Integrating Lyapunov based backstepping and neuro fuzzy logic with sliding mode control for precise trajectory tracking of differential drive robots

This paper presents the Fixed Ultra Hybrid Adaptive Controller (FUHAC) to the differential drive mobile robots to realize proper trajectory tracking in dynamic uncertainties, non-linearities, and external disturbances. FUHAC combines a number of nonlinear clustering methods, including adaptive backstepping, neural fuzzy inference, sliding mode compensation, disturbance observation and predictive error anticipation, into a multi-rate, adaptive gain scheduling model, which is Lyapunov stable. The tracking error, adaptive weighting dynamics and disturbance dynamics are coupled together to form a composite Lyapunov function, which guarantees Global Uniform Ultimate Boundedness (GUUB); when the approximation residuals are small enough, Global Asymptotic Stability (GAS) can be achieved. Three benchmark paths of lemniscate, circle, and diamond were simulated in large scale. The final error of position was less than 4 cm on all the trajectories. ISE/IAE/ITAE = (3.70/4.70/21.98) of the lemniscate, (1.08/2.62/18.81) of the circle, and (1.20/3.83/35.67) of the diamond was reported as the cumulative performance indices. Actuator torque mean was less than 10Nm, and settling time was 12.7s. Oscillation waveforms remained within 0.95 in all conditions, and the stabilized adaptive sliding mode is found to stabilize at Ks = 3.7–4.6, which confirms energy efficient stability maintenance. The controller was also tested on publicly available data on Pioneer 1 time series. Whereas the closed loop was also stable with a return to maneuverability in the aggressive maneuvers, practical errors in tracking were larger than those in simulation: average positional error 1.47 m, maximum instantaneous deviation 6.44 m, final position error 2.33 m, and RMS error 1.85 m. These transients were associated with actuator saturation around rated torque limits and extensive magnitude low frequency control actions. On the whole, FUHAC provides high performance, globally stable and computationally-efficient control of autonomous ground vehicles under uncertain or time varying conditions.