Fig. 1 Snapshot of the quadcopter tracking a roll reference command with the LQR-based attitude controller designed from the onboard framework. During the flight, the framework continuously learns the dynamics and updates the controller in execution time. The algorithm is easily integrated into th... More about this image found in Snapshot of the quadcopter tracking a roll reference command with the LQR-b...

Fig. 2 Schematic diagram for a quadcopter featured with an “X” type of airframe. Three basic rotational movements are achieved by varying the spinning speeds of motors. We denote O NED as the earth frame system, where NED represents North-East-Down . The body frame O x y z ... More about this image found in Schematic diagram for a quadcopter featured with an “X” type of airframe. T...

Fig. 3 Schematic diagram of the offboard framework More about this image found in Schematic diagram of the offboard framework

Fig. 4 A general diagram of the proposed onboard framework More about this image found in A general diagram of the proposed onboard framework

Fig. 5 Points represent the mean error ratio, and the semi-transparent ribbons indicate the variance More about this image found in Points represent the mean error ratio, and the semi-transparent ribbons ind...

Fig. 6 The value of the cumulative errors e r r cum , defined as the summation of tracking error of three attitude angles along the period, is shown in the legend More about this image found in The value of the cumulative errors e r r cum , defined as the...

Fig. 7 The tracking performance of the baseline controller follows the attitude command sent by the remote controller More about this image found in The tracking performance of the baseline controller follows the attitude co...

Fig. 8 Given the same tracking reference, the LQR controller derived from the offboard framework presents a comparative tracking ability to that of the PID with numerous parameter tuning trials More about this image found in Given the same tracking reference, the LQR controller derived from the offb...

Fig. 9 The estimation of the dynamical parameters during the learning phase which is terminated once P k reaches P th 2 . The RLS-based estimator manages to give the same results as the offboard framework (dashed lines). More about this image found in The estimation of the dynamical parameters during the learning phase which ...

Fig. 10 After the learning phase, the final derived LQR delivers a satisfying tracking ability similar to the one developed by the offboard framework More about this image found in After the learning phase, the final derived LQR delivers a satisfying track...

Fig. 1 Schematic diagram of Pendubot More about this image found in Schematic diagram of Pendubot

Fig. 2 Phase portrait of the Pendubot orbit O d More about this image found in Phase portrait of the Pendubot orbit O d

Fig. 3 Simulation results for p = 1 without parameter uncertainty More about this image found in Simulation results for p = 1 without parameter uncertainty

Fig. 4 Simulation results for p = 1 with parameter uncertainty More about this image found in Simulation results for p = 1 with parameter uncertainty

Fig. 5 Simulation results for p = 6 with parameter uncertainty More about this image found in Simulation results for p = 6 with parameter uncertainty

Fig. 6 Simulation results for p = 6 with parameter uncertainty. The gain of the terminal weighting matrix used was five times higher than the value in Eq. (26) , the results of which are presented in Fig. 5 . More about this image found in Simulation results for p = 6 with parameter uncertainty. The gain o...