0.    1.    0.  
    0.    0.    0.    1.    0.    0.  
 
-->J = eul2jac([pi/3 -pi/4 pi/6])
 J  = 
  - 0.6123724  - 0.5          0.  
  - 0.3535534    0.8660254    0.  
    0.7071068    0.           1.  
 
 -->J = rpy2jac([0.1 0.2 0.3])
 J  =
    1.    0.           0.1986693  
    0.    0.9950042  - 0.0978434  
    0.    0.0998334    0.9751703

See Also

  • delta2tr, tr2delta — Convert between differential motion and homogeneous transform
  • jacob0, jacobn — Compute Jacobian that maps joint velocity to base or end-effector spatial velocity