The knee joint of the human body involves both rotation and translation, while the magnitude of anterior-posterior translation during flexion/extension movement of the knee joint is very small compared with the length of the human lower limb. It is therefore desirable for an exoskeleton leg to have two degrees of freedom to accommodate the motion of the human knee joint, and for there to be a precision measuring method to obtain its trajectory. This paper presents a novel parallel mechanism which can be used as a precise measuring device to realize closed-loop control for a biologically inspired 3-degree of freedom (DOF) lower limb exoskeleton (BLLE-3) for human gait rehabilitation. In this work, mechanical design and kinematics of the exoskeleton are described. Errors of exoskeleton motion are modelled and analyzed. Closed-loop control law is implemented to enable accurate trajectory following the motions of the exoskeleton. Simulations and experimental results are included to show the effectiveness of the new measuring and control method.

Hysteresis nonlinearity is a common issue in nonlinear stiffness compliant actuators. In this type of actuators, the hysteresis effect is obvious and the associated torque curve is nonlinear. Although many mathematical models have been developed for describing hysteresis, they are usually developed with black-box modeling and the model parameters are difficult to tune to match the experimental data well among inputs with different amplitudes. This article presents a novel hysteresis modeling method for a nonlinear stiffness compliant actuator of which the shapes of the associate torque curves vary with amplitudes. In this method, a concept called “virtual deformation” is adopted to transform the nonlinearity curve into a polyline-based model. Then, a modified Maxwell-slip model is developed to estimate the output torque of the actuator according to the “virtual deformation.” Experiments of the proposed hysteresis modeling method applied in a nonlinear stiffness compliant actuator have been conducted and the results showed that the root-mean-square-error of the estimated torque was reduced by 18.6% and the computation cost was reduced to less than one sixteenth using our proposed hysteresis model compared with nonlinear backlash model.

The emergence of 3D Gaussian Splatting (3DGS) has recently ignited a renewed wave of research in dense visual SLAM. However, existing approaches encounter challenges, including sensitivity to artifacts and noise, suboptimal selection of training viewpoints, and the absence of global optimization. In this paper, we propose GSORB-SLAM, a dense SLAM framework that integrates 3DGS with ORB features through a tightly coupled optimization pipeline. To mitigate the effects of noise and artifacts, we propose a novel geometric representation and optimization method for tracking, which significantly enhances localization accuracy and robustness. For high-fidelity mapping, we develop an adaptive Gaussian expansion and regularization method that facilitates compact yet expressive scene modeling while suppressing redundant primitives. Furthermore, we design a hybrid graph-based viewpoint selection mechanism that effectively reduces overfitting and accelerates convergence. Extensive evaluations across various datasets demonstrate that our system achieves state-of-the-art performance in both tracking precision and rendering quality.

Compliant actuators are suitable for reliable human–robot interaction applications due to their inherent flexibility and safety. However, a limitation of this type of actuator is that nonlinear hysteresis exists especially for those actuators with nonlinear stiffness, which makes accurate system modeling difficult and further degrades force/torque tracking performance. Most hysteresis models are developed with black-boxes and the parameters of these models are obtained with optimization algorithms. However, they are applicable to accurate hysteresis modeling only for a specific hysteresis nonlinear curve, lacking the versatility when dealing with nonlinear torque curves with multiple loops at different amplitudes. In this article, a compliant actuator with nonlinear stiffness is developed and a novel hysteresis modeling method is proposed for the modeling of hysteresis curves with multiple loops; thus, a precise torque control of the actuator can be achieved. In our modeling method, a “virtual deformation” concept is defined to linearize the torque curves of the actuator. The torque curves are segmented into ascending, descending, and transition subcurves. A novel model based on a power function is designed with the model parameters adjusted to fit the multiple torque curves at different amplitudes. Experimental results show that the root-mean-square errors of the estimated torque are reduced by 53.1% and 9.4% and the computation cost is reduced by 95.2% and 66.7% when compared with the nonlinear backlash model and the modified Maxwell-slip-based model, respectively. Tests of the torque tracking verify the performance of our proposed inverse model.