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Controllability and observability of an n-link planar robot with active joints

This paper considers the linear controllability and observability of an n-link planar robot with active joints. The controllability and observability around the upright equilibrium point (UEP) are investigated. Specific properties of the mechanical parameters are used to derive a necessary and sufficient condition for the linear controllability and observability of the robot when any of the n - 2 joints other than the first or last is active. For the case that there are two active joints adjacent to each other, a necessary and sufficient condition is also established to ensure the controllability and observability at the UEP.