Added Screw calculation

Updated the algorithm theory and added relevant diagrams for better understanding

Author: exMachina316

README.md

@@ -142,6 +142,10 @@ The following parameters can be adjusted to optimize the robot's performance:
 The min turning radius of the controller should be equal to or less than the min turning radius of the planner (in case it is available). This ensures the controller can follow the path generated by the planner and not get stuck in a loop.
 
 ## Vector Pursuit Algorithm
-Vector pursuit is a geometric path-tracking method that uses the theory of screws. It is similar to other geometric methods in that a look-ahead distance is used to define a current goal point, and then geometry is used to determine the desired motion of the vehicle. On the other hand, it is different from current geometric path-tracking methods, such as follow-the-carrot or pure pursuit, which do not use the orientation at the look-ahead point. Proportional path tracking is a geometric method that does use the orientation at the look-ahead point. This method adds the current position error multiplied by some gain to the current orientation error multiplied by some gain, and therefore becomes geometrically meaningless since terms with different units are added. Vector pursuit uses both the location and orientation of
-the look-ahead point while remaining geometrically meaningful. 
-It first calculates two instantaneous screws for translation and rotation, and then combines them to form a single screw representing the required motion. Then it calculates a desired turning radius from the resultant screw.
+## Vector Pursuit Algorithm
+Vector pursuit is a geometric path-tracking method that uses the theory of screws. It is similar to other geometric methods in that a look-ahead distance is used to define a current goal point, and then geometry is used to determine the desired motion of the vehicle. On the other hand, it is different from current geometric path-tracking methods, such as follow-the-carrot or pure pursuit, which do not use the orientation at the look-ahead point. Proportional path tracking is a geometric method that does use the orientation at the look-ahead point. This method adds the current position error multiplied by some gain to the current orientation error multiplied by some gain, and therefore becomes geometrically meaningless since terms with different units are added. Vector pursuit uses both the location and orientation of the look-ahead point while remaining geometrically meaningful. 
+It first calculates two instantaneous screws for translation and rotation, and then combines them to form a single screw representing the required motion. Then it calculates a desired turning radius from the resultant screw.
+
+The centerlines of the instantaneous screws are constrained to lie on the vehicle's y-axis to accomodate one of the non-holonomic contraints. The screw for correcting the translational error, \$<sub>t</sub> is chosen as the center of a circle which intersects the origins of both the vehicle coordinate system and the look-ahead coordinate system and is tangent to the vehicle's current orientation. The screw for correcting the rotational error, \$<sub>r</sub> is chosen to be centered at the vehicle frame origin so that no translation is associated with it.
+
+![translation_screw](https://github.com/user-attachments/assets/67652137-2cf9-41d9-86a9-e43119fae68b)