this slide deals with inverse kinematics problem in soft computing.

1. INVERSE KINEMATICS PROBLEM
BY,
VIVEK KUMAR(vivek5505@gmail.com)
DEPT. OF COMPUTER ENGINEERING
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2. 2INTRODUCTION
 Kinematic analysis is one of the first steps in the design of most
industrial robots. Kinematic analysis allows the designer to obtain
information on the position of each component within the
mechanical system.
 To move the robot on a path, We need to send a series of
commands to move the robot to a specified positions. In reality, if
we have to move the robot hand in a linear path in Cartesian
coordinates, we must generate the points (positions) by doing a
series of geometric calculations.
 After generating the points we want the robot to follow, we must
find the angles that each servomotor should be at to place the
robot hand at the desired location

3. FORWARD AND INVERSE KINEMATICS 3
To come up with inverse kinematics equations, We have to first find
the forward kinematics equations of the robot.
 Forward Kinematics: all joint variables including arm length ,angles
are known in this case and we have to determine where the robot’s
hand is.
 Inverse Kinematics: Given the desired position of the robot's hand,
what must be the angles at all of the robots joints i.e it is the invers
e process of forward kinematics.

4. NEED OF IK? 4
In case of robot we have to use various calculation like forward
kinematics and reverse kinematics for the movement of its
effectors i.e its arms ,legs etc.
 Humans solve this problem all the time without even thinking
about it. While taking breakfast in the morning we just move
our hand near the plate and take the food. we don't think, "my
shoulder needs to do this, my elbow needs to do that, etc.
 We need this because on the basic of position of end effector
of robot,we can calculate the angle between the joints.

5. 5
Game programming: Inverse kinematics is important to game
programming where it is used to connect game
characters physically to the world, such as feet landing firmly on
top of terrain.
3D animation: In most 3D animation software, Inverse
Kinematics is implemented as a skeleton system. It is often
easier for computer-based designers, artists, and animators to
define the spatial configuration of a figure by moving parts, or
arms and legs, rather than directly manipulating joint angles.

6. DIFFICULTY WITH INVERSE KINEMATICS 6
Multi-valued: Often multiple solutions for a single Cartesian
pose .
Discontinuities and singularities: It Can lose one or more DOFs
in some configurations.
The main difficulty of the inverse kinematics problem in general
is that for some desired end effector configuration, sometimes
there may be no solutions, or there may be a unique solution .

7. 7
X axis
Y axis
θ
For example:
Xhand
l
 The figure above is a schematic of a simple robot lying in the X-Y plane. The
robot has one link of length l and one joint with angle θ. The position of the
robot's hand is Xhand. The inverse kinematics problem (at the position level)
for this robot is as follows:
 Given Xhand and we need to find the joint angle θ.
 We'll start the solution to this problem by writing down the forward
position equation, and then solve for θ.

8. 8
Xhand =lcosθ
cos θ =Xhand / l
θ =cos-1(Xhand / l)
let's say that this robot's link has a length of 1 foot and we want the
robot's hand to be at X = .7071 feet then value of can be calculated
as:
θ =cos-1(.7071) = +/- 45 degree.
Even for this simple example, there are two solutions to the inverse
kinematics problem: one at plus 45 degrees and one at minus 45
degrees. The existence of multiple solutions adds to the challenge of
the inverse kinematics problem.
To find the proper quadrant when given both the X and Y
arguments: θ = ATan2(Y/X).

9. 9
SOLUTION TO INVERSE KINEMATICS PROBLEM
 A number of methods and their combinations could be used to
solve the inverse kinematics. There are some advantages and
disadvantages of using these solutions.
 Algebraic methods: In order to keep numerical errors small, one
should try to transform the system of equations into an
equivalent but ‘simpler’ one by some algebraic method.
 Iterative model: It solve the inverse kinematics problem by using
a sequence of steps leading to incrementally better solutions for
the joint angles. The goal is to minimize the difference between
the current and desired positions of the end effectors.

10. 10
Various Iterative models for the solution of the Inverse
Kinematics are:
a. Jacobian inversion method.
b. Optimization based method
c. Cyclic coordinate descent
d. Genetic programming
etc..

11. THANK YOU!
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