Use a better anti-tunneling algorithm for keep-out constraints

[calcmogul]

The general idea is to formulate collision detection as a continuous problem. I've seen two ways to do that so far.

Option 1

This seems more straightforward to implement.

Differentiable Collision Detection for a Set of Convex Primitives

The paper: https://arxiv.org/pdf/2207.00669
The source code (not that helpful, imo): https://github.com/kevin-tracy/DifferentiableCollisions.jl

1. Define all the robot corners with respect to the current state as x
2. Define a keep-out shape constraint with a positive scaling parameter α as per section B of https://arxiv.org/pdf/2207.00669. r is generally the shape center and x is the robot point
3. Apply the constraint that the robot point be within the scaled shape
4. Apply the constraint that α ≥ 1 to avoid collisions (note that this also enforces the positivity constraint mentioned in step 1)

Differentiable Continuous Collision Detection for Convex Sets

The formulation above doesn't handle continuous collision detection, but the authors generalized it to work for that.

The paper: https://continuous-collisions.github.io/
An explanatory video: https://www.youtube.com/watch?v=L_AlqGmw5H8

Option 2

Implicit Swept Volume Signed Distance Field

https://arxiv.org/pdf/2405.00362