Trajectory generation is an essential knowledge in robotics because it allows the time history of position, velocity and acceleration to be specified for each of the joints for robot motion. In general, motion of the robot in space needs to be smooth with defined limits of velocity and acceleration, with the initial and target positions achieved successfully. a) Design a cubic polynomial trajectory that will move a rotational joint from initial value of 15 degrees to 60 degrees in 3 seconds. Determine the coefficients of the cubic that accomplish this motion. b) Using parabolic blend, design a trajectory for the rotational joint for two segments, as shown in Figure Q4. Given the path point in degrees: 15 40 30 and the duration of the two segments are 3s and 2s with the assumption that the constant acceleration is 55/s. 0,() 40 30 15 3 Figure Q4 (10 marks) 5 (15 marks)