I\'ve been getting stuck getting through these problems. Please show work so i c

Question

I've been getting stuck getting through these problems. Please show work so i can understand how to do these problems. Thank you!

You are given a robot as shown in Figure 1 with dimensions as shown. We observe it from an inertial frame denoted by IXIY. Let us assume r = 2m and d = 1 m. For each question, the robot starts with pose P=[4.0. 2.0, 30 degree ]r 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 zero 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 10, 5.5] in the inertial frame? What is the robot s final orientation in the inertial frame? Question 1.3: The objective for this question is to turn the robot to face the origin. What is the fastest way to drive the robot to make it face its origin? 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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