A unicycle robot moving on the plane with linear velocity v and angular velocity w can...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A unicycle robot moving on the plane with linear velocity v and angular velocity w can be modeled by the nonlinear system: Pr = v cos 0, Py = v sin 0, 0=w, where (pr, Py) denote the Cartesian coordinates of the wheel and its orientation. Regard this as a system with input u = = [v w]¹ ER². Y I = Figure 3: Unicycle model X a) Construct a state-space model for this system in the form of f(z, u) with state: Pr cos 0+ (py - 1) sin 0 Pr sin 0+ (py 1) cos 0 0 II I2 = 13 T and output y = [172] ER² W b) Compute a local linearization for this system around the equilibrium point z* = 0, u* = 0. c) It is given that the trajectory w(t) = v(t) = 1, pr(t) = sint, py(t) = 1-cost, 0(t) = t, Vt > 0 is a solution to the system. Show that a local linearization of the system around this trajectory results in an LTI system. A unicycle robot moving on the plane with linear velocity v and angular velocity w can be modeled by the nonlinear system: Pr = v cos 0, Py = v sin 0, 0=w, where (pr, Py) denote the Cartesian coordinates of the wheel and its orientation. Regard this as a system with input u = = [v w]¹ ER². Y I = Figure 3: Unicycle model X a) Construct a state-space model for this system in the form of f(z, u) with state: Pr cos 0+ (py - 1) sin 0 Pr sin 0+ (py 1) cos 0 0 II I2 = 13 T and output y = [172] ER² W b) Compute a local linearization for this system around the equilibrium point z* = 0, u* = 0. c) It is given that the trajectory w(t) = v(t) = 1, pr(t) = sint, py(t) = 1-cost, 0(t) = t, Vt > 0 is a solution to the system. Show that a local linearization of the system around this trajectory results in an LTI system.
Expert Answer:
Related Book For
Systems analysis and design
ISBN: 978-0136089162
8th Edition
Authors: kenneth e. kendall, julie e. kendall
Posted Date:
Students also viewed these general management questions
-
Identify the top three challenges you think impact human resource management (HRM) in today's workplace. How do you think these challenges and opportunities will affect HRM in the next 10 years?
-
Do you agree with privacy advocates who contend that Facebook should provide ways for users to opt out of the mobile ad targeting? Why or why not?
-
In understanding the process of perception, do you agree with the observation that people are human information processors? Why?
-
1) A survey of 200 public universities indicated that the 25th percentile of the yearly tuition cost of the universities was $4600 and the 75th percentile was $7100. The minimum value was $2000, the...
-
What is the difference between ethics and financial integrity? How are they interconnected?
-
How does the provision of several types of financial services by one firm lead to a lower cost of information production for the firm?
-
What happens if you specify an invalid format string?
-
Optimus Company manufactures a variety of tools and industrial equipment. The company operates through three divisions. Each division is an investment center. Operating data for the Home Division for...
-
An 85 kg man is completing a workout with TRX suspension straps. Holding this position in static equilibrium he experiences a pulling force on his hands of 600 N at an angle of 160 o relative to the...
-
On January 1, 2019, Cayce Corporation acquired 100 percent of Simbel Company for consideration transferred with a fair value of $126,000. Cayce is a U.S.-based company headquartered in Buffalo, New...
-
How does this expert come up with $12 in variable costs? It seems to me that -$50K in profit when producing 10,000 units means that revenue was $600K, costs were -$650K, fixed costs were $250K, which...
-
During the month of February 2019. Wolf Company employees earned wages of $50,000 with the following withholdings and Wolf payroll tax expenses: Description Tax Rate Amount Salaries 50,000 Union...
-
What are the challenges and limitations of applying conflict theory in empirical research and social policy, particularly in terms of addressing complexities and nuances in power dynamics and social...
-
22. Over the past 8 years UTX Company common stock dividends have grown from $2.70 to $5.00 per share (currently). Determine the value of UTX common stock to an investor who requires a 16% rate of...
-
"Benish M-Score Model". How it is used? Was it applied in some of the more well-known financial reporting scandals? What are the pros and cons of the the "Model'?
-
How might a program manager in a police department apply the results of this research study to help police officers? What kind of program or initiative could they propose based on the results....
-
The force vector F has a magnitude of F = 375 lb and acts at point A at an angle = 12.3 with respect to vertical as shown. The force F is balanced by the tension forces parallel to the two rods AC...
-
The tractor is used to lift the 150-kg load B with the 24-mlong rope, boom, and pulley system. If the tractor travels to the right at a constant speed of 4 m/s, determine the tension in the rope when...
-
What does extensible markup language (XML) describe?
-
As a third member of the Worlds Trend Web site development group, respond in a brief written report to Lincoln and Mary about whether you should use a prototype to elicit recommendations from...
-
Create a CRUD matrix for the files of Worlds Trend.
-
The required rate of return is 12%, and the expected rate of inflation over the life of the project is forecast to remain steady at 3%. Should you invest in this project?
-
For your answer to Problem 3.11, construct an argument as to why this selection process is useful for deciding which project is best. Now, construct a counterargument to criticize this choice. In...
-
Scoring Model. Suppose the information in Problem 3.13 was supplemented by importance weights for each of the four assessment criteria, where 1 = low importance and 4 = high importance: Assume, too,...
Study smarter with the SolutionInn App