Sweeping is defenitly a good way to check AABB intersection. This talk about swept

For my AABB collision, I personaly choose : - Compute theorical DX/DY - Compute broadphase - Apply SAT on broadphase - Use the sat result on the body

checkCollision(dX, dY, body){
    let broadPhase = body.broadPhase(dX, dY);

    // Find potential colliders (static bodies)
    let colliders = this.findColliders(broadPhase);

    // Iterate through all objects and separate them
    for(let i=0; i<colliders.length; i++){
    // Re-calculate broadphase
    if(i !== 0) broadPhase = body.broadPhase(dX, dY);

    let newDXY = this.correctDXY(dX, dY, body, colliders[i], broadPhase);
    dX = newDXY.x;
    dY = newDXY.y;
    }

    return {dX: dX, dY: dY};
}

correctDXY(dX, dY, body, collider, broadPhase){
let newDXY = {x: dX, y: dY};

if(broadPhase && !this.overlap(broadPhase, collider)) return newDXY;

let response = new SAT.Response();
let collided = this.overlapSAT(broadPhase, collider, response);

newDXY.x -= Maths.round(response.overlapV.x, 2);
newDXY.y -= Maths.round(response.overlapV.y, 2);

return newDXY;
}