Motion planning methods based on potential fields: NF1 and HF¶
These exercises are devoted to study how the potential field methods without local minima, NF1 and HF, work. A simple 2D scenario with several box-like obstacles will be used.
If not already done, first install or build Kautham. Then run the kautham-gui application.
Navigation function method NF1¶
Open the demo demos/OMPL_geo_demos/boxes_world_R2/OMPL_NF1_boxes_world_R2.xml to analyze how the NF1 planner solves the problem. Focus will be put on the discretization steps used (parameters _Discr. Steps 0 and _Discr. Steps 1) and to anlyze the nature of the solution for different configuration of the obstacles.
The intial and goal configurations are set in the problem file as:
1 2 | <Init>0.6 0.1</Init>
<Goal>0.85 0.85</Goal>
|
When the problem is loaded the cells containing these configurations are computed, corresponding in this case to cells 108 and 775, and the cells of the grid are classified as obstacle or free cells by checking if the robot located at the center of the cell is in collision or not.
Solution¶
On the NF1Planner tab press on the the GetPath button to compute the Navigation Function NF1 that may solve the problem. The potential field with the potential values of the cells, as well as the solution channel connecting the initial cell with the goal cell, can be seen in the CSpace tab:
The discretization step¶
By changing the discretization step sizes, the cells containing the initial and goal configurations are recomputed and the obstacle or free nature of the cells in the grid is recomputed, e.g. by using a 9x9 grid or a 100x100 grid the potential field landscapes and the solutions are:
The obstacles in this example can be relocated using the ObsContr tab that shows sliders to move the x and y coordinate of each obstacle.
>>> EXERCISE 1: Using a 30x30 grid, move the obstacles to represent different scenarios and find the solutions. Can the clearance of the path be controlled? Can a solution path always be found?
Discuss about the completeness of the planner and the limitations of this planning approach.
Harmonic Functions method (HF)¶
Open the demo demos/OMPL_geo_demos/boxes_world_R2/OMPL_HF_boxes_world_R2.xml to analyze how the planner based on Harmonic Function solves the problem. Focus will be put on the goal potential, the boundary conditions and on the iterations used for the relaxation of the potential field.
The algorithm implemented is sketched in the following figure:
Solution¶
On the HFPlanner tab press on the the GetPath button to compute the harmonic function that may solve the problem. Since a path is searched without waiting for the complete convergence of the potential landscape different solutions may be encountered:
In order to visualize the generation of the potential landscape, change incremental to 1 and set the HF_relax_iter and main_iter parameters to 1. Then press the GetPath button several times to visualize the evolution of the harmonic function landscape.
The boundary conditions¶
There are two types of boundary conditions:
Dirichlet boundary conditions
Neumann boundary conditions
Change the parameters HF_relax_iter and main_iter to 10 and incremental to 0.
>>> EXERCISE 2: Check the different solution found using both the Neumann and the Dirichlet boundary conditions, using the Goal Potential to -1000.
Use different environments by moving the obstacles.
>>> EXERCISE 3: Repeat for several values of the Goal Potential (e.g. -10, -100, -1000, -10000).
>>> EXERCISE 4: Which is the effect of the goal potential and of the boundary conditions on the success of the planner? Which is the best option for environments with narrow passages?
The relaxation¶
>>> EXERCISE 5: Provided that main_iter is large enough to find a solution, which is the effect of using a small or a large value of the HF_relax_iter number of iterations?
>>> EXERCISE 6: Can the clearance of the path be controlled? Can a solution path always be found? Discuss the completeness of the planner and the limitations of this planning approach.