An instrumental variable approach for rigid industrial robots identification

This paper deals with the important topic of rigid industrial robots identification. The usual identification method is based on the use of the inverse dynamic model and the least-squares technique. In order to obtain good results, a well-tuned derivative bandpass filtering of joint positions is needed to calculate the joint velocities and accelerations. However, we can doubt whether the bandpass filter is well-tuned or not. Another approach is the instrumental variable (IV) method which is robust to data filtering and which is statistically optimal. In this paper, an IV approach relevant for identification of rigid industrial robots is introduced. The set of instruments is the inverse dynamic model built from simulated data which are calculated from the simulation of the direct dynamic model. The simulation assumes the same reference trajectories and the same control structure for both the actual and the simulated robot and is based on the previous IV estimates. Furthermore, to obtain a rapid convergence, the gains of the simulated controller are updated according to IV estimates. Thus, the proposed approach validates the inverse and direct dynamic models simultaneously and is not sensitive to initial conditions. The experimental results obtained with a 2 degrees of freedom (DOF) planar prototype and with a 6 DOF industrial robot show the effectiveness of our approach: it is possible to identify 60 parameters in 3 iterations and in 11 s.     

无人车捷联惯导系统仿真器设计

捷联惯导系统仿真模块的研究对于组合导航有着重要意义,为了检验该模块性能,在无人车轨迹模拟器的基础上分别基于方向余弦法与四元素法对捷联惯导系统仿真器进行了设计。首先基于运动学模型模拟无人车行驶的平面运动轨迹,并基于高斯投影反算原理求出该轨迹中各点所对应的经纬度信息作为真实值。基于该运动轨迹将对应的三维加速度与三维姿态角输入到捷联惯导系统仿真模块中,将求解出的经纬度作为计算值。将计算值与真实值进行比较,发现经纬度误差随时间而递增,三维姿态角误差随时间呈现周期性振荡,实际应用中有必要对误差进行相应的补偿。     

A unified dynamic algorithm for wheeled multibody systems with passive joints and nonholonomic constraints

This paper presents a systematic approach to develop a generalized symbolic/numerical dynamic algorithm for modeling and simulation of multibody systems with branches and wheels. The proposed dynamic algorithm includes the direct kinematic and inverse dynamic models of the wheeled systems with prismatic/revolute as well as actuated/passive degrees of freedom. Using the geometric configuration of the system through modified Denavit–Hartenberg convention, symbolic equations in general algorithmic form are developed for kinematic constraints associated with the wheel–ground contacts. The Newton–Euler equations are used to develop an algorithm for the inverse dynamic model of the multibody system. The complete algorithm is then used to solve the kinematics and dynamics of the system, and computes: (i) the kinematics of the external/internal passive degrees of freedom of the system, (ii) the Lagrange multipliers associated with the wheel–ground contacts, and (iii) the driving forces/torques of the actuated degrees of freedom. Some examples are solved with the help of the proposed algorithm, using MATLAB, to illustrate its implementation on different wheeled systems. These examples include a differential wheeled robot, a snake-like wheeled system, and a bicycle.     

Hybrid kinematic and dynamic simulation of running machines

Dynamic simulation requires the computationally expensive calculation of joint accelerations, while in kinematic simulation these accelerations are known based on a given trajectory. This paper describes a hybrid kinematic and dynamic simulation method that can be applied to the simulation of running machines to speed up the computations over that of a dynamic simulation. This is possible because much of the time the legs of a running machine are in the air and their trajectories are directly specified and tightly controlled. The method is more flexible than dynamic simulation alone because it allows joints to be either motion-controlled or force-controlled. It is general to all robotic systems with tree structures, and fully motion-controlled or force-controlled kinematic loops. It should work best for machines with appendages that are motion-controlled, such as those encountered in underwater and space manipulation.     

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

Experimental validation of a model of an uncontrolled bicycle

In this paper, an experimental validation of some modelling aspects of an uncontrolled bicycle is presented. In numerical models, many physical aspects of the real bicycle are considered negligible, such as the flexibility of the frame and wheels, play in the bearings, and precise tire characteristics. The admissibility of these assumptions has been checked by comparing experimental results with numerical simulation results. The numerical simulations were performed on a three-degree-of-freedom benchmarked bicycle model. For the validation we considered the linearized equations of motion for small perturbations of the upright steady forward motion. The most dubious assumption that was validated in this model was the replacement of the tires by knife-edge wheels rolling without slipping (non-holonomic constraints). The experimental system consisted of an instrumented bicycle without rider. Sensors were present for measuring the roll rate, yaw rate, steering angle, and rear wheel rotation. Measurements were recorded for the case in which the bicycle coasted freely on a level surface. From these measured data, eigenvalues were extracted by means of curve fitting. These eigenvalues were then compared with the results from the linearized equations of motion of the model. As a result, the model appeared to be fairly accurate for the low-speed low-frequency behaviour.     

Contact Modeling and Identification of Planar Somersaults on the Trampoline

This paper presents an extensive study on the trampoline-performed planar somersaults. First, a multibody biomechanical model of the trampolinist and the recurrently interacting trampoline bed are developed, including both the motion equations and the determination of joint reactions. The mathematical model is then identified –the mass and inertia characteristics of the human body are estimated, and the stiffness and damping characteristics of the trampoline bed are measured. By recording the actual somersault performances the motion characteristics of the stunts, i.e. the time variations of positions, velocities and accelerations of the body parts are also obtained. Finally, an inverse dynamics formulation for the system designated as an under-controlled system, is developed. The followed inverse dynamics simulation results in the torques of muscle forces in the joints that assure the realization of the actual motion. The reaction forces in the joints during the analyzed evolutions are also determined. Using the kinematic and dynamics characteristics, the nature of the stunts, the way the human body is maneuvered and controlled, can be studied.     

Inverse Dynamic Model and a Control Application of a Novel 6-DOF Hybrid Kinematics Manipulator

Kinematics with six degrees of freedom can be of several types. This paper describes the inverse dynamic model of a novel hybrid kinematics manipulator. The so-called Epizactor consists of two planar disk systems that together move a connecting element in 6 DOF. To do so each of the disk systems has a linkage point equipped with a homokinetic joint. Each disk system can be described as a serial 3-link planar manipulator with unlimited angles of rotation. To compensate singularities, a kinematic redundancy is introduced via a fourth link. The kinematic concept leads to several technical advantages for compact 6-DOF-manipulators when compared to established parallel kinematics: The ratio of workspace volume and installation space is beneficial, the number of kinematic elements is smaller, and rotating drives are used exclusively. For a singularity-robust control-approach, the inverse dynamic model is derived using the iterative Newton–Euler-method. Feasibility is shown by the application of the model to an example where excessive actuator velocities and torques are avoided.     

Velocity control of wheeled mobile robots using computed torque control and its performance for a differentially driven robot

This article presents the development of a Computed Torque Control (CTC) scheme for Cartesian velocity control of Wheeled Mobile Robots (WMRs). The literature presents extensive study on the need and suitability of the CTC scheme for robot arms. Many researchers have identified the benefits of using a CTC scheme for mobile robots. There is however very little information on CTC schemes for controlling mobile robots. The need for the CTC scheme stems from the fact that mobile robots (industrial AGVs) employing conventional velocity control schemes experience side slip due to suspended loads while negotiating curves, and the controller gains and accelerations need to be modified for changes in the dynamics. The structure of the proposed control scheme can be employed to control any mobile robot for which an inverse dynamic model exists, as a CTC scheme requires an inverse dynamic model to compute unique values for the motor current for a given trajectory. It is demonstrated that the existence of the inverse dynamic model is guaranteed for all differentially driven WMRs for all operating conditions, and is not affected by the number of castor wheels in the WMR. In the proposed CTC scheme, the linear and angular velocities of the WMR are controlled by adjusting the WMR accelerations, which are computed based on the motor torques required to follow a given trajectory. The motor torque is pre-computed based on a dynamic model of the mobile robotic system. The simulation and experimental results presented for a differentially driven WMR demonstrate that a computed-torque control scheme provides adaptive cruising and steering control for nominally tuned controller gains compared to a conventional velocity controller to achieve proper road following in the presence of changes in the dynamics. © 1997 John Wiley & Sons, Inc.     

A compact smoothing-differentiation and projection approach for the kinematic data consistency of biomechanical systems

The estimation of the skeletal motion obtained from marker-based motion capture systems affects the results of the kinematic and dynamic analysis of biomechanical systems. The main source of error is the inaccuracy of velocities and accelerations derived from experimentally measured displacements of markers placed on the skin of joints. This error is mainly due to the amplification of high-frequency low-amplitude noise introduced by the motion capture system when the raw displacement signals are differentiated. Another source of error is the skin motion artifact that produces violations of the kinematic constraint equations of the multibody system. An integrated smoothing-differentiation-projection approach to ensure the kinematic data consistency in the context of the analysis of biomechanical systems is presented. The raw data differentiation problem is solved by applying a single-step smoothing-differentiation technique based on the Newmark integration scheme. A systematic multibody procedure is proposed based on the projection of the positions and its smoothed derivatives into their corresponding constraint manifolds to ensure the kinematic data consistency. Several benchmark kinematic signals that include an acquired nonstationary mono-dimensional motion of biomechanical origin and computer generated data of a four-bar mechanism were processed using the proposed method to study its performance.     

A bicycle model for education in multibody dynamics and real-time interactive simulation

This paper describes the use of a bicycle model to teach multibody dynamics. The bicycle motion equations are first obtained as a DAE system written in terms of dependent coordinates that are subject to holonomic and non-holonomic constraints. The equations are obtained using symbolic computation. The DAE system is transformed to an ODE system written in terms of a minimum set of independent coordinates using the generalised coordinates partitioning method. This step is taken using numerical computation. The ODE system is then numerically linearised around the upright position and eigenvalue analysis of the resulting system is performed. The frequencies and modes of the bicycle are obtained as a function of the forward velocity which is used as continuation parameter. The resulting frequencies and modes are compared with experimental results. Finally, the non-linear equations of the bicycle are used to create an interactive real-time simulator using Matlab-Simulink. A series of issues on controlling the bicycle are discussed. The entire paper is focussed on teaching engineering students the practical application of analytical and computational mechanics using a model that being simple is familiar and attractive to them.     

The derivation of a kinematic model from the dynamic model of the motion of a riderless bicycle

This work deals with the modelling and control of a riderless bicycle (see Figure 1). It is assumed here that the bicycle is controlled by a pedalling torque, a directional torque, and by a rotor mounted on the crossbar that generates a tilting torque.In particular, a kinematic model of the bicycle's motion is derived by using its dynamic model. Then, using this kinematic model, a constraint point-to-point control problem is dealt with.     

Development of computerized human static strength simulation model for job design

This article describes the development of models to predict population static strengths and low back forces resulting from common manual exertions in industry. The resulting biomechanical models are shown to be valid for their intended purposes, but limitations still exist. In particular, they are meant to aid in evaluating very slow or static exertions, such as when carefully lifting, pushing, or pulling on heavy objects, but do not allow dynamic exertions to be simulated. It is shown that use of these models in the early design of workplaces and equipment is dependent on the use of computerized homonoids and behavioral-based inverse kinematic algorithms in conjunction with CAD systems. © 1997 John Wiley & Sons, Inc.     

Supervised learning based on the self-organizing maps for forward kinematic modeling of Stewart platform

In this study, we propose an alternative technique for solving the forward kinematic problem of parallel manipulator which is designed based on generalized Stewart platform. The focus of this work is to predict a pose vector of a moving plate from a given set of six leg lengths. Since the data of parallel kinematics are usually available in the form of nonlinear dynamic system, several methods of system identification have been proposed in order to construct the forward kinematic model and approximate the pose vectors. Although these methods based on a multilayer perceptron (MLP) neural network provide acceptable results, MLP training suffers from convergence to local optima. Thus, we propose to use an alternative supervised learning algorithm called vector-quantized temporal associative memory (VQTAM) instead of MLP-based methods. VQTAM relying on self-organizing map architecture is used to build the mapping from the input space to the output space such that the training/testing datasets are generated from inverse kinematic model. The solutions from standard VQTAM are improved by an autoregressive (AR) model and locally linear embedding (LLE). The experimental results indicate that VQTAM with AR/LLE gives the outputs with nearly 100% prediction accuracy in the case of smooth data, while VQTAM + LLE provides the most accurate prediction on noisy data. Therefore, VQTAM + LLE is a very robust estimation method and can practically be used for solving the forward kinematic problem.

     

Modelling and control of the motion of a riderless bicycle rolling on a moving plane

This work deals with the modelling and control of a riderless bicycle rolling on a moving plane. It is assumed here that the bicycle is controlled by a pedalling torque, a directional torque and by a rotor mounted on the crossbar that generates a tilting torque.In particular, a kinematic model of the bicycle’s motion is derived by using its dynamic model. Then, using this kinematic model, the expressions for the applied torques are obtained.     

Two-stage approach to state and force estimation in rigid-link multibody systems

A novel two-stage approach is presented for improving the estimates of both the kinematic state and the unknown external forces in rigid-link multibody systems with negligible joint clearance. The approach is said to be a two-stage one because the estimation process is carried out by two observers running simultaneously and only partially coupled in order to reduce model uncertainties. Nonlinear Kalman filters are employed at both stages. In the first stage, a kinematic observer estimates an augmented system state (i.e., positions, velocities and accelerations) by employing the kinematic constraint equations and some measurements of kinematic quantities as inputs and outputs. Therefore, it is unbiased by external forces and uncertainties on any dynamic parameters. In the second stage, a force observer estimates the external forces by employing dynamic models. The input of the force observer is the kinematic state, while the correction is performed through some direct or indirect measurements of the known forces. Numerical assessment of the theory developed is provided through a slider–crank mechanism. The results achieved through the proposed approach are compared with those yielded by traditional unknown input observers based on a single-stage dynamic estimation. An extensive statistical analysis is carried out at varying levels of measurement noise. Two different strategies are followed in the synthesis of the non-linear Kalman filters. The comparison clearly shows the advantages and the effectiveness of the new two-stage approach.     

Dynamic path tracking control of a vehicle on slippery terrain

This paper deals with accuracy and reliability for the path tracking control of a four wheel mobile robot with a double-steering system when moving at high dynamics on a slippery surface. An extended kinematic model of the robot is developed considering the effects of wheel–ground skidding. This bicycle type model is augmented to form a dynamic model that considers an actuation of the four wheels. Based on the extended kinematic model, an adaptive and predictive controller for the path tracking is developed to drive the wheels front and rear steering angles. The resulting control law is combined with a stabilization algorithm of the yaw motion which modulates the actuation torque of each four wheels, on the basis of the robot dynamic model. The global control architecture is experimentally evaluated on a wet grass slippery terrain, with speeds up to 7 m/s. Experimental results demonstrate enhancement of tracking performances in terms of stability and accuracy relative to the kinematic control.     

Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy

High precision is still one of the challenges when parallel kinematic machines are applied to advanced equipment. In this paper, a novel planar 2-DOF parallel kinematic machine with kinematic redundancy is proposed and a method for redundant force optimization is presented to improve the precision of the machine. The inverse kinematics is derived, and the dynamic model is modeled with the Newton–Euler method. The deformations of the kinematic chains are calculated and their relationship with kinematic error of the machine is established. Then the size and direction of the redundant force acting on the platform are optimized to minimize the position error of the machine. The dynamic performance of the kinematically redundant machine is simulated and compared with its two corresponding counterparts, one is redundantly actuated and the other is non-redundant. The proposed kinematically redundant machine possesses the highest position precision during the motion process and is applied to develop a precision planar mobile platform as an application example. The method is general and suitable for the dynamic modeling and redundant force optimization of other redundant parallel kinematic machines.     

Implementation of the inverse circular radon transform‐based imaging approach for breast cancer screening

In this article, the approach based on the inverse circular radon transform technique (ICRT) is proposed to obtain the image of the breast cancer screening based on microwaves. A simplified numerical breast model is constructed and computational results are obtained with the use of synthetic aperture radar principle. A tumor phantom is produced and the experimental results are acquired by using sand, screw and phantoms with the use of an experimental setup prototype that is also presented in this study. The simulation results are verified and validated by experimental results. The resultant images generated using the simulated and experimental data show a good agreement with the designed scenarios.     

Development of an adaptive fuzzy logic-based inverse dynamic model for laser cladding process

The precision, performance, and robustness of model-based controllers depend, to a large extent, on the accuracy of the inverse dynamic model which is incorporated in the design of the controller. Due to complex nature of the laser cladding process and presence of time-varying uncertainties, derivation of an accurate mathematical inverse dynamic model of the process is very difficult, and involves many unknown parameters. The inverse dynamic model of the complex nonlinear laser cladding process, which is difficult to be described mathematically, can be described by a fuzzy logic-based inverse dynamic model constructed form input–output data. In this paper, the development of an adaptive fuzzy inverse dynamic model of the laser cladding process, using a systematic fuzzy modelling approach is presented. In a closed-loop laser cladding process, the scanning speed of the substrate is required to produce a clad with desired geometry and quality. In this paper, a fuzzy inverse dynamic model that describes the scanning speed as a function of the cladding parameters in particular the clad height is developed. The developed fuzzy model is validated by comparing the model output with experimental data. The results are very promising and show that fuzzy models can accurately describe the process dynamics.