 New York University Robotic Direct and Inverse Kinematics Matlab Coding Task

ogna

Engineering

New York University

### Question Description

Please follow the instructions in the PDF, this assignment includes Matlab coding and a report.

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ROB-6003 Foudations of Robotics New York University, Fall 2020 Due on November 30, 11:59 PM 1 Project 3 updated November 16, 2020 Direct and Inverse Kinematics Consider the SCARA manipulator depicted below. For this project only the kinematic parameters are needed. You have received a trajectory for the the manipulator end effector. The trajectory is provided in a file named kinematic traj.mat and can be read using init.m. The manipulator parameters are d0 = 1 m, a1 = a2 = 0.5 m, l1 = l2 = 0.25 m θ1min = −π/2 rad, θ1max = π/2 rad, θ2min = −π/2 rad, θ2max = π/4 rad ml1 = ml2 = 25 kg, ml3 = 10 kg, Il1 = Il2 = 5 kgm2 , Il4 = 1 kgm2 kr1 = kr2 = 1, kr3 = 50 rad/m, kr4 = 20, Im1 = Im2 = 0.0001 kgm2 , Im3 = 0.01 kgm2 , Im4 = 0.005 kgm2 Fm1 = Fm2 = 0.0001 N · m · s/rad, Fm3 = 0.01 N · m · s/rad, Fm4 = 0.005 N · m · s/rad d3min = 0.25 m, d3max = 1 m, θ4min = −2π rad, θ4max = 2π rad As done for projects 1 and 2, the frames are depicted into the figure and the DH parameters are Link Link Link Link 1 2 3 4 di 0 0 d3 0 αi 0 0 0 0 θi θ1 θ2 0 θ4 ai a1 a2 0 0 Table 1: Table with DH parameters. Please not that the 0 frame is not coincident with the b frame. There is a translation from the ground plane denoted with d0 = 1. The frame 4 is coincident with the frame 3 at the starting. Be careful on the d3 component. The range of values is always positive. When the arm is fully extended (down towards the floor) the value is 1m whereas 0.25 when retracted (away from the floor). However, when you build your matrix note that d3 moves along −z2 axis and for this reason you translation in A23 should be negative as −d3 . Questions: 1 1. Generate a trajectory in the robot operational space of 4  s with trapezoidal velocity profile for  0 −0.80 0 at time t0 = 0.0, p1 = each segment passing trough the following waypoints p = 0       0 −0.80 0.5 at time  t1 = 0.6, p2 = 0.5 −0.6 0.5 at time t2 = 2.0, p3 = 0.8 0.0 0.5 at time t3 = 3.4, p4 = 0.8 0.0 0.0 at time t4 = 4.0. The trajectory should be generated such that the robot should not stop at each waypoint so that the waypoints are via points. The anticipation time for each segment should be 0.2 s. You need show the position, velocity and acceleration of your path. The sampling time will be Ts = 0.001 s. 2. Consider a 5 kg load placed at the end effector. Generate an inverse dynamic control approach. The setpoints for each joint have to be generated starting from the trajectory generated in the operational space considering a second order inversion kinematic algorithm developed during project 2. Instructions: • Make your code as a combination of matlab and simulink. The structure is already provided in the folders. For part 1, you can create all functions you need, but your program should run by playing the init traj.m function available in the folder. Once your trajectory has been generated save it in a mat file generated traj.mat. • For part 2 as usual, you should call your initialization in a function named init.m. For the second order inverse kinematic algorithm same rules of project 2 apply, so you will find the same files. You will have as well another couple of .m files related to control. You will notice in the simulink file that there is a specific subsystem where you should put your second order inverse kinematic algorithm and will give you as output the desired joint values. The trajectory you generated is loaded in the init.m file as generated traj.mat. Copy it from the previous part in the part 2 folder once you finished part 1. You will have to show your position and velocity errors in the joint space as well as the joint trajectories. You can use the same function for projects 1 and 2 as reference. 2 Report You need to summarize your results in a report submitted in pdf format and generated with latex or word. Please add on top of your manuscript your name and NYU ID. The report should not be more than 8 pages including plots. In addition to the results, please include your models and any explanation you think is appropriate. Do not just write equation, but try to add your logic process and explain why and how you used the equations or models you have in your code. 3 Grade Policy and Submission The overall score will be 100 and will be subdivided in the following way, part 1 (30 points), part 2 (60 points), and report quality and readability (10 points). Do not modify any part of the code as specified above. Any other type of modification will result in 0 points. All the files, including code and report, should be submitted in an unique zip file. 2 ...
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## Final Answer Hi, here is your assignment.

1

Robotic Direct and Inverse Kinematics
Name
University
Date
Part 1:
Output:

Figure 1: Position

Figure 2: Velocity

2

Figure 3: Acceleration

Figure 4: trajectory in the robot operational space of 4

Summary:
A robot’s end-effectors must be moved from position [0, 0, 0] to position [0.5, 0, 0.5] within 0.6
seconds. The duration of the initial acceleration phase should be 1 second. A trapezoidal velocity
profile should be used for the end-effectors position.
For position profiles :- we have a minimum three degree of polynomial equation because
position is a point function of any system. As, velocity is the rate of change of position of the
object. we have to differentiate the position polynomial equation of the profile.

3

So, the minimum degree of polynomial function for obtaining velocity profiles is two.
Moreover, as, acceleration is the rate of change of velocity of the object. we have to differentiate
the velocity polynomial equation of the profile. So, the minimum degree of polynomial function
for obtaining accel... yrrxneyn562 (226)
Cornell University Anonymous
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