Concept Behind Segway

The Segway is a dynamic system that is commonly referred to as an inverted pendulum. The Segway and rider form a more complicated inverted pendulum that has uncertain time-varying dynamics. Non-inverted pendulums, like crane payloads and the oscillating arm inside a grandfather clock, swing back and forth in a stable manner with limited amplitude. These types of dynamic systems occur throughout the world in useful products. On the other hand, inverted pendulums do not naturally swing back and forth with a well-controlled oscillation. Rather, they fall over. The simplest form of an inverted pendulum consists of a mass attached through a massless rod to a base mass. This is commonly known as a cart-pendulum system.

INVERTED PENDULUM

  

    

      The cart is free to move horizontally. The rod is connected to the cart through a rotational pin joint. This system is in unstable equilibrium when the rod is standing upright. Mathematically, this equilibrium can be maintained as long as there are no input forces whatsoever on the system. However, such conditions do not exist in real systems and some means of stabilization is needed to maintain the pendulum in the upright position. A force F must be applied to the cart in order to move the cart pivot back and forth from one side of the pendulum mass centre to the other side. The pendulum is always falling over, but the cart motion tries to keep the leaning angle at a small level.

       When a Segway is in use, the device is driven by two wheels that are placed side-by-side, rather than the standard in-line configuration of a bicycle or a motorcycle. When the operator leans forward, the wheels turn in unison in the same direction to provide forward motion. In order to stop, the wheels must accelerate forward to get out in front of the system's centre of mass and then apply a deceleration torque to slow the system down without causing the operator to fall forward o_ the device. These operating principles are reversed to allow the system to move backward. In order to turn, the wheels rotate at unequal speeds causing the system to travel in an arc.

       If the system is not translating forward or backward, then the wheels can rotate in opposite directions to turn the machine in place. Given the side-by-side wheel configuration, and the elevated centre of mass, the mechanical design of the transporter is unstable. It will fall over if the computerized control system is not continuously turning the wheels. This constant adjusting of the device is similar to a person balancing an inverted broom in their hand. In order to keep the broom upright, the person must continually move their hand in the direction that the broom is falling. The hand must pass to the other side of the broom's centre of mass to generate a torque that will cause the broom to start rotating in the opposite direction. As a result, the broom is always falling, but the hand motion keeps changing the direction of the fall.

       Just like the inverted broom, the Segway and rider are always falling. However, it is not possible for the human operator to balance the device, as they can with a human-powered inverted pendulum such as a unicycle. The sensors in the device must constantly be measuring the state of the machine and feeding this information to the computer controller. The controller then uses this feedback signal to adjust the wheel speed so that the forward/backward (pitch) falling motion is maintained within an acceptable envelope so that device and rider do not fall over. Note that under many operating conditions, the system is mechanically stable in the side-to-side (roll) direction. Therefore, the computer does not attempt to control the roll motion. Assuming wheel-ground rolling friction, the system is also stable in the yaw direction. However, the computer must change the yaw rate in order to turn the machine in response to the operator input.