High-precision trajectory tracking in changing environments through L<inf>1</inf> adaptive feedback and iterative learning

Abstract

As robots and other automated systems are introduced to unknown and dynamic environments, robust and adaptive control strategies are required to cope with disturbances, unmodeled dynamics and parametric uncertainties. In this paper, we propose and provide theoretical proofs of a combined L1 adaptive feedback and iterative learning control (ILC) framework to improve trajectory tracking of a system subject to unknown and changing disturbances. The L1 adaptive controller forces the system to behave in a repeatable, predefined way, even in the presence of unknown and changing disturbances; however, this does not imply that perfect trajectory tracking is achieved. ILC improves the tracking performance based on experience from previous executions. The performance of ILC is limited by the robustness and repeatability of the underlying system, which, in this approach, is handled by the L1 adaptive controller. In particular, we are able to generalize learned trajectories across different system configurations because the L1 adaptive controller handles the underlying changes in the system. We demonstrate the improved trajectory tracking performance and generalization capabilities of the combined method compared to pure ILC in experiments with a quadrotor subject to unknown, dynamic disturbances. This is the first work to show L1 adaptive control combined with ILC in experiment.

Transfer learning for high‐precision trajectory tracking through adaptive feedback and iterative learning

“…Proof Theorem 4.4.1 in [5] proves the bound in (18) under the same assumptions made in this paper. It remains to show the bound in (19).…”

“…When using the L 1 controller, the estimated disturbance in the ILC component does not change much after applying the external wind disturbance since the underlying L 1 controller compensates for the change in dynamics. Overall, the three frameworks converge to a slightly higher average tracking error (iteration [17][18][19][20] due to the fact that the wind disturbance is partially non-repetitive (or noisy); learning is only able to compensate for systematic disturbances. Tab.…”

“…Learning behavior of the PD-ILC, PID-ILC, and L 1 -ILC framework in the simulator for iterations 1-10. The learned reference input and disturbance are transferred to the AR.Drone 2.0 after iteration 10, and learning continues in iteration [11][12][13][14][15][16][17][18][19][20]. Note that the scale is different than in Fig.…”

“…The addition of the two input signals couples the problems of providing a repeatable system behavior with the problem of improving tracking performance. In [18] we proposed and showed the first experimental results on a quadrotor of a serial framework of L 1 adaptive control and ILC under changing dynamics. The serial architecture uses the L 1 adaptive controller as an underlying control to achieve a repeatable system behavior despite the presence of unknown and changing disturbances.…”

“…We also show that a reference trajectory generated based on the reference model of the adaptive controller achieves more accurate tracking performance than reference trajectories generated with standard choices. We use the serial framework [18] where the L 1 adaptive controller acts as an underlying controller (see Fig. 2) that makes the system display a repeatable and reliable behavior (in other words, it achieves the same output when the same reference input is applied) even in the presence of unknown disturbances and changing dynamics; however, perfect trajectory tracking is not achieved.…”