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AN2350

An overview on robotics

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1.1.1

Kinematics analysis

Robot arm kinematics deals with the analytical study of the geometry of motion of a robot

arm with respect to a fixed reference coordinate system as a function of time without regard

to the forces/moments that causes the motion.

Thus, it deals with the analytical description of the spatial displacement of the robot as a

function of time, in particular the relations between the joint space and the position and

orientation of the end-effector of a robot arm.

In kinematics, we consider two issues:

Forward analysis: for a given manipulator, given the joint angle vector

q(t)=(q1(t), q2(t), …., qN(t))T

and the geometric link parameters, where n is the number of degrees of freedom,

what is the position and orientation of the end-effector with respect to a reference

coordinate system?

Inverse analysis: given a desired position and orientation of the end effector and the

geometric link parameters with respect to a reference coordinate system, can the

manipulator reach the desired manipulator hand position and orientation. And if it can,

how many different manipulator configurations will satisfy the same condition?

For serial robots, the forward analysis problem is usually easy and straightforward.

Unfortunately, the inverse analysis problem is of much more interest. For example, in

industrial applications, the end-effector must follow some desired path; then, we need to find

the joint angles for each position in the path.

For redundant robots, the inverse kinematics problem has then an infinite number of

solutions. The extra degrees of freedom can then be used for other purposes, for example

for fault tolerance, obstacle avoidance, or to optimize some performance criteria.

A simple block diagram indicating the relationship between these two problems is shown in

the following figure.

Figure 1.

The direct and inverse kinematics problems

Link parameters

Position and

orientation

of the end-effector

Link parameters

Direct

kinematics

Joint angles

q1(t), q2(t), ..., qN(t)

Joint angles

q1(t), q2(t), ..., qN(t)

Inverse

kinematics

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