Introducing Series Elastic Links for Affordable Torque-Controlled Robots

Modified Linear Technique for the Controllability and Observability of Robotic Arms

“…First, the linearization technique for the controllability and observability of robotic arms will be presented [25], [26], [27], [28], [29], [30], [31], [32], [33]. Second, the linear technique for the controllability and observability of robotic arms will be presented [34], [35], [36], [37], [38], [39], [40], [41]. And third, the modified linear technique for the controllability and observability of robotic arms will be presented as the main contribution of this study.…”

“…The linear technique also has been frequently applied for the controllability and observability of robotic arms [34], [35], [36], [37], [38], [39], [40], [41], the linear technique consists of the following three steps: 1) if all the joints in the robotic arm are rotational, then mathematical operations are used to rewrite the nonlinear time-variant model as a linear timevariant model, 2) this linear time-variant model is evaluated at origin to obtain a linear time-invariant model, 3) the rank condition tests the controllability and observability of the linear time-invariant model.…”

“…Now, the linear technique of [34], [35], [36], [37], [38], [39], [40], [41] is applied to the two link robotic arm.…”

“…In [34], [35], [36], authors extract properties of the mechanical parameters to demonstrate that some robotic arms are controllable and observable. In [37], [38], [39], authors design elastic, flexible, or micro robotic arms which since their design are controllable. In [40], [41], authors find a transformation for which states have the greatest contribution in the controllability and observability.…”

“…The linearization technique for the controllability and observability of robotic arms has the problem that it produces an undesired error caused by the Jacobian approximation. On the other hand, the linear technique also has been frequently applied for the controllability and observability of robotic arms [34], [35], [36], [37], [38], [39], [40], [41], the linear technique consists of the following three steps: 1) if all the joints in the robotic arm are rotational, then mathematical operations are used to rewrite the nonlinear time-variant model as a linear time-variant model, 2) this linear time-variant model is evaluated at origin to obtain a linear time-invariant model, 3) the rank condition tests the controllability and observability of the linear timeinvariant model. The linear technique for the controllability and observability of robotic arms has the problem that it can not be applied to robotic arms with prismatic joints.…”