Visual Perception is one of the strongest powers of humans. It is a natural gift which helps in perception of the world in which we have to survive. Eye-orientation is determined by a basic principle known as Listing's Law. This Law establishes the amount of Torsion for each direction of fixation. According to Listing's Law-there exists a specific eye orientation with respect to the head which is known as a primary position.


Just think; if our smart human has this feature as well, how would it be capable of its performance. Here is something about a robot which is named Domo, which has the capability to interact with the humans and can easily adapt the environment. This robot has the capability of identifying robots, easily reach for them and organized them on the cupboard; can you imagine? This robot has video cameras for its eyes which are controlled by several computers. Domo can easily recognize human faces and when it faces any human it makes a staring glance of the face.


Domo: Creation of MIT

During saccades any physiological eye orientation can be described by a unit quaternion q whose rotation axis always belongs to the head fixed plane. The Normal to plane is the eye's direction of fixation at the primary position. Vectors represent head fixed and eye fixed reference planes respectively. Without loss of generality, the vector h3 will be assumed orthogonal to the normal plane. During saccades both of the time functions conveniently described by union quaternion. If Listing's law is implemented in humans on a mechanical basis.

Geometry of Listing's Law rotation.

rotation axis-v
Vectors-xi,qi

Now to get to know about Humanoid robot eye, first we should know the basics of human eyes. So Lets look at some facts about our eye (the Human eye); the eye of Human is spherical in shape.


Human-eye

Although it is not a perfect shape and is controlled by some muscles. These muscles are six in number and known as extraocular muscles. Each of these muscles has an insertion point. It is connected with the bottom of the point at another end. The human eye is assumed as a homogenous sphere of some radius having three rotational degrees of freedom about the center.

The extraocular muscles previously described are modeled as non-elastic wires. Which are connected to pulling force generators. Lets start from the point of insertion which is on the eye-ball, the extraocular muscles are routed through pullys related to a fixed head. Out of these pulleys one of them has a role to implement the Listing's Law.

Let us assume that 'O' is the center of the eye-ball; then the position of the point-wise pulleys can be described by vector 'xi' Insertion point at primary position can be described by vector qi.

Now when the eye does rotation about a generic axis v, by an angle, the position of the insertion point can be expressed by the expression.

ri=R(v,theta)qi where i=1,2..4
R is the rotation operator from the eye to the head coordinate system.

It is assumed that extraocular muscles follow the shortest path from each of the insertion points to the corresponding pulley. Then the path of each extraocular muscle, for any eye-orientation belongs to the plane defined by the vectors. The torque which is applied on the eye by the pulling action is:
mi= a constant X ri X xi / ri X xi

A Robot eye does not have builtin rotation sensors, that is why we set an external custom-built measurement used to measure the eye rotation. A digital camera is also placed in front of an eye to acquire images. During each saccade the eye is driven by its four internal motors. There is a lot to discuss over this topic for time being keep reading and enhancing your knowledge in this area of interest. More will be elaborated upon in the next part of the series.

Resources:

How to make a Robot:Part 1

Robots:Smart humans

How to make a Robot:Part 2