Sensor-based skeleton modeling and MVEEs approach of the redundant manipulator for reaction motion

With the wide application of redundant manipulators, sharing a working space with humans and dealing with uncertainty seems an inevitable problem, especially in the dynamic and unstructured domain. How to deal with obstacle avoidance is of particular importance that robots and humans/environments are safe interactions to fulfill the complex cooperating tasks. This paper aimed at solving the problem of multiple points avoidance for the reaction motion based on the skeleton algorithm in unstructured and dynamic environments. A method named “sensor-based skeleton modeling and MVEEs approach of the redundant manipulator for the reaction motion” is proposed. The extraction of skeleton information from image is obtained to calculate the distances of the multiple control points and establish the repulsion in this method. Afterward, the force Jacobian related to the priority weighting factors is calculated and then a reaction force with damping term is established, which is corresponding nominal torque commands. For the redundant manipulator, the joint angles are obtained through torque iteration instead of inverse kinematics to reduce calculation cost. Finally, the method was tested by a 7-DOF manipulator in the ROS framework. The obtained results indicate that the method in this method can realize dynamic obstacle avoidance and time cost reduction.

Pullback $ \mathcal{D} $-attractors of the three-dimensional non-autonomous micropolar equations with damping

<abstract><p>In this paper, we consider the three-dimensional non-autonomous micropolar equations with damping term in periodic domain $ \mathbb{T}^{3} $. By assuming external forces satisfy certain condtions, the existence of pullback $ \mathcal{D} $-attractors for the three-dimensional non-autonomous micropolar equations with damping term is proved in $ V_{1}\times V_{2} $ and $ H^{2}\times H^{2} $ with $ 3 &lt; \beta &lt; 5 $.</p></abstract>

Stability Result for a Weakly Nonlinearly Damped Porous System with Distributed Delay

In this paper, we consider a one-dimensional porous system damped with a single weakly nonlinear feedback and distributed delay term. Without imposing any restrictive growth assumption near the origin on the damping term, we establish an explicit and general decay rate, using a multiplier method and some properties of convex functions in case of the same speed of propagation in the two equations of the system. The result is new and opens more research areas into porous-elastic system.

Comparison of Two Different Analytical Forms of Response for Fractional Oscillation Equation

The impulse response of the fractional oscillation equation was investigated, where the damping term was characterized by means of the Riemann–Liouville fractional derivative with the order α satisfying 0≤α≤2. Two different analytical forms of the response were obtained by using the two different methods of inverse Laplace transform. The first analytical form is a series composed of positive powers of t, which converges rapidly for a small t. The second form is a sum of a damped harmonic oscillation with negative exponential amplitude and a decayed function in the form of an infinite integral, where the infinite integral converges rapidly for a large t. Furthermore, the Gauss–Laguerre quadrature formula was used for numerical calculation of the infinite integral to generate an analytical approximation to the response. The asymptotic behaviours for a small t and large t were obtained from the two forms of response. The second form provides more details for the response and is applicable for a larger range of t. The results include that of the integer-order cases, α= 0, 1 and 2.

Criteria for the Oscillation of Solutions to Linear Second-Order Delay Differential Equation with a Damping Term

The aim of this work is to present new oscillation results for a class of second-order delay differential equations with damping term. The new criterion of oscillation depends on improving the asymptotic properties of the positive solutions of the studied equation by using an iterative technique. Our results extend some of the results recently published in the literature.

An $$L^2$$ approach to viscous flow in the half space with free elastic surface

We consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in the half space $${\mathbb {R}}^n_+$$ R + n such that on the lower boundary a function h satisfying an undamped Kirchhoff-type plate equation is coupled to the flow field. Originally, h describes the height of an underlying nonlinear free surface problem. Since the plate equation contains no damping term, this article uses $$L^2$$ L 2 -theory yielding the existence of strong solutions on finite time intervals in the framework of homogeneous Bessel potential spaces. The proof is based on $$L^2$$ L 2 -Fourier analysis and also deals with inhomogeneous boundary data of the velocity field on the “free boundary” $$x_n=0$$ x n = 0 .

Nonlinear Longitudinal Vibrations in Accreting One-dimensional Nanostructures

A governing partial differential equation that describes an accreting nanochain containing an attachment of infinite atoms was considered in this paper. We transformed the space variable u(t,r) → v(τ,x) (for a governing PDE formulated in previous research studies) and introduced a function of linear growth. The boundary conditions were also transformed into the new variables, the left end of the accreting chain was free u(t, r=0)=0 while the right end was fixed. The method of lines was also employed to numerically analyze the governing partial differential equation. We detailed the differential transformation for the change of variables used in obtaining the transformed partial differential equation. We also considered what happens with the introduction of the viscous damping term, (δ). The governing partial differential equation was formulated. Numerical simulations for both cases, was then carried out.

Optimization on hysteresis dynamic model of metal rubber material based on dry friction damping term

As one kind of porous elastic metal material, metal rubber is used in vibration isolation widely due to its better damping characteristic. During loading and unloading, the elastoplastic deformation and damping characteristics of this material are usually described by constructing its dynamic model. Although traditional models can describe the hysteresis performance, the accurate parameter identification of material structure under different preparation conductions is limited due to its complex expression or equivalent math form. In this paper, a dynamic hysteresis model is optimized through adding a dry friction damping term based on the micro-element analysis theory and analysis method of material mesoscopic structure. The relation among the manufacture technic, size of metal wire and vibration parameters were established, which accurately describes hysteresis characteristic of metal rubber by dry friction when the metal wires are in the state of slipping contact. The result is verified by the harmonic vibration experiment that the model has good adaptability and convenience, especially can improve the accuracy and convenience of parameter identification on the forming materials of metal rubber.