Inverse Dynamics Of Manipulator Research Articles

An O(n)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators Using Spatial Representation of Twists

Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required computational efficiency, recursive O(n)-algorithms were proposed to this end. Aiming at compact yet efficient formulations, a Lie group formulation was recently proposed, making use of body-fixed and hybrid representation of twists and wrenches. In this letter, a formulation is introduced using the spatial representation. The second-order inverse dynamics algorithm is accompanied by a fourth-order forward and inverse kinematics algorithm. An advantage of all Lie group formulations is that they can be parameterized in terms of vectorial quantities that are readily available. The method is demonstrated for the 7 DOF Franka Emika Panda robot.

Modeling and Simulation of Robot Inverse Dynamics Using LSTM-Based Deep Learning Algorithm for Smart Cities and Factories

In smart cities and factories, robotic applications require high dexterity and security, which requires precise inverse dynamics model. However, the physical modeling methods cannot model the uncertain factors of the manipulator such as flexibility, joint clearance and friction, etc. As an alternative, artificial intelligence (AI) techniques have become increasingly popular in robotics for smart cities and factories. In this paper, deep learning neural network based on LSTM (Long Short-Term Memory) is adopted to predict the manipulator inverse dynamics. This study aims to summarize the influence of the hyper-parameter settings on model performance and to explore the applicability of the LSTM model to joint torque prediction of multiple degrees of freedom series manipulator. Furthermore, the feasibility of using only joint position as input data for torque prediction is verified. Simulation result has shown that, for the proposed deep learning architecture, the effects of the number of maximum epochs on model performance should be prioritized. The effects of the number of hidden nodes on model performance are limited, while prediction accuracy will deteriorate as the number of hidden layers increases. It is proved that it is feasible to predict inverse dynamics when input data is joint position only. The experimental results show that the training time increases with the increase of hidden layers, neurons and epochs.

Control of Nonlinear Elastic Joint Robots using Feed-forward Torque Decoupling

This paper proposes and evaluates the feed-forward decoupling of joint torque in elastic joint robots. The joint elasticities, captured by the third-order polynomial function, are considered together with the inverse manipulator dynamics so as to provide the required driving torque for the reference trajectories. Therewith decoupled joint actuators can be robustly controlled in a feedback manner for which a convenient proportional-derivative (PD) regulation is suficient. Using the inverse manipulator dynamics and joint model the reference value in the joint output (load) and not input (motor) space is provided to the feedback control of decoupled actuators. This allows compensating for the joint torsion and improve the load positioning accuracy without output sensors. The proposed control strategy is evaluated experimentally on a single elastic joint under gravity. We show an improved accuracy of the load positioning without adapting the underlying control loop and remarkable changes in the transient response.

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.

Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work

This paper presents a systematic methodology for solving the inverse dynamics of a Stewart-Gough manipulator. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of the manipulator can be reduced to solving a system of six linear equations in six unknowns. A computational algorithm for solving the inverse dynamics of the manipulator is developed and several trajectories of the moving platform are simulated. [S1050-0472(00)00401-3]

A Parallel Computational Algorithm of the Robot Inverse Dynamics Problem

A parallelization of an algorithm of solution of the manipulator inverse dynamics problem is presented. The algorithm is based on the Lagrange formalism and makes use of (3x3) rotation matrices. A version of the algorithm with prediction of temporary data is also described. The computational complexity of the parallel algorithm with respect to the number of degrees of freedom of the manipulator and to the number of processors used is considered.

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.

Manipulator Trajectory Control by Momentum Change Inverse Models Using Multilayer Neural Networks

This paper proposes a learning method of inverse manipulator dynamics model using only position and velocity. The direct inverse modeling method that was proposed as a learning method using neural network requires sensing manipulator position, velocity, and acceleration, because this method is formularized on the basis of manipulator. motion equation. However, since it is difficult at present to sense accurately manipulator acceleration, we could hardly implement this method by original formula. In the momentum change inverse modeling; the learning method that we proposed in this paper, manipulator motion causality is modeled not on the basis of manipulator motion equation but on the manipulator momentum change equation. With this formulation, sensing acceleration becomes unnecessary, inverse manipulator dynamics model can be learned using sensible position and velocity.

Indirect discrete-time adaptive algorithm for manipulator control

An adaptive controller design is proposed for discrete-time robotic control. The position of the robot arm is shown to converge to a desired point through two control loops. The first loop is an indirect adaptive perturbation controller based on the decoupled dynamics approach and using a perturbation model for the torque generation. The second loop generates the nominal torque component through a nonlinear controller representing the inverse manipulator dynamics. Simulation results on a typical three-link manipulator have indicated the potential and applicability of the developed design.

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

AbstractThe 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.

Efficient recursive algorithm for inverse dynamics

An efficient recursive computational scheme for the robot manipulator inverse dynamics is outlined. The algorithm is a new computational approach and is based on the application of the Gibbs-function. The solution of the inverse dynamic problem is formulated as a problem in quadratic programming, and the recursive equations for the computation of the driving torques are derived from the necessary conditions of minimum usage of the Lagrange method of undetermined multipliers. The algorithm involves the recursive computations of links' angular velocities, angular accelerations and linear accelerations expressed in moving coordinate systems. Further simplification can be performed by writing the vector equations as equations of coordinates. The reduced computational scheme is presented by a Pascal program detail. The computational complexity of the algorithm is analyzed.

Existence and uniqueness of solutions of the inverse dynamics of multilink flexible arms: Convergence of a numerical scheme

AbstractThe inverse dynamics of flexible manipulators consists in finding the joint torques that drive the end effector of a manipulator along a given trajectory. A proof of the existence and uniqueness of solutions of the inverse dynamics of planar open‐chain multilink flexible manipulators and the convergence of an algorithm previously proposed by the second author for the numerical solution of the problem are presented in this article. Higher‐order strain terms leading to the geometric stiffness matrix in finite element models are included in the formulation and their influence on the inverse dynamics solution is studied.

マニピュレータモデルにおける最小動力学パラメータと逆動力学計算法

This article presents a method to determine the minimum set of dynamics parameters of manipulators. It is based on a new concept ’τi (i-th joint torque) -identifiablity’ to classify the dynamics parameters. The method permits the determination of all the minimum dynamics parameters which can be used directly to the Newton-Euler Formulations. It also presents an algorithm for efficient computation of inverse dynamics of manipulators using the minimum set. The computational efficiency of the Algorithm is compared with other published methods.

A Neural Network System for Calculation of Inverse Dynamics for Manipulators.

This paper proposes a method to calculate manipulator inverse dynamics using a neural network. In this method, two sets of neural networks are prepared. One is for the elements of inertia moment matrix, and the other is for gravitational force. Each input for the network is only a joint position. Teacher signals of each network are also calculated using only a joint position, and therefore learning of each network is fast. The neural network, which acquires a model of inertia moment matrix, is used to calculate inertial force, centrifugal force and Coriolis force. In particular, the terms of centrifugal force and Coriolis force are calculated using a characteristic of manipulator dynamics and structure of the neural network. This method can be applied to the wide area data of joint positions, joint velocities and joint accelerations to calculate manipulator inverse dynamics. To show the validity of this method, the inverse dynamics of a two-dimensional manipulator are calculated.

Parallel computation of manipulator inverse dynamics

AbstractIn this article, parallel computation of manipulator inverse dynamics is investigated. A hierarchical graph‐based mapping approach is devised to analyze the inherent parallelism in the Newton‐Euler formulation at several computational levels, and to derive the features of an abstract architecture for exploitation of parallelism. At each level, a parallel algorithm represents the application of a parallel model of computation that transforms the computation into a graph whose structure defines the features of an abstract architecture, i.e., number of processors, communication structure, etc. Data flow analysis is employed to derive the time lower bound in the computation as well as the sequencing of the abstract architecture. The features of the target architecture are defined by optimization of the abstract architecture to exploit maximum parallelism while minimizing various overheads and architectural complexity. An algorithmically specialized, highly parallel, MIMD‐SIMD architecture is designed and implemented that is capable of efficient exploitation of parallelism at several computational levels. The computation time of the Newton‐Euler formulation for a 6‐degree‐of‐freedom (dof) general manipulator is measured as 187 μs. The increase in computation time for each additional dof is 23 μs, which leads to a computation time of less than 500 μs, even for a 12‐dof redundant arm.

A comparative study of inverse dynamics of manipulators with closed‐chain geometry

AbstractThe dynamics of closed‐chain manipulators was not studied as extensively as that of open‐chain manipulators. In this article, the inverse dynamics of two types of closedchain manipulators, namely, a pantograph manipulator and a five‐bar manipulator, are studied. The recently developed computationally efficient method1 is applied to both manipulators. The computational efficiency of inverse dynamics is evaluated in terms of both formulating methods (the method in reference 1 vs. the Lagrange method), and geometric structures (the pantograph vs. the five‐bar). The inverse kinematics computation of pantogaph manipulators is expected to be simpler than that of five‐bar manipulators simply because of the decoupling nature of the pantogaph mechanisms. On the contrary, the inverse kinetics of the pantograph is less efficient than the five‐bar because more links are involved during motion. It is also found that the overall inverse dynamics which includes both the inverse kinematics and kinetics of the pantograph manipulators, is more computationally efficient than that of the five‐bar, mainly due to the simple kinematics of the pantograph.

Robot Manipulator Dynamics — Towards Better Computational Algorithms

A new robot manipulator inverse dynamics computational algorithm is announced. The novel feature resides in the computations which are a blend of ordinary and Boolean algebra. As such, this method may also be interpreted as a dedicated compiler that optimizes the on-line computing time at expenses of the off-line stage. Nevertheless, the high off-line requirements are alleviated, through the derivation of some general rules that stem from the structure of the robot manipulator equations. In a practical implementation, a computer program based on a Quine-McCluskey truth table simplification method was used and experimented on a 2R robot manipulator. The results show a considerable computational improvement on a conventional sequential machine. Furthermore, they clearly point out new computational parallel architectures, without scheduling problems, and where performance improvement is proportional to the number of processors. Finally, it is observed that the proposed algorithm is not restricted to robot inverse dynamic computations, but is also applicable to kinematic and control computations.

A real-time system for robot manipulator inverse dynamics computation

A new robot manipulator inverse dynamics computational algorithm is announced. The novel feature resides in the computations which are a blend of ordinary and Boolean algebra. As such, this method may also be interpreted as a dedicated compiler that optimizes the on-line computing time at expenses of the off-line stage. Nevertheless, the high off-line requirements are alleviated, through the derivation of some general rules that stem from the structure of the robot manipulator equations. Moreover, the on-line computing time is further optimized through the use of Binary Decision Diagrams. The results show a considerable computational improvement on a conventional sequential machine. Furthermore, they clearly point out new computational parallel architectures, without scheduling problems, and where performance improvement is proportional to the number of processors. Finally, it is observed that the proposed algorithm is not restricted to robot inverse dynamic computations, but is also applicable to many other real-time computing structures.

Microprocessor Implementation of the Inverse Dynamical System for Industrial Robot Control

The inverse system problem of robot control is resurveyed. It is found, that the body-fixed coordinate system also plays an important role in computational efficiency of inverse dynamical formulations. The driving-axis coordinate system, whose origin locates on the driving axis of each link, is proposed to derive the recursive Newton-Euler formulation of manipulator inverse dynamics. The new algorithm with considering trivial calculations is implemented using the Assembly language on an INTEL 8086/8087 microprocessor (5 MHz clock). The measurement of computational efficiency shows that this software package marginally satisties the sampling rate criterion of robot control even with a 16-bit microprocessor