Bezier Cubic Curve: Maximum Gradient and Collision Avoidance?

I use Bezier curves as paths so that my spaceships travel when they land at the station dock. I have a simple algorithm for calculating where the ship should be at time t on the cubic bezier curve:

public class BezierMovement{
    public BezierMovement(){
        // start docking straight away in this test version
        initDocking();
    }

    private Vector3 p0;
    private Vector3 p1;
    private Vector3 p2;
    private Vector3 p3;

    private double tInc = 0.001d;
    private double t = tInc;

    protected void initDocking(){

        // get current location
        Vector3 location = getCurrentLocation();

        // get docking point
        Vector3 dockingPoint = getDockingPoint();

        // ship normalised direction vector
        Vector3 direction = getDirection();

        // docking point normalised direction vector
        Vector3 dockingDirection = getDockingDirection();

        // scalars to multiply normalised vectors by 
        // The higher the number, the "curvier" the curve
        float curveFactorShip = 10000.0f;
        float curveFactorDock = 2000.0f;

        p0 = new Vector3(location.x,location.y,location.z);

        p1 = new Vector3(location.x + (direction.x * curveFactorShip),
                         location.y + (direction.y * curveFactorShip),
                         location.z + (direction.z * curveFactorShip));

        p2 = new Vector3(dockingPoint.x + (dockingDirection.x * curveFactorDock),
                         dockingPoint.y + (dockingDirection.y * curveFactorDock),
                         dockingPoint.z + (dockingDirection.z * curveFactorDock));

        p3 = new Vector3(dockingPoint.x, dockingPoint.y, dockingPoint.z);


    }

    public void incrementPosition() {

        bezier(p0, p1, p2, p3, t, getCurrentLocation());

        // make ship go back and forth along curve for testing              
        t += tInc;

        if(t>=1){
            tInc = 0-tInc;
        } else if(t<0){
            tInc = 0-tInc;
        }

    }

    protected void bezier(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, double t, Vector3 outputVector){

        double a = (1-t)*(1-t)*(1-t);
        double b = 3*((1-t)*(1-t))*t;
        double c = 3*(1-t)*(t*t);
        double d = t*t*t;

        outputVector.x = a*p0.x + b*p1.x + c*p2.x + d*p3.x;
        outputVector.y = a*p0.y + b*p1.y + c*p2.y + d*p3.y;
        outputVector.z = a*p0.z + b*p1.z + c*p2.z + d*p3.z;

    }
}

The starting point of the curve is the location of the spacecraft, and the ending point is the entrance to the docking compartment (red dots on the diagram). The spacecraft has a normalized vector for its direction, and in the docking compartment there is another normalized vector indicating the direction in which the ship should go so that it is aligned directly with the docking compartment when it arrives (yellow lines on the diagram)

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