The equations of motion of the single-pole balancer

The goal of the controller is to exert a sequence of forces, , on the center of mass of the cart such that the pole balanced for a specific (or infinite) amount of time and the cart stays within the track, that is, doesn't hit left or right walls. Taking into account the mechanics described here, we can qualify the pole-balancing task as an avoidance control problem, because the state of the cart-pole apparatus must be maintained to avoid certain regions of the state space. No unique solution exists for appropriate state estimation, and any solution of equations of motion that enables the ...

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