Basic Robotics Fundamentals presentation.pptx

Robotics fundamentals

1. Differential Kinematics

2. Skew Symmetric Matrices Complex Case: When axis of rotation are not fixed Angular velocity is the result of multiple rotations about distinct axis. For general representation of angular velocities Skew symmetric Matrices were introduced.

3. Definition Skew matrix is a square matrix A whose t ranspose is also its negative; that is, it satisfies the condition -A = A T . If the entry in the i th row and jth column is a ij ,i.e. A = (a ij ) then the skew symmetric condition is a ij = −a ji . For example, the following matrix is skew-symmetric:

4. Properties

5. Derivative of rotation matrix Differentiating both sides 1

6. Which shows that S is a skew symmetric Now as Multiplying both sides of equation-01 by R we get

7. Angular Velocity and Acceleration Kinematics Suppose that rotation Matrix R is time varying i.e.R =R(t) Time derivative of R is(as proved above)

8. Thanks