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CS 6613 Fall 2024 Project 1: Robot Path Planning E. K. Wong
Total # points = 100.
Project Description: Implement the A* search algorithm with graph search (no repeated states) for the robot path planning problem as described below. The inputs to your program are the start and goal positions of a point robot, and a 2D integer array that represents the robot workspace. The robot can move from cell to cell in any of the eight directions as shown in Figure 2. The goal is to find the lowest-cost path between the start position and the goal position, and avoiding obstacles along the path. The workspace is represented as an occupancy grid as shown in Figure 1, where the black cells represent obstacles. The red line in the figure depicts a path from the start position to the goal position. (Note: the path in the figure is not the lowest-cost path as required in our project.)
where
Formulation: The problem can be formulated in the following way. Each cell in the workspace is a state. The white cells are legal states and the black cells are illegal states. The actions are the eight moves as defined in Figure 2. The step cost for the actions is the sum of the angle cost and the distance cost; i.e.,
𝑐𝑐(𝑠𝑠, 𝑎𝑎, 𝑠𝑠′) = 𝑐𝑐𝑎𝑎(𝑠𝑠, 𝑎𝑎, 𝑠𝑠′) + 𝑐𝑐𝑑𝑑(𝑠𝑠, 𝑎𝑎, 𝑠𝑠′)
3, 5, 7.
𝑐𝑐𝑎𝑎(𝑠𝑠, 𝑎𝑎, 𝑠𝑠′) = 𝑘𝑘 ∗ ∆𝜃𝜃 ; let 𝑐𝑐𝑎𝑎(𝑠𝑠, 𝑎𝑎, 𝑠𝑠′) = 0 if s is the initial state (start position) 180
∆𝜃𝜃 = |(𝜃𝜃(𝑠𝑠′) − 𝜃𝜃(𝑠𝑠)|; if ∆𝜃𝜃 > 180, let ∆𝜃𝜃 equals 360 − ∆𝜃𝜃
𝑐𝑐𝑑𝑑(𝑠𝑠, 𝑎𝑎, 𝑠𝑠′) = 1 for horizontal and vertical moves 0, 2, 4, 6 and √2 for diagonal moves 1,
In the above, s is the current state, a is the action and s’ is the next state. The angle cost is to penalize any change in the direction of the robot between two consecutive moves. k is a constant that we can set to control the amount of penalty we want to impose for angle change. For the initial state (start position), we let the angle cost between the initial state s and next state s’ equals to 0. The distance cost is for the distance travelled in an action. Let h(𝑛𝑛) be the Euclidian distance between the current position and the goal position. h(𝑛𝑛) thus defined is admissible in this problem. During the search, only legal states (cells without obstacles) will be added to the tree.
Input and output formats: The workspace in the test input files is of size 30 × 50 (rows x columns.) We will use the coordinate system as shown in Figure 3 below. The coordinates of the lower-left corner cell are (𝑖𝑖, 𝑗𝑗) = (0,0). The input file contains 31 lines of integers as shown in Figure 4 below. Line 1 contains the (𝑖𝑖, 𝑗𝑗) coordinates of the start and goal positions of the point robot. Lines 2 to 31 contain the cell values of the robot workspace, with 0’s representing white cells, 1’s representing black cells, 2 representing the start position and 5 representing the goal position. Line 2 contains values for (𝑖𝑖, 𝑗𝑗) = (𝑖𝑖, 29), with 𝑖𝑖 = 0 to 49. Line 31 contains values for (𝑖𝑖, 𝑗𝑗) = (𝑖𝑖, 0), with 𝑖𝑖 = 0 to 49, etc. The integers in each line are separated by blank spaces.
Your program will produce an output text file that contains 34 lines of text as shown in Figure 5 below. Line 1 contains the depth level d of the goal node as found by the A* algorithm (assume that the root node is at level 0.) Line 2 contains the total number of nodes N generated in your tree (including the root node.) Line 3 contains the solution (a sequence of moves from the root node to the goal node) represented by a’s. The a’s are separated by blanks. Each a is a move from the set {0,1,2,3,4,5,6,7}. Line 4 contains the f(n) values of the nodes (separated by blanks,) from the root node to the goal node, along the solution path. There should be d number of a values in line 3 and
CS 6613 Fall 2024 Project 1: Robot Path Planning E. K. Wong
d+1 number of f values in line 4. Lines 5 to 34 contain values for the robot workspace, with 0’s representing white cells, 1’s representing black cells, 2 representing the start position, 5 representing the goal position, and 4’s representing cells along the solution path (excluding the start position and the goal position.)
Figure 3. Coordinate system of the work space.
CS 6613 Fall 2024 Project 1: Robot Path Planning E. K. Wong
Testing your program: Three input test files will be provided on Brightspace for you to test your program. For each input file, try two different runs: one with k = 2 and one with k =4. You can let k be an interactive input parameter in your program.
Recommended languages: Python, C++/C or Java. If you would like to use a different language, send me an email first.
Teammate: You can work on the project by yourself or form a team of two to work on the project. You can discuss with your classmates how to do the project, but every team is expected to write their own code and submit their own project.
Submit on Brightspace:
• Your source code file. Put comments in your source code to make it easier for someone else to read your program. Points will be taken off if you do not have comments in your source code.
• The output files generated by your program for the three input test files.
• A PDF report that contains instructions on how to run your program. If your program requires compilation, instructions on how to compile your program should also be provided. Also, copy and paste your output files and your source code onto the PDF file. This is in addition to the source code file and output files that you have to hand in
separately, as described in items (1) and (2) above.
• If you work in a team of two, only one partner needs to submit the project on Brightspace
but put down both partners’ names on the source code and the PDF report.
d
N
a a a ....a
f f f .....f
m m m m m m ....m m m m m m m ....m ...
m m m m m m ....m
Figure 5. Output file format (34 lines.) d, N, a’s, and m’s are integers. f’s are floating point numbers. The a’s, f’s and m’s are separated by blanks.
nnnn
m m m m m m ....m m m m m m m ....m ...
m m m m m m ....m
Figure 4. Input file format (31 lines.) n’s and m’s are integers separated by blanks.