Trajectory Tracking Control For Flexible-joint Robot Manipulators With Bounded Torque Inputs

In recent years,the singular perturbation theory based control approach for flexible-joint robot manipulators has aroused increasing concerns from researchers worldwide.Though certain advancements on the related investigations have been obtained in these year,there are still some open problems to be solved in the practical application of flexible-joint robot manipulators: 1)The output torque of the joint actuator has a saturation limit,but most of the existing controllers are designed on the basis of that the joint actuators can offer arbitrarily large torque required,and then select the actuators accordingly.It leads to a situation that large motors with high power are necessary to meet the theoretical requirements on big torque control inputs,which makes the mechanical structure of the robot manipulators not compact enough and causes huge resource wastes.Considering the actual situation that the output torque of the joint motor is saturated,how to design an input control law for the robot manipulators with upper and lower bounds? 2)The measurements of angular position and velocity of links and joint motors are not always available,due to installation complexity of sensors or controlling cost.Even if these states were measurable,noise pollution is still inevitable and will deteriorate the measurement accuracy.How to reduce the number of necessary feedback states to achieve non-full-state feedback control with only angular position measurements of links and joint motors?Aiming to solve the problem 1),a class of saturated controllers with definable upper and lower bounds are proposed in framework of singular perturbation theory.First,the dynamics of flexible-joint robot manipulators is decoupled into fast and slow subsystems according to singular perturbation theory.Second,for the slow subsystem,a bounded backstepping control law is designed by introducing a class of bounded functions with smooth saturation properties.With a projection operator contained RBF neural network,a complex term in the controller expression is estimated so as to gain a simple form of bounded backstepping control law.Third,for the fast subsystem,the saturation function is applied to make the fast control law bounded.A filtered tracking error of joint elastic torque is adopted in the fast control law,which makes the fast subsystem converge quickly.In addition,the Lyapunov method is used to analyze the system stability and the system error is proved to be ultimately uniformly bounded.Finally,simulation results show that the proposed bounded controller has a superior control performance,and can effectively suppress the serious oscillations of input torque at the initial moment,keeping the torque control inputs bounded all the time.For the problem 2),a partial-state feedback control law is proposed with only angular position measurements of links and joint motors.First,in order to reduce the number of state feedback measurements,a second-order nonlinear observer is designed to estimate the velocity signals of the links and joint motors.On the basis of it,the bounded control law is designed.At the same time,in order to obtain a better dynamic performance,fuzzy strategy is applied to make the control parameters self-tune online.Then,the Lyapunov method is used to analyze the system stability and semi-global stability of the system is obtained.Finally,numerical simulations were carried out to verify the effectiveness of the proposed controller.