Maze Solver - LeJOS

In this maze solver the robot follows a left hand rule as given in https://embedjournal.com/shortest-path-line-follower-robot-logic-revealed/. The program works in two phases. In the first phase, the robot samples the entire path, stores the x and y co-ordinates of the path and creates a map of maze in the memory. Given two consecutive points, the program also calculates and stores the direction of the robot at each point.  Then the program calculates the shortest path by cancelling out the U turn samples and the samples in opposite directions. In the second phase, the robot actually follows the shortest path. During path following, the robot samples the path again and whenever the direction of two consecutive points falls apart from the expected direction (which we got in the first phase) the robot aligns its direction accordingly.

Let me go through the program logic for shortest-path-finding and shortest-path-following in detail. However, before going through it, it would be better to read the article about Limited Maze Solver in order to understand the high level code structure that I have followed. Let us go through the robot path below and mark the path with directions and corresponding sample numbers in those directions. 

Let us assume that the robot path has the following directions and samples along each of them, when the robot traverses it in the first phase: (In real life, the number of samples may differ when the robot traverses, but the high level logic remains the same)

[North (20), West (10), South (30), East (30), North (35), South (20), East (15), North (40), West (20), East (20), North (20), West (20), East (20), North (25), West (20), East (20), South (25 + 20 + 40 + 20 = 105)]

According to the left-hand-rule in the reference site above, we will further reduce the samples where we have East-West and North-South directions in pairs. This is quite simple to understand, as when the robot traverses to North and then comes to South along the same path, the efforts of traversing eventually cancel out. Same for the directions East-West. After cancelling the opposite direction efforts in the first iteration, the path and the samples look like below. 

[North (20), West (10), South (30), East (30), North (15), East (15), North (40), North (20), North (25), South (25 + 20 + 40 + 20 = 105)]

We will then perform the second iteration of cancellation of East-West and North-South. Below is the result after second iteration.  

[North (20), West (10), South (30), East (30), North (15), East (15), North (40), North (20), South (20 + 40 + 20 = 80)]

We will then perform the third iteration of cancellation of East-West and North-South. Below is the result after third iteration.  

[North (20), West (10), South (30), East (30), North (15), East (15), North (40), South (40 + 20 = 60)]

We will then perform the fourth iteration of cancellation of East-West and North-South. Below is the result after fourth and final iteration. 

[North (20), West (10), South (30), East (30), North (15), East (15), South (20)]

When we reach the above iteration and the shortest path does not reduce any further with the "cancellation of samples in opposite direction strategy", we will break the logic. Let us go through few important methods which I have used in the Cruiser class to come up with the shortest path. 

run(): This is the run() method of the Cruiser thread which has the important logic to find and follow the shortest path. It calls three main methods to complete our goal.

populateFirstPathSamples()

findShortedPath()

followShortestPath()

summarize(): While explaining this method I am assuming that you have gone through Limited Maze Solver article in detail. In addition to my explanation there, I want to mention that in this method we take into account all the consecutive direction changes. With each direction change, we keep a record of the number of samples in the same direction. Let us assume that while populating the First Path samples, we get the direction sequence as follows (as known from the direction property of the summary objects):

[4, 4, 2, 2, 2, 2, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1]

This sequence will get recorded into our directionOutput objects as follows:

4 (2), 2 (4), 3 (5), 1 (5)

Here, the figures in the bracket represent the number of samples in the given direction. Each directionOutput object has four properties like summary objects, X, Y, direction and removal. In addition to that I have introduced one more property, numberOfSamples.  

findShortedPath(): Calls the methods removeOppositeDirections42, removeOppositeDirections24, removeOppositeDirections13, removeOppositeDirections31 and removeUTurn iteratively until the shortest path size cannot be further reduced. Let us take a look at removeOppositeDirections42 method in detail. We will also take a look at removeUTurn method in detail. 

removeOppositeDirections42():  

Follow entire shortest path and check whether the directions 4 and direction 2 appear consecutively. Check the corresponding number of samples with each direction as explained above. Then call the decideWhichOneToRemove() method by passing the entire shortest path and the index of direction 2. Extract the number of samples for both, the direction 2 and its previous direction 4 in the direction array. Find the difference between the samples of direction 2 and direction 4. If the difference is less than DIFFERENCE_BETWEEN_EQUAL_SAMPLES, treat the distance between the two directions 2 and 4 as equal and nullify them by removing both of them from the direction array. 

NOTE: I have created the constant DIFFERENCE_BETWEEN_EQUAL_SAMPLES = 11, because due to technical/processing lags, the difference between two equal and opposite directions, may not be exactly zero. So, I have created a threshold of 11 samples to consider the equal and opposite number of samples.    

If the difference between the samples of equal and opposite direction is greater than 11, that means there is unequal distance travelled in the directions. In such case, subtract the longer distance from the shorter distance and set the difference appropriately in either direction 2 or direction 4 (based on the direction which is travelled more)

removeUTurn(): 

Follow the entire path and check if any of the directions 1, 2, 3 and 4 has number of samples less than 11, we remove all those directions from the shortest path, considering either it is a U-Turn or it is noise.  

followShortestPath(): The algorithm for following shortest path goes as follows:

1. Extract the number of samples in the heading direction of the robot from the shortest path array
2. Follow the path with PID controller pilot for the above number of samples   
3. Get two more samples from the pilot
4. Check if the direction property of those two samples match with the next direction in the shortest path array
5. If the directions match, move the shortest path array pointer to the next direction and continue with step 1
6. If the directions do not match, align the direction by calling the alignDirection() method, then move the shortest path array pointer to the next direction. Add the STABILIZATION_ SAMPLES to the number of samples in a given direction. Then continue with step 1

NOTE: I have added the STABILIZATION_SAMPLES in order to give the robot some time, to align in a given direction appropriately. However, from the performance of the robot, it looks like it is NOT required to add them. Because due to addition of them, the effect is little different. Whenever the robot is expected to the change the direction, considerable delay is present. Like the robot should turn much earlier before taking U-Turn number 1. However, it almost reaches till the end. This is because of accumulation of all previous stabilization_samples during direction changes. Same behavior is evident at U-Turn number 5. The robot is expected to stop immediately after taking the turn, however it goes ahead much further.   

alignDirection(): This method is used to turn and align the robot in different directions based on the required direction changes in the shortest path. I call the steer API of the robot which turns it onto a circular path. Please note that the entire turning will not be in the first stretch, because I have used angle 60, -60, -90 to turn. This method may need to be called twice to get the robot at the appropriate angle. For example: we need to call the pilot1.steer(-180, 60) twice to get a turn reach 90 degrees. We may need to call the pilot1.steer(-200, -90) twice to get a turn of 180 degrees. If we leave the robot at an intermediate angle, Line-Follower behavior will come to help, to automatically bring the robot on the black stripe from the white surface. 

NOTE: The performance of the robot is dependent on tuning the following properties appropriately:

• STABILIZATION_SAMPLES
• DIFFERENCE_BETWEEN_EQUAL_SAMPLES
• U_TURN_SAMPLES
• TOTAL_SAMPLES

The TOTAL_SAMPLES constant works in the first phase of robot traversal of the path. These are the samples required to complete the traversal across complete trajectory. This number is coined with a bit of trial and error and observations.