Differential Steering System – A Tutorial
Here's a link to an excellent article covering the equations and model for steering a robot. It requires an initial familiarity with calculus, but goes to great lengths to keep the examples and equations simple and easy to follow.
"The differential steering system is familiar from ordinary life because it is the arrangement used in a wheelchair. Two wheels mounted on a single axis are independently powered and controlled, thus providing both drive and steering. Additional passive wheels (usually casters) are provided for support. Most of us have an intuitive grasp of the basic behavior of a differential steering system. If both drive wheels turn in tandem, the robot moves in a straight line. If one wheel turns faster than the other, the robot follows a curved path. If the wheels turn at equal speed, but in opposite directions, the robot pivots. So steering the robot is just a matter of varying the speeds of the drive wheels. But how exactly do we choose the speeds so that the robot will move where we want it to go? In these notes, we will try to refine this intuitive understanding into mathematical expressions that can be used for implementing robot control software."
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