The question above Consider the simplified robot shown in Figure 25.33. Suppose

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The question above

Consider the simplified robot shown in Figure 25.33. Suppose the robot's Cartesian coordinates are known at all times, as are those of its goal location. However, the locations of the obstacles are unknown. The robot can sense obstacles in its immediate proximity, as illustrated in this figure. For simplicity, let us assume the robot's motion is noise-free, and the state space is discrete. Figure 25.33 is only one example; in this exercise you are required to address all possible grid worlds with a valid path from the start to the goal location. a. Design a deliberate controller that guarantees that the robot always reaches its goal location if at all possible. The deliberate controller can memorize measurements in the form of a map that is being acquired as the robot moves. Between individual moves, it may spend arbitrary time deliberating senso goal Figure 25.33 Simplified robot in a maze. See Exercise 25.9 b. Now design a reactive controller for the same task. This controller may not memorize past sensor measurements. (It may not build a map!) Instead, it has to make all decisions based on the current measurement, which includes knowledge of its own location and that of the goal The time to make a decision must be independent of the environment size or the number of past time steps. What is the maximum number of steps that it may take for your robot to arrive c. How will your controllers from (a) and (b) perform if any of the following six conditions apply continuous state space, noise in perception, noise in motion, noise in both perception and motion, unknown location of the goal (the goal can be detected only when within sensor range), or moving obstacles. For each condition and each controller, give an example of a situation where the robot fails (or explain why it cannot fail)

Explanation / Answer

# generate and send the correct commands to the robot def _send_robot_commands( self ): ... v_l, v_r = self._uni_to_diff( v, omega ) self.robot.set_wheel_drive_rates( v_l, v_r ) def _uni_to_diff( self, v, omega ): # v = translational velocity (m/s) # omega = angular velocity (rad/s) R = self.robot_wheel_radius L = self.robot_wheel_base_length v_l = ( (2.0 * v) - (omega*L) ) / (2.0 * R) v_r = ( (2.0 * v) + (omega*L) ) / (2.0 * R) return v_l, v_r # update the estimated position of the robot using it's wheel encoder readings def _update_odometry( self ): R = self.robot_wheel_radius N = float( self.wheel_encoder_ticks_per_revolution ) # read the wheel encoder values ticks_left, ticks_right = self.robot.read_wheel_encoders() # get the difference in ticks since the last iteration d_ticks_left = ticks_left - self.prev_ticks_left d_ticks_right = ticks_right - self.prev_ticks_right # estimate the wheel movements d_left_wheel = 2*pi*R*( d_ticks_left / N ) d_right_wheel = 2*pi*R*( d_ticks_right / N ) d_center = 0.5 * ( d_left_wheel + d_right_wheel ) # calculate the new pose prev_x, prev_y, prev_theta = self.estimated_pose.scalar_unpack() new_x = prev_x + ( d_center * cos( prev_theta ) ) new_y = prev_y + ( d_center * sin( prev_theta ) ) new_theta = prev_theta + ( ( d_right_wheel - d_left_wheel ) / self.robot_wheel_base_length ) # update the pose estimate with the new values self.estimated_pose.scalar_update( new_x, new_y, new_theta ) # save the current tick count for the next iteration self.prev_ticks_left = ticks_left self.prev_ticks_right = ticks_right # return a go-to-goal heading vector in the robot's reference frame def calculate_gtg_heading_vector( self ): # get the inverse of the robot's pose robot_inv_pos, robot_inv_theta = self.supervisor.estimated_pose().inverse().vector_unpack() # calculate the goal vector in the robot's reference frame goal = self.supervisor.goal() goal = linalg.rotate_and_translate_vector( goal, robot_inv_theta, robot_inv_pos ) return goal

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