Carnegie Mellon University

The Robotics Institute.

Robotic  Motion Planning, 16735: Homework 3

Planning using Potential functions

The attractive potential field  I utilized consisted of a quadratic field near the goal at a threshold distance d* and conic potential field far away from the goal. The Equations are given below:

 

 

 

  

 

 

 

 

 

 

 

 

 

The repulsive potential field is given by:

 

 

 

 

 

 

And its gradient

 

 

 

Where D(q) is                                                          and  

 

 

 

Movies

 

 

Success                                       Failure

 

 

 

 

 

 

 

 

 

 

 

About the Robot

 

The robot a range sensor of maximum range Q*. It takes sample reading of the environment in discretized angles over 360º. The dicretization size is a parameter N. As the robot moves through the environment it finds the closest distance d_i to the i^th obstacle for each obstacle within the sensor range. It then calculates the gradient of the potential field based on the equations given above and moves in a direction negative to that of the gradient. Since this is a gradient based method it cannot avoid local minima which is seen in the failure video.

Since dynamics are not involved if the robot hits a local minima it stays there regardless of the scaling K between the velocity and gradient of the potential field

Implementation was done in Matlab

 

Why I chose this method

 

I wanted to implement a method that would mimic the systems on an actual robot. The method described above uses only local knowledge of the environment similar to how robots with ultrasonic sensors navigate an environment. The effect of sensor angular discretization can also be studied with the implementation.

 

Acknowledgements

I thank Prof. Howie Choset for the lecture slides from which the equations have been taken.

 

 

 

 

 

 

 

*Note : The blue circle in the figure is the area scanned by the sensor