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The performance of robots in high-level tasks depends on the quality of their lower level controller, which requires fine-tuning. However, the intrinsically nonlinear dynamics and controllers make tuning a challenging task when it is done by hand. In this article, we present DiffTune, a novel, gradient-based automatic tuning framework. We formulate the controller tuning as a parameter optimization problem. Our method unrolls the dynamical system and controller as a computational graph and updates the controller parameters through gradient-based optimization. The gradient is obtained using sensitivity propagation, which is the only method for gradient computation when tuning for a physical system instead of its simulated counterpart. Furthermore, we use $\mathcal {L}_{1}$ adaptive control to compensate for the uncertainties (that unavoidably exist in a physical system) such that the gradient is not biased by the unmodeled uncertainties. We validate the DiffTune on a Dubin's car and a quadrotor in challenging simulation environments. In comparison with state-of-the-art autotuning methods, DiffTune achieves the best performance in a more efficient manner owing to its effective usage of the first-order information of the system. Experiments on tuning a nonlinear controller for quadrotor show promising results, where DiffTune achieves 3.5× tracking error reduction on an aggressive trajectory in only ten trials over a 12-D controller parameter space.

The electromagnetic-driven micromirror (EDMM) is contaminated with noise measured by piezoresistive sensors located in the basement of the chip during the process of angle positioning. In this article, a novel residual weight adaptive filter (RWAF) for EDMM is proposed to deal with the problem of noise pollution and eliminating outliers. Above all, the so-called Hammerstein architecture embedded with a rate-dependent Duhem submodel is developed to describe the dynamic performance for EDMM. Then, the residual prediction generated by the random variable is taken as the sample to be estimated, and the confidence interval estimation of the given confidence degree is determined by combining the residual variance. Subsequently, the upper and lower limits of confidence intervals are used as threshold to reduce model error via application of generalized gradient that is added in the Kalman gain for compensating the nonlinear part to improve filtering accuracy. In addition, convergence analysis of the novel algorithm is analyzed using martingale convergence theorem. Finally, conducted quantitative comparisons with unscented Kalman filter (UKF) and extended KF (EKF) reveal the advantages of the proposed RWAF in noise attenuation and state reconstruction.

Viscoelasticity has been widely studied over the past few decades as a combination of the viscous effects of energy dissipation and the elastic effects of energy storage. As an application, viscoelastic dampers are commonly used to suppress the dynamic behaviour of structures. However, in an actual physical environment, it is difficult to explore the stationary probability densities of random responses for viscoelastic systems. For this purpose, we present a numerical method to investigate the dynamic behaviour of a generalized Maxwell-type viscoelastic system under harmonic and Gaussian white noise excitations. Using approximate equivalent and stochastic averaging, we establish an averaged Itô differential equation for the amplitude of the system. For primary external resonance, we solve the reduced Fokker–Planck–Kolmogorov equation by using the successive over-relaxation technique combined with a finite difference method. Through Monte Carlo simulations, we verify the applicability, accuracy and efficiency of the proposed methodology and demonstrate that viscoelasticity has a significant impact on the dynamic behaviour of the viscoelastic systems. This work reveals the remarkable influences of viscoelasticity, excitation intensities, linear and nonlinear damping and linear and nonlinear stiffness on the probability density functions of system responses, which can guide the selection of materials, stiffnesses and structures in viscoelastic damper design.

We study the reliability of stochastically excited and controlled single first-integral systems and present an approximate analytical solution for the first-passage rate (FPR). By introducing the stochastic averaging method (SAM), we reduce the dimension of the original system to an averaged one-dimensional controlled Ito^ differential equation. We then modify the classic Laplace integral method (LIM) and apply it to deal with the arduous integrals in the expression of reliability function. The procedure of acquiring the analytical solution for the reliability is illuminated in detail as well. In addition, we provide two controlled single first-integral nonlinear vibration systems, namely, the classical bistable model and the two coupled nonlinear oscillators, as examples. By comparing the results obtained from the modified Laplace integral method (MLIM) to Monte Carlo simulations (MCS), we verify the effectiveness and exactness of the proposed procedure. We identified two properties in the obtained analytical solution: One is that the solutions are independent of the initial system state. The other is that they are only effective in the high passage threshold range. Finally, a reasonable explanation has been given to explain these two properties.