Problem 2 (Map Building): Suppose at one time instance the robot has translated the amount of d with an initial orientation 0 and a range sensor reading of distance s. Compute the position of the obstacle that is detected by the sensor. Notice that the sensor is installed on the robot facing to its left. 10 y 5 0 -5 = [5,-4] =-40° -10 -10 -5 0 5 d=10 2 P 10 10 S=11 15 20

2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…

Problem 3: A coordinate frame, {B}, is located at the base of a robot manipulator. ŻB points upward. Three cameras are used to view the manipulator. Coordinate frames {C}, {D}, and (E} describe the camera positions and orientations. The origin of {C} is on the Xg - 2g plane. The cameras are mounted on tripods 1.5 units tall placed at the vertices of an equilateral triangle having {B} at the incenter. The robot frame is on the focal axis of each camera (the camera's 2- axis), and the Euclidean distance from (B} to any camera is 5 units, thus "PBORG = "PBORG = "PBORG = [0 0 5]" Compute the camera transformation matrices: T, T, and T. %3D