LAUSR

In this study, a modified linear technique is proposed for the controllability and observability of robotic arms, the modified linear technique consists of the following steps: a transformation is used to rewrite a nonlinear time-variant model as a linear time-variant model, this linear time-variant model is evaluated at origin to obtain a linear time-invariant model, and the rank condition tests the controllability and observability of the linear time-invariant model. The modified linear technique is better than the linearization technique because the modified linear technique does not use the Jacobian approximation, while the linearization technique needs the Jacobian approximation. The modified linear technique is better than the linear technique because the modified linear technique can be applied to robotic arms with rotational and prismatic joints, while the linear technique can only be applied to robotic arms with rotational joints.