Camera movement around a sphere - c++

Question

I am trying to convert moving around the xz plane to movement around a sphere. Originally, I had my camera moving forward at a constant speed at a constant height on the y axis. The user can move left/right by adjusting the yaw, however they can not move up/down or roll. Here is how I accomplished that:
float turnRate = 1.0;
float stepDist = 0.1;
if (keys['d']) {
yaw += M_PI * (turnRate / 180.0);
}
if (keys['a']) {
yaw += M_PI * (-turnRate / 180.0);
}
position.x += stepDist * sinf(yaw);
position.z += stepDist * cosf(yaw + M_PI);
...
glm::mat4 P = glm::rotate(pitch, glm::vec3(-1.0, 0.0, 0.0));
glm::mat4 Y = glm::rotate(yaw, glm::vec3(0.0, -1.0, 0.0));
glm::mat4 T = glm::translate(position);
glm::mat4 C = T * Y * P;
This worked well for me. Now what I am trying to achieve is instead of moving across the xz plane, I would like to move across the surface of a sphere. I still want to be moving forward at a constant speed at a constant radius from the center of the sphere with only allowing adjustment of the yaw. This is what I have currently:
float turnRate = 1.0;
float stepDist = 0.01;
step += stepDist;
if (keys['d']) {
yaw += M_PI * (turnRate / 180.0);
}
if (keys['a']) {
yaw += M_PI * (-turnRate / 180.0);
}
pitch = M_PI / 8.0; // angle the camera down towards the sphere a bit
glm::vec3 f = glm::vec3(sinf(yaw), 0.0, cosf(yaw + M_PI));
glm::vec3 up = glm::vec3(0.0, 1.0, 0.0);
glm::vec3 forward = glm::normalize(f);
right = glm::cross(up, forward);
float sphereRadius = 50.0;
float camRadius = sphereRadius + 8.0;
radius = glm::vec3(0.0, camRadius, 0.0);
...
glm::mat4 P = glm::rotate(pitch, glm::vec3(-1.0, 0.0, 0.0));
glm::mat4 Y = glm::rotate(yaw, glm::vec3(0.0, -1.0, 0.0));
glm::mat4 T = glm::translate(radius);
glm::mat4 S = glm::rotate(step, right);
glm::mat4 C = S * T * Y * P;
This works when the camera is simply moving forward. However, the problem is that when the yaw is changing (the user is turning right/left) and the step gets to certain values the sphere will start rotating in the wrong direction underneath the camera. It is not an instant switch. It seems to be reversed when step is between increments of PI to 2PI (i.e. it is reversed between pi and 2pi, 3pi and 4pi, etc..).
Any ideas on how I might fix this or what I am doing wrong?
UPDATE:
Here is a similar example of what I am trying to achieve:
http://www.youtube.com/watch?v=izVtTcq_his&t=0m23s
Except I want to be able to rotate the camera at smaller intervals than 90 degrees. If anyone has any links to example code/tutorials of how to achieve this I would really appreciate it.