A VHDL application for kinematic equation solutions of multi-degree-of-freedom systems

As kinematic calculations are complicated, it takes a long time and is difficult to get the desired accurate result with a single processor in real-time motion control of multi-degree-of-freedom(MDOF) systems. Another calculation unit is needed, especially with the increase in the degree of freedom. The main central processing unit(CPU) has additional loads because of numerous motion elements which move independently from each other and their closed-loop controls. The system designed is also complicated because there are many parts and cabling. This paper presents the design and implementation of a hardware that will provide solutions to these problems. It is realized using the Very High Speed Integrated Circuit Hardware Description Language(VHDL) and field-programmable gate array(FPGA). This hardware is designed for a six-legged robot and has been working with servo motors controlled via the serial port. The hardware on FPGA calculates the required joint angles for the feet positions received from the serial port and sends the calculated angels to the servo motors via the serial port. This hardware has a co-processor for the calculation of kinematic equations and can be used together with the equipment that would reduce the electromechanical mess. It is intended to be used as a tool which will accelerate the transition from design to application for robots.

Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method

Modal parameter identification is a mature technology.However,there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination.This paper proposes a new time-frequency method based on intrinsic chirp component decomposition(ICCD)to address these issues.In this method,a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction.The effectiveness and accuracy of the proposed method are illustrated using three examples:a cantilever beam structure with intensive noise contamination or environmental interference,a four-degree-of-freedom structure with two closely spaced modes,and an impact test on a cantilever rectangular plate.By comparison with the identification method based on the empirical wavelet transform(EWT),it is shown that the presented method is effective,even in a high-noise environment,and the dynamic characteristics of closely spaced modes are accurately determined.

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.

Flexible Bio-tensegrity Manipulator with Multi-degree of Freedom and Variable Structure

Conventional manipulators with rigid structures and sti ness actuators have poor flexibility,limited obstacle avoidance capability,and constrained workspace.Some developed flexible or soft manipulators in recent years have the characteristics of infinite degrees of freedom,high flexibility,environmental adaptability,and extended manipulation capability.However,these existing manipulators still cannot achieve the shrinking motion and independent control of specified segments like the animals,which hinders their applications.In this paper,a flexible bio-tensegrity manipulator,inspired by the longitudinal and transversal muscles of octopus tentacles,was proposed to mimic the shrinking behavior and achieve the variable motion patterns of each segment.Such proposed manipulator uses the elastic spring as the backbone,which is driven by four cables and has one variable structure mechanism in each segment to achieve the independent control of each segment.The variable structure mechanism innovatively contains seven lock-release states to independently control the bending and shrinking motion of each segment.After the kinematic modeling and analysis,one prototype of such bionic flexible manipulator was built and the open-loop control method was proposed.Some proof-of-concept experiments,including the shrinking motion,bending motion,and variable structure motion,were carried out by controlling the length of four cables and changing the lock-release states of the variable structure mechanism,which validate the feasibility and validity of our proposed prototype.Meanwhile,the experimental results show the flexible manipulator can accomplish the bending and shrinking motion with the relative error less than 6.8%through the simple independent control of each segment using the variable structure mechanism.This proposed manipulator has the features of controllable degree-of-freedom in each segment,which extend their environmental adaptability,and manipulation capability.

Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.

CYLINDER-SPHERE 3-DOF ULTRASONIC MOTOR AND ITS CONTROL

A three degree-of-freedom (DOF) ultrasonic motor (USM) with a cylinder-shaped stator and a spherical rotor is introduced, which uses one first order longitudinal and two second order bending nature vibration modes of the cylinder. Control strategies for the two DOF trajectory following are studied and applied to the prototype USM. Vibration amplitude control is employed for speed regulation. The first trajectory following strategy is a step-by-step interpolation. The second strategy is vector decomposition control. Three pulse width modulation (PWM) methods for the exciting voltage regulation are investigated. These methods are compared and verified by several experiments. The key is to keep the phase differences of the three vibration constants and small exciting voltage distortion while the exciting voltages are changed for simplifing the control process and obtaining good control performance. The vector control method has advantages of small trajectory following error, smooth moving and low noise.

Error modeling and compensating of a novel 6-DOF aeroengine rotor docking equipment

In the docking process of aeroengine rotor parts,docking accuracy that indicates the gaps between the end faces is strictly required.A key issue is improving docking accuracy using automated docking equipment.In this paper,a systematic study is carried out on the error modeling and compensation of a novel six-degrees-of-freedom(6-DOF)docking equipment for aeroengine rotors.First,a new model for indicating the main indexes of docking accuracy is proposed.Then,the error model of a specially designed 6-DOF docking equipment is established based on a modified Denavit Hartenberg method with five parameters.Subsequently,two error compensation methods are proposed.Based on the above models,a docking accuracy simulation algorithm is proposed using the Monte Carlo method.Finally,verification experiments are conducted.The results show that,for the maximum values and standard deviations of the gaps between the rotor end-faces in the actual and target positions and attitudes,i.e.,main indexes that represent docking accuracy,the deviation rates between the simulation and experimental results are less than20%.The modeling methods have referential significance.The decline rates of these values are 50–65%when using the two proposed compensation methods.The compensation methods significantly improve the docking accuracy.