ICubHeadKinematics

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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 0th 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 nth 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.

HeadFwdKinNew.jpg HeadCADRefFrame.jpg

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