Q2. What are the future works in "Stable force control and contact transition of a single link flexible robot using a fractional-order controlleri" ?
Their future work will consider the study of contact at any point of the link. Moreover, the authors plan to extend this strategy to a flexible link robot with several degrees of freedom.
Q3. How many vibration modes are usually taken into account?
since the amplitude of the vibration modes decreases as their frequency increases, as much as four vibration modes are usually taken into account.
Q4. How is the stability of a flexible robot guaranteed?
Asymptotic stability in the case of rebounds is guaranteed by using a recent resulton hybrid fractional-order systems developed in [29].
Q5. What is the condition used to determine when the coupling torque is steady state?
Note that665if the steady state motor and tip positions coincided with q d m and q d l respectively, the steady state coupling torque would coincide with Gd c , in accordance with (6), and the force control process would not require any further step.
Q6. What is the advantage of changing the reference instead of changing the control scheme?
The advantage of changing the references instead of changing the control scheme or the controller law is that the stability of the system is not affected by environment impedance changes, provided that conditions presented in Section 4 are fulfilled.
Q7. How was the control of a rigid robot interacting with the environment proposed?
Control of rigid robots interacting with the environment has been proposed, that switches from position to force control in function of a contact detection mechanism, e.g., [15].
Q8. What is the simplest way to obtain stable contact with stiff objects?
According to Lemmas 2 and 3, stable contact with stiff objects is obtained only using integer order controllers Ci(s) having kp < 0 or fractional-order controllers Cf (s) having a > 1, respectively.
Q9. What is the phase margin of the closed-loop system?
The phase margin of the system must be relatively high for any pair (K,u) thatbelongs to the defined range of impedances, i.e., robust phase margin condition.
Q10. What is the transfer function between the motor and the fictitious input?
Ĵ ¨̂q m(t)+ ĥ ˙̂q m(t)+ ĜCoul(t) (26)Moreover, if the Coulomb friction is regarded as a step like disturbance that can becompensated by the loop closed around the motor, the transfer function from the ficti-tious input, u(s), to the motor angular position, q̂m(s), can be obtained:295q̂m(s) u(s) = Ĝm(s) = K̂m s · (Ĵ · s+ ĥ) (27)The transfer function Gm(s) between the motor angle at the link side of the gear, qm(t), and the fictitious control signal, u(t), is given by Gm(s) = Ĝm(s)/n.
Q11. What is the simplest way to assess the stability of the robot-environment system?
the robustness of the integer and fractional-order controllers to changesin the parameters of the robot-environment system is analyzed.
Q12. What is the optimum frequency response of a flexible link?
Since flexible links with dis-tributed mass have an infinite number of vibration modes, this experimental result supports the hypothesis of a massless link with all the robot mass concentrated at its tip.
Q13. What is the condition used to determine when the coupling torque has reached its steady state?
The condition used to determine when such steady state has been reached iss(Gc(t)) |Gc(t)| < L (68)being s(Gc(t)) and Gc(t) the standard deviation and the mean values respectively of the coupling torque in a time window [t D, t] whose length, D, is adjustedexperimentally.
Q14. What was the first application of a single link flexible robot?
This controller was later extended to a two links - three degrees of freedom 1 (DOF) flexible robot in [18], in which a hybrid positionforce control combined with a collision detection algorithm was developed.
Q15. What is the first paper to address the fractional-order force control of flexible link robots?
Their paper addresses for the first time the fractional-order force control of flexible link robots in contact tasks, that is robust to rebounds, environment uncertainties and joint friction.
Q16. What is the simplest way to verify the stability of a multimodel system?
Then this system is quadratically stable (i.e. there exists a Lyapunov function which guarantees the stability) if it were verified that:1. All the Hi(s) are of the same order.
Q17. What is the condition for a hybrid system that switches between two linear time invariant systems?
Theorem 2. Consider a hybrid system that switches among a set of linear time410invariant systems described by transfer functions Hi(s), given by (35), a finite number of times at unknown instants.
Q18. What is the difference between the proposed and the proposed control system?
the proposed control system attains higher stability robustness and phase margin than a PD tip position controller, which is the integer-order controller of complexity similar to the proposed one.