# ICubInertiaSensorKinematicsV2

This page describes how to construct the matrix T_RoIs whose definition is given in ICubForwardKinematics. The matrix is constructed in three steps i.e. T_RoIs = T_Ro0 * T_0n * T_nIs. 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 matrix T_0n correspond to the Denavit-Hartenberg description of the waist and neck 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 neck forward kinematics.

The matrix T_0n is itself the composition of n matrices as defined by the DH convention: 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: ICubFwdKinNewV2.zip.

The sensor reference frame is 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 | 0 | -223.3 | -pi/2 | -90 + (-59 -> 59) |

i = 3 | 9.5 | 0 | pi/2 | 90 + (-40 -> 30) |

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

i = 5 | 18.5 | 110.8 | -pi/2 | 90 + (-55 -> 55) |

Here is the matrix T_nIs:

1 | 0 | 0 | 0 |

0 | 0 | -1 | 0 |

0 | 1 | 0 | 6.6 |

0 | 0 | 0 | 1 |

In some circumstances it might be convenient to think of coding T_nls as a further virtual link located at the end of the chain and with its joint constantly kept at 0 value. The DH parameters of this virtual link are:

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

i = 6 | 0 | 6.6 | pi/2 | 0 |