Thankfully we now have excellent controllers on CD-i, but that was different in 1991 when the system was released. CD-i initially released to market with only the Thumbstick, an innovative way to move the cursor on screen with one hand, easily point and click on buttons to navigate through educational content. That's because Philips intended the CD-i to be close to education, rather than pure entertainment. At a later stage, it seemed to gather a higher interest, games were going to be more important on CD-i. This is when Philips introduced the CD-i Touchpad, based on the Gravis Ultrapad and was built by Logitech. The nice thing about this touchpad is that it is also suitable for left-handed people.
In 1994, Philips released the Gamepad, which was, in my opinion, a step back from the original Touchpad. That was mainly because the buttons were less responsive. It was also licensed by a Logitech design.
In the years that came after it, we saw a few third party efforts like the Gamester gamepad and the Tecno Plus Joystick, which were both excellent and both surpass the Philips versions, but nowadays both are very rare.
[Thanks, Matthew Henzel, Videogame Obsession]