I have an object that is an airplane. I have made it so it rotates toward a location in space (position). Its forward vector rotates toward this position. It also moves (translates) toward it.

What I would like to make now is to also lean (roll). So if a target location is to the left of airplane the airplane should lean to left. And when it reaches 0 degrees between location and forward, that is when is directly in front of it, its up vector should point up (0, 1, 0). The same applies if location is to the right. The airplane should lean right.

So it should never be rotated upside down, that is its up always needs to point in upward direction.

Here is the code:

Vector3 distance = waypoint.position - transform.position;

// Find rotation toward desired location
Vector3 desiredForward = Quaternion.Inverse(transform.rotation) * distance;
Vector3 rotationDir = Vector3.Cross(Vector3.forward, desiredForward);
rotationDir.Normalize();

// Find rotation vector for roll, it should be forward or -forward
Vector3 up = Vector3.Cross(transform.forward, distance);
up.Normalize();
Vector3 forwardRoll = Vector3.Cross(-transform.right, up);

// angle is for rotation toward location
// angleX is for roll
float angle = Vector3.Angle(Vector3.forward, desiredForward);
float angleX = Vector3.Angle(new Vector3(transform.forward.x, 0.0f, transform.forward.z), new Vector3(distance.x, 0.0f, distance.z));

// Rotate the object
rotation *= Quaternion.AngleAxis(angle*Time.deltaTime, rotationDir);
rotation = Quaternion.AngleAxis(angleX*Time.deltaTime, forwardRoll) * rotation;
		
transform.rotation = Quaternion.Slerp(transform.rotation, rotation, damping*Time.deltaTime);
transform.Translate(new Vector3(0.0f, 0.0f, 1.0f)*Time.deltaTime*speed);

where distance is a direction vector toward a desired location, rotation is a quaternion that rotates the object and forwardRoll is a vector about which I'm trying to roll so it can lean left or right.

The airplane rotates toward a desired location and rolls. But the roll is flickering and sometimes is pointing down.

I don't know what is wrong.

I assume the rotation should be made different but I don't know what to change.

I was going for a solution without physics.

I have found the solution and its actually similar to the suggested one.

Here is the code:

// Find rotation toward desired location
distance = waypoints[next].position - transform.position;
		
// we need to find local direction vector to target location
desiredForward = Quaternion.Inverse(transform.rotation) * distance;
rotationDir = Vector3.Cross(Vector3.forward, desiredForward);
rotationDir.Normalize();
		
// find the global up in local coords
forward = RotationVectorForward(desiredForward);
localUp = Quaternion.Inverse(transform.rotation) * Vector3.up;
localUp = new Vector3(localUp.x, localUp.y, 0.0f);
localUp.Normalize();
		
// find local direction to which we need to rotate
desiredAngle = Vector3.Angle(new Vector3(transform.forward.x, 0.0f, transform.forward.z), new Vector3(distance.x, 0.0f, distance.z));
localDir = Quaternion.AngleAxis(desiredAngle, forward) * localUp;
rotationDirForward = Vector3.Cross(Vector3.up, localDir);
rotationDirForward.Normalize();
desiredAngle = Vector3.Angle(Vector3.up, localDir);

// Rotate the object		
angle = Vector3.Angle(Vector3.forward, desiredForward);
rotation *= Quaternion.AngleAxis(angle*Time.deltaTime, rotationDir) * Quaternion.AngleAxis(desiredAngle*Time.deltaTime, rotationDirForward);
		
transform.rotation = Quaternion.Slerp(transform.rotation, rotation, damping*Time.deltaTime);
transform.Translate(new Vector3(0.0f, 0.0f, 1.0f)*Time.deltaTime*speed);

There needed to be defined vectors in local coords for the up vector in second quaternion composition.