This problem can be easily solved by A* without any modifications. The implementation, however, is not trivial. You want your A* run not in the actual world, but rather in C-space of your world (or even state space given you have extra constraint).
Most interesting for you is the paragraph mentioning that while for 1 particle in 3D the C-space has 3 dimentions, for n particles the space has 3 n dimensions.
Applied to you problem, you want to construct a 4D graph where obstacles in each 2D slice(the first two dimensions) are generated by overlaying current obstacles translated by the actor displacement vector(the second two dimensions), with connection between 2D slices made only near obstacles, e.g. as you identified in your example, at [(2,0),(0,6)] you can move to the [(2,0),(0,5)] slice of world.
For example (=one slice), finding path for two points in scene on left is equivalent to finding path for one point in scene on the right (light gray obstacle is due to the world boundary).
As you can see, if you build you A* graph as described above, A* will workno longer have any problems with second actor and as expected, will find the correct path given one exists.
This problem can be easily solved by A* without any modifications. The implementation, however, is not trivial. You want your A* run not in the actual world, but rather in C-space of your world (or even state space given you have extra constraint).
Most interesting for you is the paragraph mentioning that while for 1 particle in 3D the C-space has 3 dimentions, for n particles the space has 3 n dimensions.
Applied to you problem, you want to construct a 4D graph where obstacles in each 2D slice(the first two dimensions) are generated by overlaying current obstacles translated by the actor displacement vector(the second two dimensions), with connection between 2D slices made only near obstacles, e.g. as you identified in your example, at [(2,0),(0,6)] you can move to the [(2,0),(0,5)] slice of world.
For example (=one slice), finding path for two points in scene on left is equivalent to finding path for one point in scene on the right (light gray obstacle is due to the world boundary).
As you can see, if you build you A* graph as described above, A* will work and find the correct path given one exists.
This problem can be easily solved by A* without any modifications. The implementation, however, is not trivial. You want your A* run not in the actual world, but rather in C-space of your world (or even state space given you have extra constraint).
Most interesting for you is the paragraph mentioning that while for 1 particle in 3D the C-space has 3 dimentions, for n particles the space has 3 n dimensions.
Applied to you problem, you want to construct a 4D graph where obstacles in each 2D slice(the first two dimensions) are generated by overlaying current obstacles translated by the actor displacement vector(the second two dimensions), with connection between 2D slices made only near obstacles, e.g. as you identified in your example, at [(2,0),(0,6)] you can move to the [(2,0),(0,5)] slice of world.
For example (=one slice), finding path for two points in scene on left is equivalent to finding path for one point in scene on the right (light gray obstacle is due to the world boundary).
As you can see, if you build you A* graph as described above, A* will no longer have any problems with second actor and as expected, will find the correct path given one exists.
This problem can be easily solved by A* without any modifications. The implementation, however, is not trivial. You want your A* run not in the actual world, but rather in C-space of your world (or even state space given you have extra constraint).
Most interesting for you is the paragraph mentioning that while for 1 particle in 3D the C-space has 3 dimentions, for n particles the space has 3 n dimensions.
Applied to you problem, you want to construct a 4D graph where obstacles in each 2D slice(the first two dimensions) are generated by overlaying current obstacles translated by the actor displacement vector(the second two dimensions), with connection between 2D slices made only near obstacles, e.g. as you identified in your example, at [(2,0),(0,6)] you can move to the [(2,0),(0,5)] slice of world.
For example (=one slice), finding path for two points in scene on left is equivalent to finding path for one point in scene on the right (light gray obstacle is due to the world boundary).
As you can see, if you build you A* graph as described above, A* will work and find the correct path given one exists.