Robust Tracking Control of Aerial Robots Via a Simple Learning Strategy-Based Feedback Linearization

Abstract

To facilitate accurate tracking in unknown/uncertain environments, this paper proposes a simple learning (SL) strategy for feedback linearization control (FLC) of aerial robots subject to uncertainties. The SL strategy minimizes a cost function defined based on the closed-loop error dynamics of the nominal system via the gradient descent technique to find the adaptation rules for feedback controller gains and disturbance estimate in the feedback control law. In addition to the derivation of the SL adaptation rules, the closedloop stability for a second-order uncertain nonlinear system is proven in this paper. Moreover, it is shown that the SL strategy can find the global optimum point, while the controller gains and disturbance estimate converge to a finite value which implies a bounded control action in the steady-state. Furthermore, utilizing a simulation study, it is shown that the simple learning-based FLC (SL-FLC) framework can ensure desired closed-loop error dynamics in the presence of disturbances and modeling uncertainties. Finally, to validate the SL-FLC framework in real-time, the trajectory tracking problem of a tilt-rotor tricopter unmanned aerial vehicle under uncertain conditions is studied via three case scenarios, wherein the disturbances in the form of mass variation, ground effect, and wind gust, are induced. The real-time results illustrate that the SL-FLC framework facilitates a better tracking performance than that of the traditional FLC method while maintaining the nominal control performance in the absence of modeling uncertainties and external disturbances, and exhibiting robust control performance in the presence of modeling uncertainties and external disturbances. INDEX TERMS Feedback linearization control, nonlinear system, uncertain systems, learning control, unmanned aerial vehicle.

Adaptive model predictive control design using multiple model second level adaptation for parameter estimation of two‐degree freedom of helicopter model

“…It is evident from Table 2 that the smoothness of the control input is better in the case of the proposed ANMPC control algorithm as compared to the existing control algorithm. Also, the proposed ANMPC is more energy‐efficient than the FLC 28 and SL‐FLC 45 …”

“…Numerically, the tracking performance of the controllers is evaluated by taking integral absolute error (IAE), root mean square error (RMSE), and integral square error (ISE) as the performance index. From Table 2, it is observed that the proposed ANMPC provides low RMSE, IAE, and ISE than the FLC 28 and SL‐FLC 45 . The respective control inputs for both the vertical and horizontal subsystems are presented in Figures 6 and 7 respectively.…”

“…The proposed control algorithm is validated on 2‐DoF helicopter model in simulation as well as a real‐time environment. For a fair comparison, we have also designed the feedback linearization controller (FLC) 28 and simple learning based feedback linearization control (SL‐FLC) 45 by considering the same initial values of the parameter vector, state vector, and observer gain matrix, as mentioned below. Here, the constants for the virtual input signals are chosen as and .…”

“…As the sampling time of the proposed ANMPC is considered as 0.001 s, it is found that the maximum time taken by the algorithm to generate the control input is 0.0010],s. Whereas, the time taken to estimate the state and parameter of the system is 0.000053 and 0.000039 s respectively. The comparative simulation result for pitch and yaw angle tracking by the proposed ANMPC with the existing FLC 28 and SL‐FLC 45 is presented in Figures 4 and 5 respectively. From the zoomed portions of Figures 4 and 5, it is observed that the proposed ANMPC provides better tracking performance than the FLC 28 and SL‐FLC 45 control algorithm.…”

“…The comparative simulation result for pitch and yaw angle tracking by the proposed ANMPC with the existing FLC 28 and SL‐FLC 45 is presented in Figures 4 and 5 respectively. From the zoomed portions of Figures 4 and 5, it is observed that the proposed ANMPC provides better tracking performance than the FLC 28 and SL‐FLC 45 control algorithm. Moreover, the variation of the adaptive gain for the SL‐FLC framework is depicted in Figures 8 and 9, respectively.…”