The Maxwell-slip (MS) model is extended to a distributed parameter Maxwell-slip (DPMS) model, and a DPMS model parameter identification process is proposed for the hysteresis in piezoelectric actuators (PEAs). This model is governed by a saturation deformation function (SDF) and a stiffness function (SF); it requires only a few parameters and can capture nonconvex hysteresis. It has a clear interpretation in the mechanical domain and provides insight into the mechanism of hysteresis generation; hence, it can predict the performance in the unidentified range. With a linear SDF, exponential, power-law, and polynomial SFs are studied for a PEA-based nanopositioning system. The normalized root mean square (NRMS) errors for these SFs are 0.60%, 0.43%, and 0.47%, respectively. With parameters identified from the middle hysteresis loop, the NRMS error is 0.68%. For nonconvex hysteresis, the NRMS error is 2.78%. With compensation by DPMS models with the above three SFs, the hysteresis decreases by 86.95%, 87.13%, and 97.13%, respectively. The rate dependence of the frequency response is eliminated, and the -3-dB bandwidth increases from 320 Hz to 890 Hz.

Piezoelectric actuators (PEAs) are increasingly applied to the field of ultraprecision positioning; however, unwanted nonlinearities, such as hysteresis, degrade their performance. This article integrates a Gaussian process (GP) with a Maxwell-slip (MS) model to capture nonlinearities in PEAs. The GP predicts the output of a PEA or the error of the MS model by using the current and historical applied input voltages, as well as the measured historical output displacements, as input. The measured output is replaced by the output of the MS model in the case that a displacement sensor is unavailable. The experimental results show that by properly selecting system order, the proposed approach achieves a precise result and provides the boundary of the prediction error in terms of variance. If the output displacement is available and the GP predicts the output of a PEA directly, the normalized root-mean-square error (NRMSE) is as low as 0.29%. The NRMSE is reduced further to 0.14% if the dataset used for prediction is updated online.

Energy optimization is crucial for unmanned aerial vehicle (UAV) path planning, particularly in complex wind-field environments. Most existing path-planning algorithms rely on simplified energy consumption models, which often fail to adequately capture the effects of wind fields. To address this limitation, a wind-adaptive lifelong planning A* algorithm (WA-LPA*) is proposed for energy-aware path planning in dynamic wind environments. WA-LPA* constructs a composite heuristic function incorporating wind-field alignment factors and integrates a hierarchical height-aware optimization strategy. Meanwhile, an adaptive replanning mechanism is designed based on the change characteristics of the wind field. Simulation experiments conducted across representative scenarios demonstrate that, compared to conventional algorithms that neglect wind-field effects, WA-LPA* achieves energy efficiency improvements of 5.9–29.4%.

Modeling and compensating for hysteresis are widely adopted to eliminate hysteresis. The distributed parameter Maxwell-slip (DPMS) model is developed from the Maxwell-slip model by replacing the spring-slider elements with an elastic-sliding cell with distributed parameters. Motivated by the mechanism of human memory, this article proposes a finite-memory (FM) discretization approach for the DPMS model. The change in the infinite internal state is represented by updating the finite peak points. The FM approach is verified using a piezoelectric actuator, and the normalized mean square error is 0.27%. Thus, the FM approach is also advantageous for managing small-amplitude excitations.

In the nanoindentation testing of metallic materials, mechanical properties often decrease significantly when the indentation position shifts from the central region to the edge due to edge effects, leading to premature edge failure and potential device malfunctions. In this work, molecular dynamic (MD) simulations were conducted to investigate the anisotropic edge effects of nanoindentation on monocrystalline copper with a specific crystal orientation. The results reveal that changes in indentation position strongly influence surface collapse and lateral pile-up behaviors. Notably, edge positions resulted in significant reductions in indentation force and hardness, accompanied by pronounced anisotropy in nanoindentation hardness. Additionally, distinct von Mises stress distributions were observed at different indentation positions, highlighting the crystallographic orientation’s role in modulating edge effects. This study provides new insights into the atomic-scale mechanisms underlying edge effects in metallic materials and their anisotropic characteristics.