Differences

This shows you the differences between two versions of the page.

--- robotic_manipulators_ik [2016/08/06 21:22] – joaomatos
+++ robotic_manipulators_ik [2016/10/23 20:14] (current) – dwallace
@@ Line 1: / Line 1: @@
 ===== Inverse Kinematics Solver using Damped Least Squares Method =====
+**Author:** Joao Matos Email: <[email protected]> <!-- replace with your email address -->
+\\
+**Date:** Last modified on 6/8/2016
+\\
+**Keywords:** Inverse Kinematics , Damped Least Squares, Serial Arm
+\\
+ This tutorial presents an algorithm to implement the Damped Least Squares method to calculate Inverse Kinematics problems.
+----
  Between many algorithm to solve the Inverse Kinematics problem , the damped least squares method avoids many of the problems with the peusoinverse algorithm , and can give a good nummerical solution for the problem.The goal is to find the value of delta theta that minimizes the quantity:
@@ Line 38: / Line 52: @@
 ===== Pseudo Algorithm =====
-  * [[robotic_manipulators_ik_cpp|Inverse Kinematics Using Damped Least Squares method in C++]]
+  * [[robotic_manipulators_ik_cpp|Inverse Kinematics Using Damped Least Squares method in Cpp]]
+    * Example of the method programmed in Cpp using Visual Studio and Eigen library
   * [[robotic_manipulators_ik_matlab|Inverse Kinematics Using Damped Least Squares method in Matlab]]
+    * Example of the method programmed in Matlab and Simulated by RVC toolbox
- The algorithm to be programmed will follow this idea:
+ These two codes above were programmed using the same algorithm. The pseudo algorithm used is shown bellow.
   - Calculate A1,A2,A3,A4 and A5 given the initial position.
@@ Line 75: / Line 91: @@
-Running in Visual Studio ,C++ and Eigen library (library to deal with matrices).
+Running in Visual Studio ,Cpp and Eigen library (library to deal with matrices).
 <Code>
@@ Line 138: / Line 154: @@
  Be careful here , the rotation matrix R , is from frame 0 to frame i-1 , but our homogeneous transformation matrices are from frame j-1 to frame j. For example , A1 is from frame 0 to frame 1 , A2 is from frame 1 to frame 2. But to find the Jacobian linear velocity we will need frame 0 to frame 2 , frame 0 to frame 3  , and so on... We can easily find this multiplying the transformation matrices. This way ,R(00) is the k vector itself ,  R(01) come from A1 , R(02) come from A1.A2 , R(03) come from A1.A2.A3 , R(04) come from A1.A2.A3.A4 .
- Note here that the R matrix will multiply the "k" vector , (0,0,1) transposed , this way, the information we need is in the third column of the transformation matrix ( third column and first third rows, the last row does not contain any information , is just a neutral row ). **THIS IS SIGNED IN RED IN THE FIRST PICTURE OF THIS SECTION**
+ Note here that the R matrix will multiply the "k" vector , (0,0,1) transposed , this way, the information we need is in the third column of the transformation matrix ( third column and first third rows, the last row does not contain any information , is just a neutral row ). **THIS IS SIGNED IN RED IN THE LAST PICTURE OF LAST SECTION**
  So, the next step of the IK code is to find the result from the homogeneous transformation matrices multiplication. Just create new matrices , for example:
@@ Line 192: / Line 208: @@
  The end effector position can be found in the multiplication A1.A2.A3.A4.A5 . O(00) is 0 because is the distance from frame 0 to frame 0. 0(01)can be found in A1, O(02) can be found in A1.A2 , O(03) can be found in A1.A2.A3 , O(04) can be found in A1.A2.A3.A4.
-  For example (is convenient to define a vector with the difference - the second term of the cross product ) to organize better the code:
+ For example (is convenient to define a vector with the difference - the second term of the cross product ) to organize better the code:
  <Code>