Graphviz---how do I make edges not cross each other; choose self-loop edge position

Question

I have the following dotfile:

digraph finite_state_machine {                                                                                                                                                                                  
    pad=0.2;
    {
        rank=same;
        node [shape = doublecircle]; q_3;
        node [shape = circle];
        q_1 [ label = <<b><i>q<sub>1</sub></i></b>> ];
        q_2 [ label = <<b><i>q<sub>2</sub></i></b>> ];
        q_3 [ label = <<b><i>q<sub>3</sub></i></b>> ];
        q_1 -> q_1 [ label = <<b><i>^a</i></b>> ];
        q_1 -> q_2 [ label = <<b><i>a</i></b>> ];
        q_2 -> q_2 [ label = <<b><i>^b</i></b>> ];
        q_2 -> q_3 [ label = <<b><i>b</i></b>> ];
    }
}

And I get the following output:

I want the self loops to be on top of the nodes, and not cross the other edges. And, if possible, more loopy loops. How can I achieve that?

I want it to look something like this:

Answer 1

You may use ports/compass points:

q_1:e -> q_1:w [ label = <<b><i>^a</i></b>> ];
q_2:e -> q_2:w [ label = <<b><i>^b</i></b>> ];

or using nw/ne as compass points: