Introduction to Robotics

Transcription

1 Université de Strasbourg Introduction to Robotics Bernard BAYLE, bernard

2 Modelling of a SCARA-type robotic manipulator SCARA-type robotic manipulators: introduction SCARA-type manipulators are 4 joint-robotic systems with a RRP R structure. Figure 1.1 represents two industrial SCARA robots. The second one, the Samsung RSM-5, is the subject of this study. (a) Robot EPSON EL-653M (b) Robot Samsung RSM-5 Figure 1.1: SCARA-type robotic manipulators Because of their geometry these robots are well adapted to robotic paletization, when objects have to be picked and placed. There are many such SCARA-type robots in industrial production sites. The main characteristics of the Samsung RSM-5 robot are given in figure 1.2. Scheme 1.2(a) allows to understand the kinematic architecture of this robotic manipulator. ii

3 (a) Scheme and dimensions (b) Specifications Figure 1.2: Characteristics of the Samsung RSM-5 robot 1.1 Robot geometry Workspace 1. The robot is a RRP R serial robot. The last two joints are related to the vertical motions ( P- joint) and to the rotation ( R joint) of the end effector. Draw the kinematic scheme of this robot. We now consider the manipulator workspace. Without obstacles, the first vertical axis, the joint limits and of course the links length and positions are the only limitations of the system workspace. 2. Note the values of the joint angular limits. 3. The robot is symmetric and has symmetric joint limits. Represent the system (upper view) when the robot joint limits are reached for joints 1 and 2. Keep an adequate scale for the figure. 4. In this figure, i.e. in an horizontal plane, represent the workspace bounds (joints 3 and 4 are not considered). iii

4 5. Precise the interest points of the workspace limit. 6. What is the dimension of the operational space? Do all the joints have the same influence on the robot end effector position? From the previous remarks, represent the 3D shape of the manipulator workspace, for any orientation of its end effector. Parameterization 1. Draw the system scheme in an adequate configuration for modelling using the modified Denavit Hartenberg parameterization. 2. Place frames F 0 to F 4 on the scheme, according to the DH convention. 3. Write in a table the values of the modified Denavit-Hartenberg parameters: a i 1, α i 1, r i, θ i. Add a line to give the configuration parameters q i corresponding to the scheme. 4. Find in the robot specifications the values of the parameters. 1.2 Robot modelling Kinematics Direct kinematic model 1. Recall the expression of the homogeneous transformation matrix T i 1, i from a frame F i 1 to F i, using the modified DH parameters. Compute matrices T i 1, i, for i = 1,..., Multiply the matrices in order to obtain the direct kinematic model of the robot. 3. Check the obtained result in the case of one or two particular configurations, such as those corresponding to the workspace bounds. 4. Give the end effector orientation with the Euler angles. Is this the best representation of orientation for this manipulator? Propose an alternative choice. Inverse kinematic model 1. What can we say about the number of admissible solutions? 2. Find the inverse kinematic model of the robot. iv

5 1.2.2 Differential kinematics 1. Recall the definition of the differential kinematic model and of the Jacobian matrix J(q). 2. If the end effector orientation is represented by the yaw angle α = x 4 : ẋ 1 v x q 1 ẋ 2 ẋ 3 = v y v z = J(q) q 2 q 3. ẋ 4 ω z q 4 Compute the Jacobian matrix using velocities compositions. 3. Check the result by the direct calculation of the Direct Differential Kinematic Model partial derivatives. 4. The Jacobian rank gives the degree of freedom of the robot end effector. When the rank is not maximum, the robot can no longer move in one or more workspace directions. Find the configurations for which J(q) decreases. Comments. v