# ICubHeadKinematics

This page describes how to construct the matrices T_RoLe and T_RoRe whose definition is given in ICubForwardKinematics. The matrices are constructed in two steps i.e. T_RoRe = T_Ro0 * T_0n and T_RoLe = T_Ro0 * T'_0n. The first matrix T_Ro0 describes the rigid roto-translation from the root reference frame to points in the
0*th* reference frame as defined by the Denavit-Hartenberg convention.
In this case T_Ro0 is just a rigid rotation which aligns the z-axis with the first joint of the waist.
The second matrices T_0n and T'_0n correspond to the Denavit-Hartenberg description of the right and left eye forward kinematic, i.e. the roto-translation from the 0th reference frame to the n*th* reference frame being n the number of degrees of freedom. The forward kinematic T_0n in this case includes the waist and the right eye forward kinematics. The forward kinematic T'_0n in this case includes the waist and the left eye forward kinematics.

The matrices T_0n and T'_0n are themselves the composition of n matrices as defined by the DH convention: T_0n = T_01 T_12 ... T_(n-1)n and T'_0n = T'_01 T'_12 ... T'_(n-1)n. Here is the updated matlab code for computing the forward kinematics with the Denavit Hartenberg notation Media: ICubFwdKinNew.zip.

The eyes reference frames are located in the palm as shown in the CAD figure. The **x** axis is in **red**. The **y** axis is in **green**. The **z** axis is in **blue**.

Here is the matrix T_Ro0:

0 | -1 | 0 | 0 |

0 | 0 | -1 | 0 |

1 | 0 | 0 | 0 |

0 | 0 | 0 | 1 |

Here is the table of the actual DH parameters which describe T_01, T_12, ... T_(n-1)n.

Link i / H – D | Ai (mm) | d_i (mm) | alpha_i (rad) | theta_i (deg) |
---|---|---|---|---|

i = 0 | 32 | 0 | pi/2 | -22 -> 84 |

i = 1 | 0 | -5.5 | pi/2 | -90 + (-39 -> 39) |

i = 2 | 2.31 | -193.3 | -pi/2 | -90 + (-59 -> 59) |

i = 3 | 33 | 0 | pi/2 | 90 + (-40 -> 30) |

i = 4 | 0 | 1 | -pi/2 | -90 + (-70 -> 60) |

i = 5 | -54 | 82.5 | -pi/2 | 90 + (-55 -> 55) |

i = 6 | 0 | 34 | -pi/2 | -35 -> 15 |

i = 7 | 0 | 0 | pi/2 | -90 + (-50 -> 50) |

Here is the table of the actual DH parameters which describe T'_01, T'_12, ... T'_(n-1)n.

Link i / H – D | Ai (mm) | d_i (mm) | alpha_i (rad) | theta_i (deg) |
---|---|---|---|---|

i = 0 | 32 | 0 | pi/2 | -22 -> 84 |

i = 1 | 0 | -5.5 | pi/2 | -90 + (-39 -> 39) |

i = 2 | 2.31 | -193.3 | -pi/2 | -90 + (-59 -> 59) |

i = 3 | 33 | 0 | pi/2 | 90 + (-40 -> 30) |

i = 4 | 0 | 1 | -pi/2 | -90 + (-70 -> 60) |

i = 5 | -54 | 82.5 | -pi/2 | 90 + (-55 -> 55) |

i = 6 | 0 | -34 | -pi/2 | -35 -> 15 |

i = 7 | 0 | 0 | pi/2 | -90 + (-50 -> 50) |

Joint Poses (x y z, roll, pitch, yaw) w.r.t. root:

Eyes tilt (G_sl6) = -62.81 0 340.8 1.57079 0 0

Right Eye (G_sl7) = -62.81 34 340.8 -3.14159 0 0

Left Eye (Gp_sl7) = -62.81 -34 340.8 -3.14159 0 0

Right Eye (G_sl8) = -62.81 34 340.8 0 1.57079 0

Left Eye (Gp_sl8) = -62.81 -34 340.8 0 1.57079 0