FYP Presentation
FYP Presentation
FYP Presentation
Presented by:
BOUAMER Tarek
ELGHERIBI Abdellah Nabih
Outlines
General Introduction
Robot Kinematics
Drive Circuit
Digital Controller
Robot Control
Trajectory Planning
ROS
Motion Planning
Conclusion
Introduction
Our Goal
Replacing the drive/control box and software of ED-7220C Arm with
an open one
Steps :
Mathematical analysis for the forward and inverse kinematics of the
robot.
Design the Actuators Power drive system.
Design a digital position controller for the robot arm joints.
Design an interface to generate and simulate robot trajectories for
pick-and-place task in a cell environment with obstacles.
Integrate the interface with the robot control system.
Robot Kinematics
Kinematics is the description of motion without regard to the forces that cause it.
Kinematics analysis is divided into:
Direct/Forward Kinematics
F(1,2 ,..,n ) = [x, y, z, R]
Inverse Kinematics
F(x, y, z, R) = 1, 2,, n
Direct/Forward Kinematics
Tii1 = Rot (z, i) Trans (z, di) Trans (x, ai) Rot (x, i)
Where the four quantities i , ai , di , i are the parameters of link i and joint i.
1 = 1 ( )
1
=
0
0
=
0
0
0
0 =
0
1
1
0
1
0
1
0 1 , 2 , = 10 (1 ) 21 2 1 ( )
1 is a homogenous transformation matrix of the coordinates of frame i to frame i-1
0 is a 3x3 rotation matrix
0 is a three dimensional vector
ED-7220C DH Paramters
Table (1.1): DH parameter for ED-7220C robot arm
Using the paramters from table (1.1) the matrix T1 to T6 can be obtained as shown
below
0
0 1 2 3 4
5 = 1 2 3 4 5 =
= 50
Inverse Kinematics
1. Geametric Approach
2. Analytical (algebraic) Approach
Geametric Approach
1= atan2(y, x)
= 2 + 3 + 4
4 = 5 cos()
4 = 5 sin
= 2( 2 +22 32 , 22 s)
= 2 4 1 , 4
2 =
3 = 2 2 22 32 , 22 3
4 = 2 3
Drive Circuit
Enable Pins Encoders Motos Direction
Limit Switches
Bridge Diodes
L298 H-bridge
Digital Controller
3.3V
7-12V
6-16V
54 (of which 12 provide PWM output)
130 mA
800 mA
800 mA
512 KB all available for the user applications
96 KB (two banks: 64KB and 32KB)
84 MHz
Robot Control
Control Techniques
Coupled control
a manipulator with n DOFs can be described in
coupled control :
+ , + =
: Inertia matrix; Symmetric Positive Definite
matrix.
: Gravity vector from the inertial frame.
: Coriolis and centripetal matrix.
Disadvantages
Extremely complicated and difficult to determine the
parameter of the equation.
Dynamic effects are not taking consideration in the equation:
elastic deformation of bearing and gears.
deflection of the links under load, and vibration.
Decoupled control
The manipulator is controlled as (SISO)
system.
Any coupling effect due to the motion of the
other links .
Disturbance D
The force of gravity acting on the Links.
Design of Controllers
Cascade compensator:
Feedforward compensator.
No overshoot (critical
damping).
PI compensator
Shoulder
Elbow
PI compensator
Tuning the PI parameters using experimental
iterative technique.
Procedure:
1) Set the Integral and derivative gains to zero.
PI compensator
= +
()
0
Feedforward compensator
From 90 to 35
From 35 to 90
Shoulder compensator
14.71%
31.08%
Trajectory Planning
The trajectory should respect:
Joints limits.
Max. velocities.
Max. accelerations.
Max effort (joint torques).
At time tf:
Requires 4 constraints
Requires 6 constraints
Smooth acceleration
Ramp-up
Blend Region
Ramp-down
Initial configuration:
q(0) = q0
q(0) = 0
Final configuration:
q t f = qf
q tf = 0
Between 0 and tb (Ramp-up) we have :
LSPB trajectory q0= 0, qf = 40, and t0 =0, tf =1, Vmax = 60. In this
case tb=1/3 .
Tree
(RRT)
No
FAILURE
Yes
No
The motion is
collision-free
?
Yes
Yes
No
Pnew is a goal
?
3D exploration
Robot Modeling
Unified Robot Description Format (URDF).
Continuous.
Fixed.
Revolute.
Prismatic.
ED 7220 C in Rviz
Home Pose
Pick pose
Place Pose
Planning algorithm
RRT configuration
Scene Obstacles
Final Scene
BASE Joint
Waypoints
Waypoints are selected points in the resulting
path.
Cartesian waypoints [X Y Z].
Joint Space [ ].
Remarks:
To execute the motion planning in the real
robot we use the joint space waypoints (FK).
The waypoints are send serially from the PC
to the Arduino.
Between two waypoints; a time delay Td is set.
Td
Td is selected experimentally:
To get a smooth motion; where the controller has
to be updated before the joint ( ) settle at the
previous command.
Path achieved in reality has to have small error
with simulated robot motion planning.
Video
CONCLUSION
Study the Kinematic of ED 7220C:
Forward Kinematic.
Inverse Kinematic.
Design controllers:
Precision.
steady state error.
Cancel the disturbances and reduce the vibrations.