- Questions & Answers
- Accounting
- Computer Science
- Automata or Computationing
- Computer Architecture
- Computer Graphics and Multimedia Applications
- Computer Network Security
- Data Structures
- Database Management System
- Design and Analysis of Algorithms
- Information Technology
- Linux Environment
- Networking
- Operating System
- Software Engineering
- Big Data
- Android
- iOS
- Matlab

- Economics
- Engineering
- Finance
- Thesis
- Management
- Science/Math
- Statistics
- Writing
- Dissertations
- Essays
- Programming
- Healthcare
- Law

- Log in | Sign up

robotics

Problem 5: Consider the motion of a thin flat disk rolling on a plane shown in Figure: Problem 3. The configuration space of the system is parameterized by the xy location of the contact point of the disk with the plane, the angle 0 that the disk makes with the horizontal line, and the angle ¢ of a fixed line on the disk with respect to the vertical axis. Figure: Problem 3: Disc Rolling on a Plane ‘We assume that the disk rolls without slipping. Writing these equations with q = (6, x, y, ©) we have the corresponding kinematic equations of motion z— pcosf =0 §— psinfé =0, where, p > 0 is the radius of the disk. ---------Continued on next page Page 1 of 2 ‘Writing the above equations in the corresponding control system format as 0 ree ba]. ul] _ _ a0=|3|=lo1 921] = [email protected][email protected] + gu: ¢ : Here, g1 and g; are 4x1 column vectors; control inputs u; = ¢ = the rate of rolling, and uz = 6 = rate of turning about the vertical axis. 1) Find the column vectors gi and ga. Using Lie algebra, 2) Evaluate g3 = [g1, g2] and ga = [g2, g3]. 3) Check if the complete span {g1, g2, g3, g4} is of full rank for the controllability of the system. Problem1: For trajectory generation of an industrial robot, evaluate the coefficients of the fifth-order polynomial s(t) = ast’ + ast* + ast’ + at? + ast + ao with time scaling that satisfies s(T) = 1 and s(0) = $(0) =5(0) = $(T) =8(T) = 0, where the initial time t = 0 and the final time T =1. Problem 2: For a one degree-of-freedom (DOF) robotic system of the form mi + bx + kx =f, where fis the control force and m = 4 kg, b=2 Ns/m, and £ = 0.1 N/m, obtain a proportional — derivative (PD) controller that yields critical damping and a 2% settling time of 0.01 sec.

Problem 5: Consider the motion of a thin flat disk rolling on a plane shown in Figure: Problem 3. The configuration space of the system is parameterized by the xy location of the contact point of the disk with the plane, the angle 0 that the disk makes with the horizontal line, and the angle ¢ of a fixed line on the disk with respect to the vertical axis. Figure: Problem 3: Disc Rolling on a Plane ‘We assume that the disk rolls without slipping. Writing these equations with q = (6, x, y, ©) we have the corresponding kinematic equations of motion z— pcosf =0 §— psinfé =0, where, p > 0 is the radius of the disk. ---------Continued on next page Page 1 of 2 ‘Writing the above equations in the corresponding control system format as 0 ree ba]. ul] _ _ a0=|3|=lo1 921] = [email protected][email protected] + gu: ¢ : Here, g1 and g; are 4x1 column vectors; control inputs u; = ¢ = the rate of rolling, and uz = 6 = rate of turning about the vertical axis. 1) Find the column vectors gi and ga. Using Lie algebra, 2) Evaluate g3 = [g1, g2] and ga = [g2, g3]. 3) Check if the complete span {g1, g2, g3, g4} is of full rank for the controllability of the system. Problem1: For trajectory generation of an industrial robot, evaluate the coefficients of the fifth-order polynomial s(t) = ast’ + ast* + ast’ + at? + ast + ao with time scaling that satisfies s(T) = 1 and s(0) = $(0) =5(0) = $(T) =8(T) = 0, where the initial time t = 0 and the final time T =1. Problem 2: For a one degree-of-freedom (DOF) robotic system of the form mi + bx + kx =f, where fis the control force and m = 4 kg, b=2 Ns/m, and £ = 0.1 N/m, obtain a proportional — derivative (PD) controller that yields critical damping and a 2% settling time of 0.01 sec.

Answered Same DayDec 16, 2022

To evaluate the coefficients of a fifth-order polynomial for trajectory generation of an industrial

robot, we need to satisfy

ṡ(T) = s(̈T) = 0.

The polynomial s(t) can be written in the following form:

s(t) = a5t^5 + a4t^4 + a3t^3 + a2t^2 + a1*t + a0

To satisfy the condition s(0) = 0, we set t = 0 and solve for a0:

s(0) = a50^5 + a40^4 + a30^3 + a20^2 + a1*0 + a0 = 0

Therefore, a0 = 0.

To satisfy the condition ṡ(0) = 0, we take the first derivative of s(t) and set t = 0:

ṡ(t) = 5a5t^4 + 4a4t^3 + 3a3t^2 + 2a2t + a1

ṡ(0) = 5a50^4 + 4a40^3 + 3a30^2 + 2a20 + a1 = 0

Therefore, a1 = 0.

To satisfy the condition s(̈0) = 0, we take the second derivative of s(t) and set t = 0:

s(̈t) = 20a5t^3 + 12a4t^2 + 6a3t + 2*a2

s(̈0) = 20a50^3 + 12a40^2 + 6a30 + 2*a2 = 0

Therefore, a2 = 0.

To satisfy the condition ṡ(T) = 0, we take the first derivative of s(t) and set t = T:

ṡ(T) = 5a5T^4 + 4a4T^3 + 3a3T^2 + 2a2T + a1

ṡ(T) = 5a51^4 + 4a41^3 + 3a31^2 + 2a21 + a1 = 0

Therefore, a4 = 0.

To satisfy the condition s(̈T) = 0, we take the second derivative of s(t) and set t = T:

s(̈T) = 20a5T^3 + 12a4T^2 + 6a3T + 2*a2

s(̈T) = 20a51^3 + 12a41^2 + 6a31 + 2*a2 = 0

Therefore, a3 = 0.

Finally, we need to satisfy the...

SOLUTION.PDF## Answer To This Question Is Available To Download

- HW06 with Milestones EE6560 Power System Protection 1Do 12.47kV distribution protection and coordination. The HW06 ASPEN model, coordination summary table, and an excerpt from Ameren PS-50 are...Mar 25, 2023
- Answer the 3 problems, please include all work leading to the answerMar 25, 2023
- Page 1 of 5 HW08 EE6560 Power System Protection 1For HW08 1) Set transformer differential relay. Complete the ABB HU differential relay table below for this transformer carrying...Mar 24, 2023
- Research Report Purpose: The purpose of this project is to research and report on a communications standard that has not been studied in this course. A report must be written based upon...SolvedMar 21, 2023
- Please solve the 4 problems listed in the PPT presentation, make sure to show where all units come from, and show all work and all steps to the answers.Use the attached video for guidance and details...SolvedMar 17, 2023
- Design of a High Frequency Ring Oscillators and Drive a Standard 50 Ω Load In this project, you have to design and simulate a ring oscillator and rig oscillator will drive a standard load,...Mar 15, 2023
- I have ONLINE EXAM 10 MARCH. Need to do everything by RIGHT HANDING AND SEND ME BY ONE TASK! BECAUSE I NEED TO REWRITE. ALSO I NEED TO GET MINIMUM 90% GRADE. I have all HW and SOLUTIONS FROM...Mar 05, 2023
- https://jcpseschool.blackboard.com/webapps/assessment/take/launch.jsp?course_assessment_id=_59621_1&course_id=_5098_1&content_id=_360563_1&step=nullFeb 27, 2023
- HW05 EE6560 Power System Protection 1For HW05 assume that the ground overcurrent Device 51N provides adequate and sufficient single line to ground fault coverage (perhaps you'll do 51N in a...SolvedFeb 25, 2023
- Please answer the problems and provide all steps to the answerSolvedFeb 14, 2023

Copy and Paste Your Assignment Here

Copyright © 2023. All rights reserved.