Inverse Dynamics Algorithm Research Articles

Dynamics Modelling of Hexaslides using the Decoupled Natural Orthogonal Complement Matrices

In this paper, dynamic model of a class of parallel systems, namely, the hexaslides, is proposed. The model developed is based on the concept the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere. The dynamic model of hexslides, though complex due to the existence of multi-loop kinematic chains, is required for actuator power estimation, computed-torque control, optimum tool trajectory generation, etc. The use of DeNOC offers many physical interpretations, recursive algorithms, and parallel computations. Using the proposed dynamic model, a parallel inverse dynamics algorithm has been presented to compute the actuator forces. This is useful to choose suitable motors for an application. An illustration is provided using an existing machine tool based on hexaslides, namely, the HexaM, while it is carrying out a circular contouring. Secondly, the effect of leg and slider inertias is also studied, which clearly suggests that neither of these can be neglected while finding the actuator forces.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

Effect of Fore-Aft Seat Position on Shoulder Demands During Wheelchair Propulsion: Part 1. A Kinetic Analysis

Background/Objective: The highly repetitive and weight-bearing nature of wheelchair (WC) propulsion has been associated with shoulder pain among persons with spinal cord injury (SCI). Manipulation of WCseat position is believed to reduce the overall demand of WC propulsion. The objective of this investigation was to document the effect offore-aft seat position on shoulder joint kinetics.Methods: Thirteen men with complete motor paraplegia propelled a test WC in 2 fore-aft seat positions during free, fast, and graded conditions. The seat-anterior position aligned the glenohumeral joint with the wheel axle and the seat-posterior position moved the glenohumeral joint 8 cm posteriorly. The right wheelof the test chair was instrumented to measure forces applied to the pushrim. An inverse dynamics algorithm was applied to calculate shoulder joint forces, external moments, and powers.Results: For all test conditions, the superior component of the shoulder joint resultant force was significantly lower in the seat-posterior position. During graded propulsion, the posterior component of the shoulder joint force was significantly higher with the seat posterior. Peak shoulder joint moments and power were similar during freeand fast propulsion. During graded propulsion, the seat-posterior position displayed increased internal rotation moment, decreased sagittal plane power absorption, and increasedtransverseplane power generation.Conclusions: This investigation provides objective support that a posterior seat position reduces the superior component of the shoulder joint resultant force. Consequently, this intervention potentially diminishes the risk for impingement of subacromial structures.

Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator

Abstract We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

A Dynamic Model Based Robot Arm Selection Criterion

The selection of robot manipulator architecture, i.e. the determination of link lengths, their relative orientations, types of joints, e.g. revolute or prismatic, etc., has been largely done so far by experience, intuition and at most based on the kinematic considerations like workspace, manipulability, etc. Dynamics is generally ignored at this stage even though it is widely used for control and simulation. This paper attempts to introduce a criterion based on the dynamics of a robot manipulator, namely, simplicity of the associated generalized inertia matrix (GIM). Since the GIM influences both the control and simulation algorithms significantly, its fast computation and / or making its shape diagonal will certainly enhance the speed, precision, and stability of the robots. Two measures of simplicity, the computation complexity of the GIM in terms of floating point operations and the computer CPU time of an algorithm where the GIM appears, e.g., the inverse dynamics algorithm, are used here to evaluate a robot arm. The proposed criterion is illustrated with two -link robot arms with revolute and prismatic joints and compared with the two commonly used criteria, namely, the workspace, and manipulability. Finally, an example is taken to select an arm from the two spatial robot architectures, RTX and Stanford.

Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Finger joint impedance during tapping on a computer keyswitch

We studied the dynamic behavior of finger joints during the contact period of tapping on a computer keyswitch, to characterize and parameterize joint function with a lumped-parameter impedance model. We tested the hypothesis that the metacarpophalangeal (MCP) and interphalangeal (IP) joints act similarly in terms of kinematics, torque, and energy production when tapping. Fifteen human subjects tapped with the index finger of the right hand on a computer keyswitch mounted on a two-axis force sensor, which measured forces in the vertical and sagittal planes. Miniature fiber-optic goniometers mounted across the dorsal side of each joint measured joint kinematics. Joint torques were calculated from endpoint forces and joint kinematics using an inverse dynamic algorithm. For each joint, a linear spring and damper model was fitted to joint torque, position, and velocity during the contact period of each tap (22 per subject on average). The spring-damper model could account for over 90% of the variance in torque when loading and unloading portions of the contact were separated, with model parameters comparable to those previously measured during isometric loading of the finger. The finger joints functioned differently, as illustrated by energy production during the contact period. During the loading phase of contact the MCP joint flexed and produced energy, whereas the proximal and distal IP joints extended and absorbed energy. These results suggest that the MCP joint does work on the interphalangeal joints as well as on the keyswitch.

High performance algorithm to obtain Johansson adaptive control in robot manipulators

The dynamics equation of robot manipulators is nonlinear and coupled. An inverse dynamic control algorithm that requires a full knowledge of the dynamics of the system is one way to solve the control movement. Adaptive control is used to identify these unknown parameters. These algorithms are based on the linear relationship of inertial parameters in the dynamic equation. A formulation to generalize this relationship is applied to the Johansson adaptive algorithm. The objective of this paper is to present the optimizations to obtain the matrices of the Johansson adaptive algorithm using the Lagrange–Euler formulation and apply it to an on-line identification problem.

Inverse dynamic analysis of mechanical systems in joint coordinate space

An inverse dynamic analysis algorithm for spatial flexible mechanical systems with closed loops is developed in the relative joint coordinate space. System equations of motion and constraint acceleration equations are derived using the velocity transformation technique. An inverse velocity transformation operator, which transforms the Cartesian velocities to the relative velocities, is derived systematically, corresponding to the types of kinematic joint connecting the bodies. Using the resulting matrix, the joint reaction forces and moments are analysed in the Cartesian coordinate space. The joint coordinates and the deformation modal coordinates are used as the generalized coordinates of a flexible mechanical system. The algorithm is verified by means of two numerical examples.

Properties and Data Structures for Efficient Adaptive Control Algorithms in Robot Manipulators

The dynamics equation of robot manipulators is non linear and coupled. One way to solve the control movement is to use an inverse dynamic control algorithm that requires a full knowledge of the dynamics of the system. This knowledge is unusual in industrial robots, so adaptive control is used to identify these unknown parameters. In general their linear regressor is based on the linear relationship between the unknown inertial parameters and their coefficients. It is difficult to obtain a general algorithm for this relationship when more than two links are considered. In this paper a formulation to generalize this relationship is presented. This formulation is applied to Slotine & Li adaptive algorithm. The results have been obtained by simulation for a robot Puma with six links.

Implementation of a robust dynamic control for SCARA robot

A control system for SCARA robot is designed for implementing a robust dynamic control algorithm. This study focuses on the use of DSPs in the design of joint controllers and interfaces in between the host controller and four joint controllers and in between the joint controllers and four servo drives. The mechanical body of SCARA robot and the servo drives, are selected from the commercially available products. The four joint controllers, assigned to each joint separately, are combined into a common system through the mother board hardwarewise and through the global memory softwarewise. The mother board is designed to connect joint controllers onto the board through the slots adopting PC/104 bus structures. The global memory stores the common data which can be shared by joint controllers and used by the host computer directly, and it virtually combines the whole system into one. To demonstrate the performance and efficiency of the system, a robust inverse dynamic algorithm is proposed and implemented for a faster and more precise control. The robust inverse dynamic algorithm is basically derived from an inverse dynamic algorithm and a PID compensator. Based upon the derived dynamic equations of SCARA robot, the inverse dynamic algorithm is initially implemented with l msec of control cycle—0.3 msec is actually used for the control algorithm—in this system. The algorithm is found to be inadequate for the high speed and precision tasks due to inherent modelling errors and time-varying factors. Therefore a variable PID algorithm is combined with the inverse dynamic algorithm to reinforce robustness of control. Experimental data using the proposed algorithm are presented and compared with the results obtained from the PID and the inverse dynamic algorithms.

Analysis of joint reaction forces of flexible multibody system with closed loops

The analysis of dynamic forces is essential to the design of systems, stress analysis, or life prediction of part of machine. Calculation of dynamic forces has very close relations with multibody dynamics algorithm. In this paper, an algorithm which calculates joint reaction force/moment of flexible multibody dynamic systems is proposed by using inverse dynamic algorithm and velocity transformation technique.

A decomposition of the manipulator inertia matrix

A decomposition of the manipulator inertia matrix is essential, for example, in forward dynamics, where the joint accelerations are solved from the dynamical equations of motion. To do this, unlike a numerical algorithm, an analytical approach is suggested in this paper. The approach is based on the symbolic Gaussian elimination of the inertia matrix that reveal recursive relations among the elements of the resulting matrices. As a result, the decomposition can be done with the complexity of order n, O(n), where n being the degrees of freedom of the manipulator, as opposed to an O(n/sup 3/) scheme, required in the numerical approach. In turn, O(n) inverse and forward dynamics algorithms can be developed. As an illustration, an O(n) forward dynamics algorithm is presented.

Inverse dynamics of redundant manipulators using a minimum number of control forces

AbstractThe number of the control actuators used by the inverse kinematics and dynamics algorithms that have been developed in the literature for generating redundant robot joint trajectories is equal to the number of the degrees of freedom of the manipulator. In this article, an inverse dynamics algorithm that performs the tasks using only a minimum number of actuators is proposed. The number of actuators is equal to the dimension of the task space, and the control forces are solved simultaneously with the corresponding system motion. It is shown that because all degrees of freedom are not actuated, the control forces may lose the ability to make an instantaneous effect on the end‐effector acceleration at certain configurations, yielding the dynamical equation set of the system to be singular. The dynamical equations are modified in the neighborhood of the singular configurations by utilizing higher‐order derivative information, so that the singularities in the numerical procedure are avoided. Asymptotically stable inverse dynamics closed‐loop control in the presence of perturbations is also discussed. The algorithm is further generalized to closed chain manipulators. Three‐link and two‐link redundant planar manipulators are analyzed to illustrate the validity of the approach. © 2995 John Wiley & Sons, Inc.

Transputer-Based Multibody System, Dynamic Simulation, Part II: Parallel Implementation—Results∗

Abstract This paper continues demonstration of the benefits of parallel multibody simulation. In Part I implicit integration schemes combined with a modified inverse dynamic formulation were proposed for parallel multibody simulation. In Part II the modified inverse dynamics algorithm and computation of the integrator's Jacobian are split up into independent work packages for parallelization on medium-and coarse-grain levels, respectively. The farming concept, which organizes the flow of work and result packages through a network of processors, is presented. Transputers are used to build a distributed memory multiprocessor system, where both the medium- and coarse-grain approaches are implemented, resulting in the PARSIM-package for parallel multibody dynamics. The simulation of an off-road vehicle and a multibody model for a cable demonstrate the considerable savings in simulation times achieved by the new software package.

Recursive dynamics algorithm for multibody systems with prescribed motion

This paper uses spatial operator techniques to develop a new algorithm for the dynamics of multibody systems with hinges undergoing prescribed motion. This algorithm is spatially recursive, and its computational complexity grows only linearly with the number of degrees of freedom in the system. Its structure is a hybrid of known recursive forward and inverse dynamics algorithms for regular multibody systems. Changes to the prescribed/nonprescribed nature of hinges can be implemented during run time since they are handled with very low overhead in the algorithm.

Implementation of a unified robot kinematics and inverse dynamics algorithm on a DSP chip

The feasibility and performance of implementing kinematics and inverse dynamics algorithms on a DSP chip for real-time robot arm control is investigated. The algorithms include the following modules: forward and inverse kinematics; Jacobian, inverse Jacobian, and Jacobian derivative term; and Newton-Euler inverse dynamics. These modules are unified under a common coordinate system, and then computationally optimized by eliminating the redundancies among the modules. Further optimization is indicated for the PUMA-like arms. The algorithms are implemented on a TI TMS320C30 DSP chip. It is found that the execution time for the entire set of algorithms is about 0.78 ms for a six-degree-of-freedom robot with a spherical wrist, and is about 0.63 ms for a PUMA-specific arm. The communication time between the host PC and the DSP chip is about 0.376 ms. Thus, it is possible to implement a complete Cartesian controller at a 1000 Hz sampling rate. The algorithms have been successfully tested on a PUMA arm with a PC-based advanced controller.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

Parallelized inverse dynamics algorithm for dynamic control of a robot manipulator : Seungdo Kim, Hyung Kyi, Yi, C.L. Roh, M.J. Chung, pp 49–53

Parallelized inverse dynamics algorithm for dynamic control of a robot manipulator : Seungdo Kim, Hyung Kyi, Yi, C.L. Roh, M.J. Chung, pp 49–53

Computational requirements for a discrete Kalman filter in robot dynamics algorithms

SUMMARYIn standard classical kinematic and dynamic considerations the equations of motion for an n-link manipulator can be obtained as recursive Newton-Euler equations. Another approach to finding the inverse dynamics equations is to formulate the system dynamics and kinematics as a two-point boundary-value problem. The equivalence between these two approaches has been proved in this paper. Solution to the two-point boundary-value problem leads to the forward dynamics equations which are similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The extensive numerical studies conducted by the author on the new inverse and forward dynamics algorithms derived from the two-point boundary-value problem establish the same level of confidence as exists for current methods. In order to obtain the algorithms with the smallest coefficients of the polynomial of order O(n), the categorization procedure has been implemented in this work.