ROBOTICS EXPERIMENT 3 Basics of Trajectory Planning for Robot Arm with Matlab
LECTURER
: DR. MUHAMMAD JUHAIRI AZIZ SAFAR PM. DR. WAN KHAIRUNIZAM WAN AHMAD
PLV
: MR. WAN MOHD NOORIMAN WAN YAHYA MR. ERDY SULINO MOHD MUSLIM TAN
TECHNICIAN
: MR. MOHD AL HAFIZ
GROUP
:____________
NAME: 1)_____________________________ DATE
:____________
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MATRIC NO: __________________
ENT372 Robotics Laboratory Module
EXPERIMENT Basics of Trajectory Planning for Arm Robot with Matlab
1. OBJECTIVES: 1.1 To understand the basic principle of robot arm. 1.2 To understand the kinematics and simulate using Matlab.
2. COMPONENTS & EQUIPMENTS: 1 Desktop Computer with Matlab
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ENT372 Robotics Laboratory Module
3. TRAJECTORY PLANNING FOR ROBOT ARM:
3.1 Introduction Trajectory planning relates to the way a robot is moved from one location to another in a controlled manner. A trajectory contains a sequence of movements between motion segments, in straight-line motions, or in sequential motions. Trajectory planning requires the use of both kinematics and dynamics of robots. 3.2 Kinematics The kinematics of a robot can be solved using numerical or analytical approach. The forward kinematics will enable us to determine where the robot’s end (hand) will be if all joint variables are known. Inverse kinematics will enable us to calculate what each joint variable must be if we desire that the hand be located at a particular point and have a particular orientation. Figure 1 shows a general structure for a three degrees of freedom (3-DOF) planar arm robot.
Figure 1. 3-DOF Planar Arm Robot
The geometrical approach to solve the inverse kinematics are as follows: The position of C can be written as
b = x ¡ l3 cos µ
(1)
a = y ¡ l3 sin µ
(2)
Therefore, the angle³of ´ OC to the X -axis is
a µb ¶ y ¡ l3 sin µ ¡1 = tan x ¡ l3 cos µ
Á = tan¡1
The inner angle of OAC µ and OBC¶are
® = cos¡1
l12 + c2 ¡ l22 2l1 c
(3)
(4)
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ENT372 Robotics Laboratory Module
µ ¡1
¯ = cos
l12 + l22 ¡ c2 2l1l2
¶
(5)
where,
c=
p
a2 + b2
Thus, the joint angles can be obtained as
µ1 = Á § ®
(6)
µ2 = §(¯ ¡ ¼)
(7)
µ3 = µ ¡ µ1 ¡ µ2
(8)
3.3 Basics Trajectory Planning If the trajectory is a straight line and the division number of approximation calculation as N, the changes in the variables can be calculated as
xf ¡ xi N yf ¡ yi ¢y = N µf ¡ µi ¢µ = N
(9)
¢x =
(10) (11)
where, i and f are referring to the initial and final position of the trajectory. Thus, the orientation and position of the joints can be determined by replacing back the value into forward and inverse kinematics equations.
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ENT372 Robotics Laboratory Module
4. PROCEDURE: Task: Simulate a two degrees of freedom (2-DOF) planar arm robot as shown in Figure 2. The required trajectory will be provided during laboratory session.
Figure 2. 2-DOF Planar Arm Robot 4.1 Forward and Inverse Kinematics Solve the forward and inverse kinematics using geometrical approach.
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