Improved SDF objective function.

For two colliding SDFs `A` and `B`, the function is `(A+B)+abs(max(A,B))`. This can also be written as `clearance + abs(intersection)`. This function has the following properties:

- On the penetrating surface, it is equal to `A+B`, i.e. the clearance field which is the penetration depth.
- The object boundary is a set of local minima in 3D space, since `abs(max(A, B))>0` away from the surface.
- Along the penetrating surface, the maximum penetration is a local minimum of the clearance since this field is orthogonal to the midsurface field `A-B`, which acts as a support plane for the contact.

[Level sets of the improved function for two colliding circles](https://www.wolframalpha.com/input?i=plot+sqrt%28x%5E2%2By%5E2%29-1+%2B+sqrt%28%28x-1%29%5E2%2B%28y-1%29%5E2%29-1+%2B+max%28max%28sqrt%28x%5E2%2By%5E2%29-1%2C+sqrt%28%28x-1%29%5E2%2B%28y-1%29%5E2%29-1%29%2C+0%29+-+min%28max%28sqrt%28x%5E2%2By%5E2%29-1%2C+sqrt%28%28x-1%29%5E2%2B%28y-1%29%5E2%29-1%29%2C+0%29+).

PiperOrigin-RevId: 585106580
Change-Id: I5b18a1ef262ceb0a1ab8abcad8acfd6dc1992e2c
This commit is contained in:
Alessio Quaglino
2023-11-24 09:06:19 -08:00
committed by Copybara-Service
parent 6a83b86553
commit d070b1893e
3 changed files with 22 additions and 23 deletions
+1 -1
View File
@@ -28,7 +28,7 @@ typedef enum mjtSDFType_ { // signed distance function (SDF) type
mjSDFTYPE_SINGLE = 0, // single SDF
mjSDFTYPE_INTERSECTION, // max(A, B)
mjSDFTYPE_MIDSURFACE, // A - B
mjSDFTYPE_QUADRATIC, // max(A, 0)^2/2 + max(B, 0)^2/2 + min(A, 0)*min(B, 0)
mjSDFTYPE_COLLISION, // A + B + abs(max(A, B))
} mjtSDFType;
struct mjSDF_ {