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COMP4620/8620 – Advanced Topics in AI
Decision-making under Uncertainty in Robotics
Semester-2 2023 – Assignment 1
Due date: Monday, 4 September 2023 23:59 Canberra time
In each primitive step, the chair cannot move more than 0.10 rad 0.10.The time limit used will be CPU time. The time limit for the examples in the accompanyingsupporting codes are: 4 seconds for the no gripper example and 10 seconds for the examplewith gripper.Update 14/08/23: Replace all hypen (‘-’) in class/file/folder names with underscore (‘’)
Notes:
- This is an individual assignment.
- This assignment consists of two parts: Programming and Report. The maximum total mark is100 points, with a maximum of 60 points for the Programming component and a maximum of40 points for the Report component.
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Submission Instruction:(a) You must write your program in Java. Supporting code (for checking the validity of aconfiguration) is provided.(b) Your main program should be placed in a file named a1 [courseCode] [UID].java.(c) Your program should compile from command prompt (e.g., using ant) and generate a filethat can be run from command prompt as: java -jar a1 [courseCode] [UID].jar inputFileName outputFileNameORjava a1 [courseCode] [UID] inputFileName outputFileName [courseCode] must be replaced with 4620 or 8620, depending on which class you areenrolled in.[UID] must be replaced with your ANU ID.(d) The report should be in .pdf format and named a1 [courseCode] [UID].pdf.(e) The report and all the source codes necessary to compile your program should be placedinside a folder named a1 [courseCode] [UID]. Please submit only source codes (i.e.,remove all object an executable files).(f) The folder should be zipped under the name a1 [courseCode] [UID].zip and the zip
file should be submitted via wattle before the due date.Page 1 of 5 – Advanced Topics in AI – (COMP4620/8620)(a) (b) (c)Figure 2: Illustration of a simplified wheelchair robot and its environment.Figure 1: Wheelchair robotUNA has purchased the hardware for a robotics wheelchairthat staff and students in need can use for free. It is essen-tially a wheelchair with a robotics arm and gripper, as il-lustrated in Figure 1. To provide better functionality, UNAis developing the software package to plan the wheelchairrobot motion autonomously, given initial and goal config-
urations. COMP4620/8620 has been hired to develop thecore motion planning component of the software, and thisassignment is about developing a simplified prototype of theplanner.Specifically, in this assignment, you need to develop a mo-tion planning method and its implementation for a simplifiedversion of the above wheelchair and analyse its performance.The simplification is detailed below.
The simplified wheelchair robot operates in a 2D workspace (rather than 3D). In particular, the 2Dworkspace is a plane, represented as [0, 1] × [0, 1] ? R2 and is populated by rectangular obstacles.
The exact dimension and position of each obstacle in the environmentis known prior to execution.Figure 2(a) illustrates an example of this environment.The wheelchair robot is composed of three parts: The chair (base), a robot arm, and a gripper (illus-trated in Figure 2(b)). The details of each part are: - The chair can be thought of as a base for the arm (and gripper) and is a square of size 0.04×0.04unit2. The base can only translate. A local coordinate system is attached to this base. The origin
of this coordinate system is at the center of the square, while the X and Y axis are parallel tothe X and Y axis of the workspace, as illustrated in Figure 2(c). - The robot arm forms a chain and consists of J links and J joints, where J is a positive integer.Each link is a line segment attached to a joint. We number the joints and links sequentially (with
the index starting at 1), i.e., joint-1 is located at the center of the base, link-1 is a line-segmentattached to joint-1, joint-2 lies at the other end of link-1, etc. Each joint is a rotational joint.
A local coordinate system is attached to each joint. The origin of this coordinate system is theposition of the joint. For joint-1, this coordinate system coincides with the coordinate systemof the base. For other joints, the X axis is the line that coincides with the previous link. Eachjoint is a rotational joint, which means it can only rotate. We define the joint angle of joint-i as
Page 2 of 5 – Advanced Topics in AI – (COMP4620/8620)
the angle between link-i and the X axis of the coordinate system attached to joint-i. The jointangle of each joint is limited to be within [?1500, 1500]. Figure 2(c) illustrates the coordinate
system of the rotational joints. Each link is of size 0.05 unitlength. - The gripper consists of 2 L shape segments: upper and lower gripper, as illustrated in Fig-ure 2(c). It is attached to the last link of the arm and has a fixed relative orientation withrespect to the last link of the arm. However, the length of the segments can be altered and isdefined as (u1, u2) for the upper gripper and as (l1, l2) for the lower gripper, where u1, u2, l1, l2 ∈[0.03, 0.07].
What your program should doGiven the initial and goal configurations of the wheelchair robot, as well as a map of the environment,
your program must find a valid path from the initial to the goal configuration. A valid path means thatwhen the wheelchair robot executes the path, it will satisfy the following requirements: - The path consists of primitive steps. In each primitive step, the chair cannot move more than0.001 unit, each joint angle cannot move more than 0.10 rad 0.10, and the length of a segmentin the gripper cannot move more 0.001 unit.
- The robot will not collide with any of the obstacles in theworkspace.
- The robot will not collide with itself.
- The entire wheelchair robot must lie inside the workspace.
- The joint angles for the robot arm and the segment length for the gripper must be inside theirrespective lower and upper limit as described in the previous section (i.e. [?1500, 1500] for the
joint angles and [0.03, 0.07] for the segment length). - Since a primitive step is very small, it is sufficient to satisfy requirements 2-5 at the beginningand end of each primitive step.
To help you develop the motion planning solution, we provide a supporting program (in Java) to testif a configuration satisfies the above validity requirements.Your program should take a .txt file containing the problem scenarios as input and output a .txt file
containing the resulting path. The input and output should follow the format described in the nextsection.Input and Output formatTo describe the format of the input file, we first need to describe the format of a configuration.Format of a configuration. A configuration is represented by n real numbers, where n is the dimension
of the C-space. Each number is separated by a white space. The first two numbers are the position ofthe origin of the chair’s coordinate system in the workspace. If the wheelchair does not have a gripper,
the last n ? 2 numbers are the joint angles in sequential order (i.e., the third number is the joint angleof joint-1, the fourth number is the joint angle of joint-2, etc.). Each joint angle is defined in radian.If the wheelchair has a gripper, the subsequent n ? 6 numbers are the joint angles in sequential order,while the last 4 numbers are the values of u1, u2, l1, l2, respectively.Input format. The program you develop should accept a .txt file as input. The file contains the type ofwheelchair, the initial and goal configurations, and the obstacles position and dimension. The format
of the input file is as follows.Page 3 of 5 – Advanced Topics in AI – (COMP4620/8620)1. The file consists of k + 4 lines, where k is the number of obstacles in the environment.2. The first line is the type of wheelchair robot. There is only two possibilities, i.e., withGripperand noGripper for a wheelchair robot with a gripper and without a gripper, respectively.3. The second line is the initial configuration.4. The third line is the goal configuration.5. The fourth line is the number of obstacles in the environment.6. Each line in the next k lines represents an obstacle and consists of 4 real numbers. The first twonumbers represent the X and Y position of the upper-left vertex of the rectangle, while the lasttwo represent the X and Y position of the lower-right vertex of the rectangle.
Output format. Your program should output the wheelchair robot’s path to a .txt file with the following3. Evaluate your method. If you use sampling-based method, this evaluation needs to consider therandom nature of the method.