Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity

Dynamic Learning from Adaptive Neural Control of Uncertain Robots with Guaranteed Full-State Tracking Precision

“…For comparison purpose, the plant controlled, the reference trajectory, and the constrained tracking error performance are chosen the same as Section 5.1, while the initial conditions and the neural network structures are unchanged. In the simulation, with the control gains selected as 10 = 3, 20 = 15, and 21 = 8, simulation results for static neural learning control (45) are shown in Figures 11-15. From Figures 11-14, it can be seen that the smaller overshoot and the faster convergence are obtained using the learned knowledge in (55), while full-state tracking errors satisfy the prescribed performance.…”

“…Consider the closed-loop system consisting of the robotic system (1), the bounded reference trajectory (2), the full-state tracking performance condition (3), the transformed error (10), the static neural learning control law (45) with the stored constant weight given in (39), and the virtual control law (15). Then, for the same or a similar recurrent reference orbit ( ( )) given in Theorem 6 and the initial conditions satisfying the prescribed performance (3), it can be guaranteed that all the closed-loop signals are uniformly ultimately bounded, and the constrained full-state tracking errors satisfy the prescribed performance (3) and converge to a small residual set of zero.…”

“…Recently, adaptive neural prescribed performance controller was proposed in [43,44] for feedback linearizable nonlinear systems by means of transformation functions. The proposed method was also developed to deal with the constrained output tracking control problem in many applications such as robotic systems [45], nonlinear servo mechanisms [46], marine surface vessels [33], nonlinear stochastic large-scale systems with actuator faults [47], and switched nonlinear systems [48]. To solve partial tracking error constraints, a fuzzy dynamic surface control design was developed in [49,50] for a class of strict-feedback nonlinear systems by transforming the state tracking errors into new virtual variables.…”

“…To solve partial tracking error constraints, a fuzzy dynamic surface control design was developed in [49,50] for a class of strict-feedback nonlinear systems by transforming the state tracking errors into new virtual variables. However, the existing control schemes, such as [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51], can only guarantee the stability of closed-loop systems with different constraints, which are not capable of achieving the learning of unknown system dynamics. The main reason is that the derived closed-loop error system is extremely complex, such that its exponential convergence is difficult to be verified using the existing stability analysis tools.…”

Time domain passivity control of time-delayed bilateral telerobotics with prescribed performance

“…The performance of error evolution within prescribed bounds in both problems of regulation and tracking in robotic system is achieved in [6]. Kostarigka et al analyse the pre-set performance control problem for a flexible joint robot with unknown and possibly variable elasticity [7]. In the bilateral teleoperation research, Yang et al firstly apply the PPC to enhance the position synchronization performance [8]- [9] of the master and the slave robots.…”