TY - JOUR
T1 - A Trajectory Tracking Control Based on a Terminal Sliding Mode for a Compliant Robot with Nonlinear Stiffness Joints
AU - Song, Zhibin
AU - Ma, Tianyu
AU - Qi, Keke
AU - Spyrakos-Papastavridis, Emmanouil
AU - Zhang, Songyuan
AU - Kang, Rongjie
N1 - Funding Information:
In the NSA, due to the imperfect performance of the elastic mechanical component, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. To perform accurate trajectory-tracking of the end effector on a compliant robot, (a) (a controller based on terminal b) (sliding mode is designed. A stability proof is c) derived based on Lyapunov theory, which considers the application of the proposed control scheme onto the presented dynamical model. Moreover, the resulting closed-loop system’s time tracking error. (c) The third joint tracking error. convergence and its robustness are verified. The single-joint sinusoidal trajectory experiment, and the end-effector planar prototype trajectory experiment, are carried out under the same experimental conditions on a compliant 3-DoF robot with NSAs IInn tthhee NNSSAA,, dduuee ttoo tthhee iimmppeerrffeecctt ppeerrffoorrmmaanncceeooff tthhee eellaassttiiccmmeecchhaanniiccaall ccoommppoonneenntt, , developed in our team, while the PD parameters are assigned with optimal values. These iitt iiss mmoorree ddiiffffiiccuulltt ttoo aacchhiieevvee aaccccuurraattee ppoossiittiioonn ccoonnttrroollccoommppaarreedd ttoo tthhee rrigigidid aacctutuaatotorr.. experiments verify the effectiveness and superiority of the proposed algorithm. In the MMoorreeoovveerr,, ffoorr aac ocmomplpialinatnrtorboobtowt iwthitmhumltiupllteipdleegdreeegorefef roeefdforemesdo(DmOs F(sD) OdrFivs)e ndrbiyveNnS Abys , future, the proposed algorithm will be applicable in compliant robots including industrial NthSeAisn, ftlhuee nincfeluoefnecveeorfy evNeSryA NoSnAthone tthraej etrcatjoercytooryf othf etheen edndefefeffcetcotrorisisd diiffffeerreenntt aanndd eevveenn robots, wearable robots and exoskeletons. coupled. To perform accurate trajectory-tracking of the end effector on a compliant robot, a a controller based on terminal sliding mode is designed. A stability proof is derived based on Lyapunov theory, which considers the application of the proposed control scheme onto t&h ee dpitrinegse, nE.tSe.d-P .d Aylnl aaumthicoarsl hmavoed reela. dM anodr eaogvreeerd, ttoh teherpesuubllitsinhegd cvleorsseiodn- loofo tphe smyasnteumsc’rsip tt.i me convergence and its robustness are verified. The single-joint sinusoidal trajectory Funding: This research was funded by the National Key R&D Program of China (2019YFB1312404), experiment, and the end-effector planar prototype trajectory experiment, are carried out the Natural Science Foundation of China (Project No. 51975401), the Opening Project of State Key Laboratory of Robotics and System (Harbin Institute of Technology), and the Natural Science developed in our team, while the PD parameters are assigned with optimal values. These experiments verify the effectiveness and superiority of the proposed algorithm. In the future, the proposed algorithm will be applicable in compliant robots including industrial robots, wearable robots and exoskeletons.
Funding Information:
Funding: This research was funded by the National Key R&D Program of China (2019YFB1312404), the Natural Science Foundation of China (Project No. 51975401), the Opening Project of State Key Laboratory of Robotics and System (Harbin Institute of Technology), and the Natural Science Foundation of China (Project No. 51875393).
Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/3/4
Y1 - 2022/3/4
N2 - A nonlinear stiffness actuator (NSA) can achieve high torque/force resolution in the low stiffness range and high bandwidth in the high stiffness range. However, for the NSA, due to the imperfect performance of the elastic mechanical component such as friction, hysteresis, and unmeasurable energy consumption caused by former factors, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. Therefore, it is a challenge to implement precise trajectory control on a robot driven by such NSAs. In this paper, a control algorithm based on the Terminal SlidingMode (TSM) approach is proposed to control the end effector trajectory of the compliant robot with multiple DOFs driven by NSAs. This control algorithm reduces the coupling of the driving torque, and mitigates the influence of parametric variation. The closed-loop system’s finite time convergence and stability are mathematically established via the Lyapunov stability theory. Moreover, under the same experimental conditions, by the comparison between the Proportion Differentiation (PD) controller and the controller using TSM method, the algorithm’s efficacy is experimentally verified on the developed compliant robot. The results show that the trajectory tracking is more accurate for the controller using the TSM method compared to the PD controller.
AB - A nonlinear stiffness actuator (NSA) can achieve high torque/force resolution in the low stiffness range and high bandwidth in the high stiffness range. However, for the NSA, due to the imperfect performance of the elastic mechanical component such as friction, hysteresis, and unmeasurable energy consumption caused by former factors, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. Therefore, it is a challenge to implement precise trajectory control on a robot driven by such NSAs. In this paper, a control algorithm based on the Terminal SlidingMode (TSM) approach is proposed to control the end effector trajectory of the compliant robot with multiple DOFs driven by NSAs. This control algorithm reduces the coupling of the driving torque, and mitigates the influence of parametric variation. The closed-loop system’s finite time convergence and stability are mathematically established via the Lyapunov stability theory. Moreover, under the same experimental conditions, by the comparison between the Proportion Differentiation (PD) controller and the controller using TSM method, the algorithm’s efficacy is experimentally verified on the developed compliant robot. The results show that the trajectory tracking is more accurate for the controller using the TSM method compared to the PD controller.
UR - http://www.scopus.com/inward/record.url?scp=85126613180&partnerID=8YFLogxK
U2 - 10.3390/mi13030409
DO - 10.3390/mi13030409
M3 - Article
SN - 2072-666X
VL - 13
JO - Micromachines
JF - Micromachines
IS - 3
M1 - 409
ER -
