Please show work! I want to udnerstand how to get these answers for my midterm.

Question

Please show work! I want to udnerstand how to get these answers for my midterm. Thank you!

Given robot You are given a robot as shown in Figure with dimensions as shown. We observe it from an inertial frame denoted by IXIY. Let us assume r - 2m and d - 1m. For each question, the robot starts with pose P-[4.0, 2.0, 30degree]T in the inertial frame. Further, you set the robot velocities at the start, and keep it unchanged for each question. Finally the robot can drive its wheels between 2ero and one radians per second. Question 1.1: Assume for this question that the robot is only capable of driving both wheels at the same angular velocity. Assuming we drive the robot as fast as we can. what is its position in the inertial frame after five seconds? Question 1.2: We will now relax the condition that both wheels spin at the same angular velocity. What should the angular velocities of the individual wheels be set to, to reach [Ix, 3-5, 87.3degree]T in the inertial frame in five seconds? What is the value of Ix? Question 1.3: The objective for this question is to turn the robot to align the robot x axis parallel to the inertial x axis facing the negative direction. What is the fastest way to drive the robot to do the same? How long does this take? What is the final pose of the robot in the inertial frame?

Explanation / Answer

Hi,

Please find the links to the solutions. Took me nearly 2 hours!

Part 1.1

https://drive.google.com/file/d/0BzsApW5yffhsODZWekF4X0psVnM/edit?usp=sharing

Part 1.2

https://drive.google.com/file/d/0BzsApW5yffhsWk9wR3RXaks1dEE/edit?usp=sharing

https://drive.google.com/file/d/0BzsApW5yffhsWk9wR3RXaks1dEE/edit?usp=sharing

https://drive.google.com/file/d/0BzsApW5yffhscFNWZlRfVHNoX3c/edit?usp=sharing

Part 1.3

https://drive.google.com/file/d/0BzsApW5yffhsZnQyUkNGZ2lHNmM/edit?usp=sharing

https://drive.google.com/file/d/0BzsApW5yffhsVEJBNk91YUZ6TDg/edit?usp=sharing

Let me know if anything is unclear. And do rate!

Cheers,

Saurav

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