Algorithm 4 Enhanced combined RRT and elliptical path

Input: Initial and desired configuration of the robot, the maximum number of samples, Nmax

Output: Tree, T

1.Add initial configuration to the tree, T   2. For i = 1 to Nmax: Repeat Algorithm 3 from 2.a to 2.d to get {C} from configuration Cs Find best of {C}, Cnew, that gives least estimated distance based on Equation (4) or (5) If Cnew used Equation (5): Repeat Algorithm 2 from 1.a to 1.d with initial condition assigned as Cnew to create a new ellipse Execute a set of points from Cnew which the robot can follow and closely satisfy the ellipse to generate a new set of configurations {C’} Find best of {C’} based on Equations (4) and add it to T If the robot reaches the goal position, then immediately return T

Else:

Add Cnew to T

3.Return T