simple robotics calculations

1. “A“ robot has wheels with a 5cm radius and which are 30cm apart. A Segway robot has wheels with a 30 cm radius and which are 60cm apart. Both robots have a differential drive. For both robots, compute the velocity of the robot, measured in terms of ẋR, ẏR, and ̇, when the robot’s wheels are rotating as follows (i.e. one set of answers for each condition): (a) Both wheels are rotating clockwise (when viewed from position A in Figure 1, on the next page) at a speed of 1 radian per second. (b) The right wheel is rotating clockwise (when viewed from position A in the figure) at a speed of 1 radian per second, and the left wheel is rotating in the opposite direction at the same speed. (c) The right wheel is rotating clockwise (when viewed from position A in the figure) at a speed of This is pretty much all that needs to be done: 1 radian per second, and the left wheel is rotating in the opposite direction at a speed of 0.5 radians per second. Your answer should give ẋR and ẏR in meters per second, and ̇in radians per second. 2. Consider the Create, as described in the previous question. If both its wheels are rotating clockwise (when viewed from position A in Figure 1, on the next page) at a speed of 1 radian per second (as in part (a) of the previous question), and θI is 35 degrees, what is the velocity of the robot in terms of ẋI, ẏI, and ̇? 3. If the robot from the previous question starts at a location of xI = 2 and yI = 1 (both coordinates in meters), and drives for 10 seconds with both wheels rotating at 1 radian per second, what will its final location be? 4. If the robot from the previous question drives another 10 seconds with its wheels rotating at 2 radians per second, what will its final location be after the combined motion described in Questions 4 and 5?