Differentiator-based Time Delay Control For High-precision Trajectory Tracking Of Robotic Systems

High-precision trajectory tracking control has presented even more challenges facing the fields of robotic application and automation all the time.Time delay control(TDC),regarded as one significant branch of robust control schemes,can provide an alternative solution for high-precision robotic trajectory tracking control due to its special advantages,which are summarized as clear physical meaning,no demand for model knowledge of the controlled object,compatibility with different control schemes,strong robustness,low computational requirements,and easy implementation for engineering.But it is worth to note that the current TDCs strictly depend on the acceleration signal feedback,and the implementation of TDC is largely limited due to the fact that lots number of robots only offer the high-quality joint position.In practice,TDC applied in robots obtains joint velocity and acceleration using numerical differentiation.However,these differential signals estimated by numerical differentiation are too rough to easily cause excessive TDC control torque consumption and poor control quality.Meanwhile,it is also difficult to estimate high-quality velocity and acceleration in engineering.Furthermore,the demands for robot systems are increasing,but its high nonlinearity and joint couplings,as well as more and more higher tracking standards motivate researchers to develop high-performance composite TDC using nonlinear controls.Based on the problem of high-precision trajectory control for uncertain multi-degree-ofdegree robots,this dissertation proposes two methods of acceleration estimation,and then constructs three TDC schemes for high-precision trajectory tracking of robotic systems based on the framework of model-free TDC.The details are illustrated as follows:1.A fast transient tracking differentiator(FTD)based on the measured position only is proposed to extract high-quality velocity.Global asymptotic convergence of the proposed FTD is proved in agreement with the tracking differentiator lemma,Lyapunov direct method and La Salle’s invariance theorem.Then,the two proposed FTDs are cascaded to construct an acceleration estimator based on position measurement only,and the cascaded FTDs-based TDC of trajectory tracking for robots is also proposed.Due to the high-quality acceleration estimation,the proposed scheme significantly improves the control quality of TDC,which is compared with the traditional TDC.2.A fast third-order tracking differentiator(FTTD)based on the measured position only is proposed to obtain high-quality acceleration.The high-order tracking differentiator lemma,Lyapunov direct method and La Salle’s invariance theorem are employed to prove the global asymptotic convergence of proposed fast third-order nonlinear tracking differentiator.After that,the cascaded FTTD-based TDC of trajectory tracking for robots is also proposed.Compared with the FTDs-based TDC,the proposed scheme further improves the convergence speed together with the steady-state errors in tracking.3.A non-singular terminal sliding mode surface based on a monotonic and smooth nonlinear odd function is designed,and a proximate finite-time delay control of trajectory tracking for robots(PTDC)is proposed.Using finite-time stability lemma,global exponential stability lemma and Lyapunov direct method,the closed-loop system controlled by proposed PTDC controller is proved to be globally proximate finite time stable,which ensuring that its tracking trajectories first converge to an arbitrary small domain around the origin in a finite time,and then converge to the origin exponentially.And the cascaded FTTD-based proximate finite-time delay control of trajectory tracking for robots is also proposed.4.The improvements of velocity and acceleration estimations of the proposed FTD,cascaded FTDs,and FTTD,and the performances of the cascaded FTDs and FTTD-based TDCs for uncertain robots are testified during numerical simulation,respectively.Through the real-time experiment performed on 2 degree-of-freedom uncertain robotic system,it strongly shows that above proposed time delay control schemes are feasible,reliable and advanced for improving the high-precision tracking control for robots.