Not a whiff of rotations.

Edge.java

package sample;

import roboflight.Robot;
import roboflight.RobotPeer;
import roboflight.UpdateEvent;
import roboflight.util.Vector;

public class Edge implements Robot {
    public RobotPeer peer;
	@Override
	public void setRobotPeer(RobotPeer peer) {
		this.peer = peer;
	}

	@Override
	public void onTurnStarted() {}
	
	@Override
	public void onUpdate(UpdateEvent e) {
		//fire at the enemy
		peer.setFireBullet(e.getPosition().sub(peer.getPosition()));
	}
	
	Vector thrust = new Vector(1,0,0);
	@Override
	public void onTurnEnded() {
		//set in some direction
		peer.setThrust(thrust);
		
		Vector p = peer.getPosition();
		
		if(p.length() > 900) {
			//basically we need a perpendicular tangent space vector,
			//this sounds complicated but is actually rather simple
			
			//We need an outward vector from the origin to our position,
			//which we can get by normalizing our position
			p.normalize();
			
			//Now we need a sample perpendicular tangent space vector,
			//in this case, up
			Vector up = new Vector(0,1,0);
			
			//now we just take the cross product and use that as our thrust
			thrust = Vector.cross(p, up);
			
			
			//WHOOPS, now we have a problem, when we run into the walls we
			//stop, so we have to point inward a bit.
			
			//So lets just add the inverse of the outward vector to our
			//thrust, that will make us thrust more inward.
			
			//the inverse of our outward from origin vector
			p.scale(-1);
			
			//But if we scale down the inward to origin vector, we can
			//make a smoother turning curve
			p.scale(0.25);
			
			//Add it
			thrust.add(p);
			
			//This step isn't required as the game normalizes the thrust
			//if it is over MAX_ROBOT_THRUST.
			thrust.normalize();
			
			peer.setThrust(thrust);
			
			//Now you're thinking with vectors!
		}
	}
}