Differences

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

--- robotic_manipulators [2016/07/21 10:53] – joaomatos
+++ robotic_manipulators [2016/08/06 23:28] (current) – joaomatos
@@ Line 1: / Line 1: @@
 ===== Robotic Manipulators Basics =====
+**Author:** Joao Matos Email: <jcunha@id.uff.br> <!-- replace with your email address -->
+\\
+**Date:** Last modified on 6/8/2016
+\\
+**Keywords:** Robotic Manipulator , Serial Arm, Denavit Hartenberg, Inverse kinematics
+\\
  This page is to introduce the theory behind the robotic manipulators. It will be used the Denavit-Hartenberg parameters notation to describe the geometry of a serial chain of links and joints (Serial-Link).Using the robotic toolbox developed by Peter Corke (RVCtoolbox) we can visualize and understand more about the Denavit-Hartenberg parameters and how the process of the inverse kinematics works.
@@ Line 45: / Line 52: @@
 **Four steps and rules to define the frame on each joint **
-  - You will define the z axes as the joints rotation axes. Start drawing only the z axis on all your joints, starting from z(0) at the base and going to z(....) at the end effector . DON'T FORGET that the z axis of the end effector must be in the same direction of the z axis of the last joint.
+  - You will define the z axes as the joints rotation axes (CCW). Start drawing only the z axis on all your joints, starting from z(0) at the base and going to z(....) at the end effector . DON'T FORGET that the z axis of the end effector must be in the same direction of the z axis of the last joint.
-  - Now you will draw the x axes , the x axis must be perpendicular to both z(j-1) and z(j). Do it for every joint. If you have more than one direction that satisfy this condition , you can choose the direction that goes from z(j-1) to z(j) axes. DON'T FORGET that the x axis of the end effector must be in the same direction of the x axis from the last joint
+  - Now you will draw the x axes , the x axis must be perpendicular to both z(j-1) and z(j). Do it for every joint. If you have more than one direction that satisfy this condition , choose the direction that goes from z(j-1) to z(j) axes. DON'T FORGET that the x axis of the end effector must be in the same direction of the x axis from the last joint
   - Now you will draw the y axes.The y axis must follow the right hand rule , from z axis to x axis. And don't forget that the y axis of the end effector must be in the same direction of the y axis of the last joint.
   - Now that you drawn the three axis on every joint , you must check if the x(j) axis intersect the z(j-1) axis. To your DH notation be right , every x(j) axis must intersect the z(j-1) axis. If you don't have this , you must translate your (j) frame , in order to guarantee this intersection.
@@ Line 55: / Line 62: @@
-  * **(aj)**: Is the displacement along the xj axis between the center of the frame (j-1) and frame (j).
+  * **(aj)**: Is the displacement along the xj axis DIRECTION between the center of the frame (j-1) and frame (j).
   * **(αj)**: Is the Rotation around the xj axis that make the axis z(j-1) and z(j) to match each other.
-  * **(dj)**: Is the displacement along the z(j-1) between the center of the frame (j-1) and frame (j).
+  * **(dj)**: Is the displacement along the z(j-1) DIRECTION between the center of the frame (j-1) and frame (j).
   * **(θj)**: If you have only revolute joints , you can call them q1,q2,q3,q4.......
@@ Line 82: / Line 89: @@
  Following the step by step and rules presented previously, lets calculate the DH parameter for the serial arm available on the DASL at UNLV.
- {{ ::eixos_e_distancias.jpg?direct |}}
+{{ ::novos_frames.jpg?direct |}}
  ** Defining the Frames **
@@ Line 94: / Line 101: @@
 -> checking if every x(n) axis intersect the z(n-1) axis.
 {{ ::ded4.jpg?direct |}}
--> Create the table and get the DH parameters.
+-> Change the axis that don't follow rule 4.
 {{ ::ded5.jpg?direct |}}
+-> Create the table and get the DH parameters.
+{{ ::ded6.jpg?direct |}}
+----
@@ Line 277: / Line 289: @@
 L1=11;
-L2=14;
+L2=15;
-L3=8.5;
+L3=10;
 L4=21;
 L5=8;
 pi=3.1416;
-L(1)=Link([0 -L1 0 pi/2 0]);
+q0=[0 0 0 0 0];
-L(2)=Link([0 0 -L2 0 0]);
-L(3)=Link([0 0 -L3 0 0]);
+L(1)=Link([0 -L1 0 -pi/2 0]);
-L(4)=Link([0 0 0 -pi/2 0]);
+L(2)=Link([0 0 L2 0 0]);
+L(3)=Link([0 0 L3 0 0]);
+L(4)=Link([0 0 0 pi/2 0]);
 L(5)=Link([0 -(L4+L5) 0 0 0]);
@@ Line 292: / Line 306: @@
 DaslArm=SerialLink(L,'name','DaslArm');
-DaslArm.teach()
+DaslArm.teach(q0)
 </Code>
-{{ ::teach_serial.jpg?direct |}}
+{{ ::novoteach.jpg?direct |}}
 The teach command will create a window that allow you to change the q1,q2,q3,q4,q5 rotation and see how the arm moves , it's good to change this rotation by hand to check if your Denavit-Hartenberg parameters are OK.
+ If everything is moving as the arm moves , we can use the IK solver available on the RVC toolbox to get the joints angles given a desired end effector pose , you just need to add this code after defining your serial link object :
+<Code>
+%END EFFECTOR POSITION
+% trotx(angle) = rotate (angle) about the x axis
+% troty(angle) = rotate (angle) about the y axis
+% trotz(angle) = rotate (angle) about the z axis
+% transl(x,y,z) = pure translation of x , y , z
+% The end effector pose will be a combination of tranls and trot
+%For example lets use a pure translation .
+T=transl(20,35,-30);
+%IK SOLVER
+%Initial pose (all rotations = 0)
+q0=[0 0 0 0 0];
+%Mask to be used on the IK solver (x y z rotx roty rotz)
+m=[1 1 1 0 0 0];
+%Solving the IK and converting to degrees
+q_ikine=DaslArm.ikine(T,q0,m);
+q_degrees=q_ikine*(180/pi);
+%Creating a trajectory from q0 to the IK solution
+%Time variable
+t=[0:0.05:4];
+%trajectory
+q_TRAJ=jtraj(q0,q_ikine,t);
+%Plot the result
+DaslArm.plot(q_TRAJ)
+</Code>
+ This code will open a window to show the animation of the serial arm , going from an initial position q0 ( we defined as all the joint angles =0 ) to a final position - which is the IK solution. Is important to note that some end effector poses cannot be reached by the arm , so when you input these values , you will get some errors saying that the IK solver took more than 1000 iterations to find a solution and you will get an approximated solution. This IK solver available on the toolbox is not 100% accurate , the best choice is to program the IK solver by yourself , you can easily find a lot of algorithm to solve an IK problem on the internet.