An efficient method for inverse dynamics of kinematically defective parallel platforms

In addition the general six‐degree‐of‐freedom parallel platforms, parallel platforms with fewer than six DOF can also be used in the structural design of robotic manipulators. The common property of these parallel platforms is that the motion parameters used to describe the position and orientation of the movable platform are six, but fewer than six are independent. In their general configurations, arbitrary six‐dimensional motion of the platform cannot be achieved by the actuators mounted on the legs, therefore they are kinematically defective. Because of this defect, the inverse dynamic analysis method, which is applicable to the general six‐DOF parallel platforms, cannot be directly used for the kinematically defective parallel platforms (KDPPs). In this paper, an effective method for formulating the inverse dynamics of KDPPs is presented. Using the proposed method, three different KDPPs are studied and their inverse dynamic formulas are derived. © 2002 John Wiley & Sons, Inc.     

Static analysis of spatial parallel manipulators by means of the principle of virtual work

It is presented a comprehensive approach for the static analysis of spatial parallel manipulators using the principle of virtual work, equipped with a recursive and systematic formulation, which is intended for conducting an efficient manipulation of the kinematics associated with the problem. Thus, it is possible omitting all internal forces and nonworking external constraint forces in the problem formulation. As a result, the actuator drive forces and/or torques can be directly related with the external loads supported by the manipulator, including the weight of the mobile platform and also the weight of the links of the connecting legs. A thorough understanding of these forces and/or torques is important for proper sizing of actuators at the design stage. In order to prove the feasibility and the validity of the proposed method, two fully detailed examples are presented.     

On adaptive inverse dynamics for free-floating space manipulators

This paper is devoted to the investigation of adaptive inverse dynamics for free-floating space manipulators (FFSMs) suffering from parameter uncertainties/variations. To overcome the nonlinear parametric problem of the dynamics of FFSMs, we introduce a new regressor matrix called the generalized dynamic regressor. Based on this regressor, and with Lyapunov stability analysis tools, we obtain a new parameter adaptation law and show that the closed-loop system is stable, and that the joint tracking errors converge asymptotically to zero. Simulation results are provided to illustrate the performance of the proposed adaptive algorithm. Furthermore, we conduct a comparative study between adaptive inverse dynamics, prediction error based adaptation, and passivity based adaptation.     

An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators

In this article, we present an inverse dynamics control strategy to achieve small tracking errors for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms that ensure stable operation of the closed loop system under specific conditions. The controller is designed in a two-step process. First, a new output is defined such that the zero dynamics of the original system are stabilized. Next, to ensure stable asymptotic tracking, the control input is modified such that stable asymptotic tracking of the new output or approximate tracking of the actual output may be achieved. This is illustrated for the case of single- and two-link flexible manipulators. ©1997 John Wiley & Sons, Inc.     

An algorithm for the inverse dynamics of n-axis general manipulators using Kane''s equations

Presented in this paper is an algorithm for the numerical solution of the inverse dynamics of robotic manipulators of the serial type, but otherwise arbitrary. The algorithm is applicable to manipulators containing n joints of the rotational or the prismatic type. For a given set of Hartenbeg-Denavit and inertial parameters, as well as for a given trajectory in the space of joint coordinates, the algorithm produces the time histories of the n torques or forces required to drive the manipulator through the prescribed trajectory. The algorithm is based on Kane's dynamical equations of mechanical multibody systems. Moreover, the complexity of the algorithm pressented here is lower than that of the most efficient inverse-dynamics algorithm reported in the literature. Finally, the applicability of the algorithm is illustrated with two fully solved examples.     

翻滚目标逼近的虚拟域逆动力学轨迹规划

针对追踪星自主逼近和跟踪翻滚目标特定部位的最优规划问题,提出了一种基于虚拟域逆动力学的多约束最优逼近轨迹规划方法.首先,在翻滚目标本体系下建立追踪星相对于翻滚目标特定部位的相对轨道动力学方程,并建立追踪星本体系相对于翻滚目标期望固连坐标系的相对姿态动力学方程;其次,考虑目标星外形、敏感器视场和执行机构控制能力等约束条件,建立时间/能量最优规划模型;然后,采用序列二次规划(sequential quadratic programming,SQP)方法求解时间/能量最优规划问题;最后,数值仿真验证了该方法在满足多约束条件下,可实现对翻滚目标自主逼近与跟踪的最优轨迹规划,同时与高斯伪谱法进行了对比,验证了本方法在计算效率方面的优势.     

基于逆运动学和动力学的虚拟人行走仿真

在计算机上模拟真实人行走是计算机仿真的一个基本问题。人体行走是一种伴随着碰撞、摩擦和滑动的复杂的系统运动,为了实现模拟的逼真性,需要着重在运动控制上进行研究。首先对人体行走进行分析并建立了简单的人体模型,然后详细给出行走过程中关节点位置的数学描述,最后采用逆运动学求解雅可比矩阵的方法并结合动力学知识,运用VC＋＋．NET和OpenGL为编程工具以骨架模型实现了虚拟人行走。     

An improved approach to the inverse dynamic analysis of parallel manipulators by a given virtual screw

This paper provides an improved approach to the inverse dynamic analysis of parallel manipulators (PMs) based on the screw theory and Jourdain’s principle of virtual power. First, velocity and acceleration mappings from the Cartesian coordinate system to the screw system are established. Next, by introducing a novel concept of virtual screw that is formulated by a combination of virtual angular velocity and virtual linear velocity, four theorems are defined and proven to build the dynamic equations of PMs. Owing to the existing expression of acceleration screws and the introduced virtual screw, the proposed approach not only has the advantages of intuitive physical concepts and universal form but also avoids the difficult derivatives of time and the determination of generalized velocities, which is employed by conventional methods and is determined difficultly for some hybrid PMs. Finally, taking a 1PU?+?3UPS PM as an instance, the inverse dynamic analysis and numerical examples are presented to demonstrate the feasibility of the proposed approach.     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

A systematic method of dynamics for flexible robot manipulators

In this article, a systematic method to derive dynamic equations of motion for flexible robot manipulators is developed by using the Lagrangian assumed modes method. The proposed method can be applied to dynamic simulation and control system design for flexible robot manipulators. In the proposed method, the link deflection is described by a truncated modal expansion. The operations of only 3x3 matrices and/or 3 × 1 vectors exist in the method. All the dynamics computations are performed in the link coordinate systems, where the kinematics informations are computed with the forward recursion from the base to the hand tip and the dynamics informations are computed with the return recursion. As generally compared with other existing methods, the method proposed in this article is, computationally, more simple, systematic, and efficient. A computational simulation for a single-link flexible robot manipulator is presented to verify the proposed method. © 1992 John Wiley & Sons, Inc.     

Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software

This work deals with the problem of computing the inverse dynamics of complex constrained mechanical systems for real-time control applications. The main goal is the control of robotic systems using model-based schemes in which the inverse model itself is obtained using a general purpose multibody software, exploiting the redundant coordinate formalism. The resulting control scheme is essentially equivalent to a classical computed torque control, commonly used in robotics applications. This work proposes to use modern general-purpose multibody software to compute the inverse dynamics of complex rigid mechanisms in an efficient way, so that it suits the requirements of realistic real-time applications as well. This task can be very difficult, since it involves a higher number of equations than the relative coordinates approach. The latter is believed to be less general, and may suffer from topology limitations. The use of specialized linear algebra solvers makes this kind of control algorithms usable in real-time for mechanism models of realistic complexity. Numerical results from the simulation of practical applications are presented, consisting in a “delta” robot and a bio-mimetic 11 degrees of freedom manipulator controlled using the same software and the same algorithm.     

An improved approach to the solution of inverse kinematics problems for robot manipulators

A structured artificial neural-network (ANN) approach has been proposed here to control the motion of a robot manipulator. Many neural-network models use threshold units with sigmoid transfer functions and gradient descent-type learning rules. The learning equations used are those of the backpropagation algorithm. In this work, the solution of the kinematics of a six-degrees-of-freedom robot manipulator is implemented by using ANN. Work has been undertaken to find the best ANN configurations for this problem. Both the placement and orientation angles of a robot manipulator are used to fin the inverse kinematics solutions.     

Inverse dynamics based robust control method for position commanded servo actuators in robot manipulators

In this paper, a simple torque to position conversion method is proposed for position commanded servo actuators used in robot manipulators. The torque to position conversion is based on the low level controller of the servomotor. The proposed conversion law is combined with a backstepping sliding mode control method to realize a robust dynamic controller. The proposed torque based method can control a servomotor which can otherwise be operated only through position inputs. This method facilitates dynamic control for position controlled servomotors and it can be extended to position commanded robotic manipulators also. Simulation and experimental studies are conducted to validate the proposed torque to position conversion based robust control method.     

A survey of efficient computational methods for manipulator inverse dynamics

In this paper, we present an up-to-date survey of various numerically efficient methods for solving the problem of computing manipulator inverse dynamics. The literature on this subject is extensive. However, in this paper, we review only those algorithms which have been derived based on the Euler—Lagrange, Newton—Euler and Kane's formulations of the dynamic equations of motion and are applicable to rigid-link open-chain robot manipulators. In particular, for each of these formulations we present a chronological account of the development of the most important algorithms which compute manipulator inverse dynamics. In this process some classical algorithms are given and a number of issues which make it possible to reduce their computational complexity are emphasized. Also, the most efficient algorithms currently available are compared in terms of their computational complexity.This research was supported by a postdoctoral fellowship funded from NSERC of Canada Grant OGP0001345 and a grant from the Institute of Robotics and Intelligent Systems (IRIS), both awarded to Dr. R. V. Patel.     

An offset-free neural controller based on a non-extrapolating scheme for approximating the inverse process dynamics

This work presents a novel control scheme based on approximating the inverse process dynamics with a radial basis function (RBF) neural network model, trained with the fuzzy means algorithm. The produced RBF network constitutes an inverse model of the process, which can be applied as an explicit control law. In order to avoid extrapolation in the RBF model predictions, a concept borrowed from chemometrics, namely the applicability domain, is incorporated to the proposed framework. Moreover, an error correction term is added, allowing the inverse neural controller to account for modeling errors and process uncertainty and eliminate offset. The proposed approach is applied to the control of a nonlinear Continuous Stirred Tank Reactor (CSTR) exhibiting multiple equilibrium points, including an unstable one. A comparison with other control schemes on various tests, including set-point tracking, unmeasured disturbance rejection and process uncertainty highlights the advantages of the proposed controller.     

A geometric method for determining joint rotations in the inverse kinematics of robotic manipulators

An inverse‐kinematics algorithm has been developed to evaluate the joint rotations of a robotic manipulator given the orientation of its hand link. The method mimics the way a person would determine the joint rotations by assembling the links comprising the robot mechanism and making adjustments in the joint displacements until the hand link is in the desired situation. An example is given where it is shown that the method is reasonably robust, can be applied to any design of robot, and is competitive with alternative highly‐mathematical, specific‐robot specialized, computational‐intensive schemes. ©2000 John Wiley & Sons, Inc.     

An efficient image-mosaicing method based on multifeature matching

Mosaicing is connecting two or more images and making a new wide area image with no visible seam-lines. Several algorithms have been proposed to construct mosaics from image sequence where the camera motion is more or less complex. Most of these methods are based either on the interest points matching or on theoretical corner models. This paper describes a fully automated image-mosaicing method based on the regions and the Harris points primitives. Indeed, in order to limit the search window of potential homologous points, for each point of interest, regions segmentation and matching steps are being performed. This enables us to improve the reliability and the robustness of the Harris points matching process by estimating the camera motion. The main originality of the proposed system resides in the preliminary manipulation of regions matching, thus making it possible to estimate the rotation, the translation and the scale factor between two successive images of the input sequence. This estimation allows an initial alignment of the images along with the framing of the interest points search window, and therefore reducing considerably the complexity of the interest points matching algorithm. Then, the resolution of a minimization problem, altogether considering the couples of matched-points, permits us to perform the homography. In order to improve the mosaic continuity around junctions, radiometric corrections are applied. The validity of the herewith described method is illustrated by being tested on several sequences of complex and challenging images captured from real-world indoor and outdoor scenes. These simulations proved the validity of the proposed method against camera motions, illumination variations, acquirement conditions, moving objects and image noise. To determine the importance of the regions matching stage in motion estimation, as well as for the framing of the search window associated to a point of interest, we compared the matching points results of this described method with those produced using the zero-mean normalized cross correlation score (without regions matching). We made this comparison in the case of a simple motion (without the presence of a rotation around optical axis and/or a scale factor), in the case of a rotation and in the general case of an homothety. For justifying the effectiveness of this method, we proposed an objective assessment by defining a reconstruction error.