Motivation and Background

Consider a diKerential drive robot with wheel radius r ∈ (0, ∞), illustrated in Figure 1. Note that the wheels are perfectly aligned and placed along the robot’s y −axis, which crosses the robot centre, such that each wheel is 2/l away from the centre of the robot.

Consider that each wheel can be independently controlled with linear velocity signals vl(t) and vr(t) for the left and right wheels, respectively. The lower bound for the wheel velocities for both wheels are vmin = −0.1 and the upper bound is vmax = 0.1.

The robot is designed in such a way that when vl(t) = vr(t) > 0,  the robot moves towards its x −axis. The pose x(t) ∈ R3 of the centre of the robot with respect to the global reference frame. is such that

where px(t) is the position in the x −axis, py(t) is the position on the y −axis, and Φz is the rotation of the robot centre about the ? −axis. Note that Px(0) = py(0) = Φ(0) = 0. In addition, at x(0), the robot's reference frame. matches the global reference frame.

The sampling time of the robot is ? = 0.01. When necessary to integrate velocity into position, use the diKerence quotient equation. For instance, for any a(t) ∈ R with time derivative a(t), we have that

• All variables are defined in the International System of Units (SI), unless otherwise stated. For example, time is in seconds, lengths in meters, and angles in radians.

Figure 1 Illustration of a di2erential drive robot. The z-axis is found with the right-hand rule.

Tasks

Solve all tasks. Create a compressed file (.zip) containing the folder coursework1 containing all your submission files. The compressed file must be submitted to BB.

Task 1

I. interface_package must be a valid ament_cmake ROS2 package [1 mark]. This package is meant for semantically meaningful ROS2 interfaces used in this coursework.

II. The package must have valid ROS2 interface files in the correct folders as follows.

a. WheelVelocities.msg must have only the two fields described below [1 mark]

i. The first field must be “right_wheel_velocity” with type “float64”.

ii. The second field must be “left_wheel_velocity” with type “float64”.

b. TaskSpacePose.msg must have only the three fields described below [1 mark]

i. The first field must be “x” with type “float64”.

ii. The second field must be “y” with type “float64”.

iii. The third field must be “phi_z” with type “float64”.

c. TurnRobotOn.srv must have an empty Request and the Response should be the field “success” with type “bool”. [1 mark]

d. TurnRobotOff.srv must have an empty Request and the Response should be the field “success” with type “bool”. [1 mark]

Task total [5 marks]

Task 2

The following behaviour will only be checked for marks if all tasks above are working correctly.

I. robot_package must be a valid ament_python ROS2 Package [1 mark]

II. The package must have a valid rclpy ROS2 node with the name robot_node [1 mark]

a. The node must finish cleanly when an interrupt signal is sent and stay alive otherwise, according to the tutorials. Deviations from this might award a mark of zero for any marking below.

III. The expected behaviour of robot_node:

a. You can choose how to manage the following internal variables as long as the behaviour below is achieved.

i. The node must have an OFF state and an ON state managed by the node.

ii. The node must store internally the current pose ?(?).

iii. The values ? for the wheel radius and ? for the distance between wheels must be hard coded into the node.

b. it must have a service server providing the service robot/turn_robot_on with type TurnRobotOn.srv

i. The service must be available regardless of state. [1 mark]

ii. When the robot is in the OFF state. Upon receiving a request, it must change the robot state to ON and return “success=True”. [1 mark]

iii. When the robot is in the ON state. Upon receiving a request, it must not change the robot state and return “success=False”. [1 mark]

c. it must have a service server providing the service robot/turn_robot_off with type TurnRobotOff.srv.

i. The service must be available regardless of state. [1 mark]

ii. When the robot is in the ON state. Upon receiving a request, it must change the robot state to OFF and return “success=True”. [1 mark]

iii. When the robot is in the OFF state. Upon receiving a request, it must not change the robot state and return “success=False”. [1 mark]

d. it must have a publisher to the topic robot/task_space_pose with message type TaskSpacePose.msg. It must be used to publish the current robot pose x(t) according to the specifications below.

i. The publisher must be connected to the topic regardless of state. [1 mark]

ii. When the robot is in the OFF state. It must not publish any messages. [1 mark]

iii. When the robot is in the ON state. It must publish ?(?), that is the current pose of the robot at a frequency of 10 Hz. The fields of the message must reflect the “x”, “y”, and “phi_z” explained in Eq. (1). [1 mark]

e. It must have a subscriber to the topic robot/wheel_velocities with message type WheelVelocities.msg. It must be used to receive wheel velocity commands from an external publisher according to the specifications below.

i. The subscriber must be connected to the topic regardless of state. [1 mark]

ii. When the robot is in the OFF state. It must ignore any messages received from the topic. [1 mark]

iii. When the robot is in the ON state. The node must store the right wheel velocity and the left wheel velocity received through the topic in the internal states vr and vl, respectively. The velocities received must be clamped to be above the lower limit vmin and below the upper limit vmax. [1 mark]

f. The following behaviour will only be checked for marks if all points above are working correctly.

i. Whenever the robot is triggered to the OFF state. The internal states vr and vl must be set to zero. There should be no update of the pose x(t). [1 mark]

ii. Whenever the robot is in the ON state. The pose ?(?) must be updated at a frequency of 10 Hz according to the diGerential drive robot equations of motion. [1 mark]

Task total [15 marks]

Task 3

The following behaviour will only be checked for marks if all tasks above are working correctly.

I. controller_package must be a valid ament_python ROS2 Package. [1 mark]

II. The package must have a valid rclpy ROS2 node with the name controller_node. [1 mark]

a. The node must finish cleanly when an interrupt signal is sent or stay alive otherwise, according to the tutorials. Deviations from this might award a mark of zero for any marking below.

III. The expected behaviour of controller_node:

a. When started, it must call robot/turn_robot_on when the service becomes available. [1 mark]

b. Using ? robot/wheel_velocities, it must rotate the robot from its initial angle Φz(0) to the desired angle Φz,d given by desired_angle_deg (in degrees) in 60 seconds or less. [1 mark] Please be attentive to the conversion between degrees and radians where needed.

c. After the rotation is complete. Using robot/wheel_velocities, it must move the robot in a straight line from its initial position and Φz,d forward (about the x −axis) for a length of 1 meter (tolerance of 1 mm) in 60 seconds or less, stop, and turn oK the robot. [1 mark]

Task total [5 marks]

Coursework Total [25 marks]