Contact-space resolution model for a physically consistent view of simultaneous collisions in articulated-body systems: theory and experimental results

2020 ◽  
Vol 39 (10-11) ◽  
pp. 1239-1258
Author(s):  
Shameek Ganguly ◽  
Oussama Khatib
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Rigid Bodies ◽  
Computationally Efficient ◽  
Space Resolution ◽  
Resolution Model ◽  
Space Dynamics ◽  
Contact Space

Multi-surface interactions occur frequently in articulated-rigid-body systems such as robotic manipulators. Real-time prediction of contact-interaction forces is challenging for systems with many degrees of freedom (DOFs) because joint and contact constraints must be enforced simultaneously. While several contact models exist for systems of free rigid bodies, fewer models are available for articulated-body systems. In this paper, we extend the method of Ruspini and Khatib and develop the contact-space resolution (CSR) model by applying the operational space theory of robot manipulation. Through a proper choice of contact-space coordinates, the projected dynamics of the system in the contact space is obtained. We show that the projection into the dynamically consistent null space preserves linear and angular momentum in a subspace of the system dynamics complementary to the joint and contact constraints. Furthermore, we illustrate that a simultaneous collision event between two articulated bodies can be resolved as an equivalent simultaneous collision between two non-articulated rigid bodies through the projected contact-space dynamics. Solving this reduced-dimensional problem is computationally efficient, but determining its accuracy requires physical experimentation. To gain further insights into the theoretical model predictions, we devised an apparatus consisting of colliding 1-, 2-, and 3-DOF articulated bodies where joint motion is recorded with high precision. Results validate that the CSR model accurately predicts the post-collision system state. Moreover, for the first time, we show that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon in articulated-rigid-body systems.

Distributed Operational Space Formulation of Serial Manipulators

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Kishor D. Bhalerao ◽  
James Critchley ◽  
Denny Oetomo ◽  
Roy Featherstone ◽  
Oussama Khatib
Keyword(s):  
Parallel Algorithms ◽  
Time Complexity ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Divide And Conquer ◽  
Serial Manipulators ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Space Formulation ◽  
Space Dynamics

This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

A Computationally Efficient Planar Rigid Body Velocity Measure

2009 ◽  
Author(s):  
Luis E. Criales ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Computationally Efficient ◽  
Straight Line ◽  
Body Velocity ◽  
Velocity Measure ◽  
Rigid Body Motions ◽  
Line Path ◽  
Planar Motions

A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.

On Analytical Evaluation of Gear Dynamic Factors Based on Rigid Body Dynamics

1985 ◽  
Vol 107 (2) ◽  
pp. 301-311 ◽  
Author(s):  
C. C. Wang
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Time Derivative ◽  
Transmission Error ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Dynamic Factor ◽  
Lumped Mass ◽  
Body Dynamics ◽  
Cubic Spline Curve

This paper proposes an initial step to rationalize the dynamic factor calculation and bring it under the control of the laws of mechanics. The theory is straight forward. The concept of mathematical scaling is utilized to simplify the system dynamics’ formulation. The rigid body dynamics accounts for the gear dynamic tooth loads resulting from the prescribed transmission error of each gear step—including the artificial ones. The latter converts a lumped-mass-elastic system into a rigid-bodies-transmission-error system subjected to the solution of the rigid body system dynamics according to Newton’s law. The entire concept of the solution has been implemented into a FORTRAN program approximately 600 statements in length. The results obtained through computer simulation of various test cases demonstrate the potential and effectiveness of the proposed concept. Contrary to the current practice of grossly ignoring the inertial and system effects, this paper has taken all these important factors into account. The transmission-error-induced acceleration is approximated by the second-order time derivative of one of the cubic spline curve-fitting methods. The approach is cost effective and numerically satisfactory. The model can be further improved to reduce the extent of basic assumptions, or to increase the number of conditional constraints without losing economical attractiveness.

Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Line Trajectories

1987 ◽  
Vol 109 (1) ◽  
pp. 116-124 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bernard Roth
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Two Degrees Of Freedom ◽  
Global Properties ◽  
New Concepts ◽  
Line Trajectory

A general framework is presented for the study of the properties of trajectories generated by lines embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Several new concepts, such as a line’s angular and linear velocities and accelerations, are introduced and used to (1) characterize the differences between line trajectories generated by different mechanisms; (2) distinguish trajectories generated by different lines in the same rigid body; (3) distinguish properties at different positions in the same trajectory. Line trajectories are classified according to the number of degrees of freedom of the motion, and local and global properties are discussed. These techniques are illustrated in an example of a line trajectory generated by a two-degrees-of-freedom manipulator.

Rigid body refinements in GSAS/EXPGUI

2011 ◽  
Vol 26 (S1) ◽  
pp. S13-S21 ◽  
Author(s):  
Charles H. Lake ◽  
Brian H. Toby
Keyword(s):  
Rigid Body ◽  
Software Package ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Atomic Motion ◽  
Bond Lengths

Rigid bodies provide a way to simplify the model used in a crystallographic refinement by removing parameters that describe degrees of freedom that are unlikely to change based on chemical experience. The GSAS software package provides a powerful implementation of rigid bodies that allows for refinement of classes of bond lengths, grouping of bodies to further reduce parameterization and where atomic motion can be described from group displacement parameters (TLS) representation. However, use of rigid bodies in GSAS is complex to learn and time-consuming to perform. This paper describes how the rigid body definition process has been simplified and extended through implementation in the EXPGUI interface to GSAS.

KINEMATIC INVERSION OF FUNCTIONALLY-REDUNDANT SERIAL MANIPULATORS: APPLICATION TO ARC-WELDING

2005 ◽  
Vol 29 (4) ◽  
pp. 679-690 ◽  
Author(s):  
Liguo Huo ◽  
Luc Baron
Keyword(s):  
Arc Welding ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Computationally Efficient ◽  
Secondary Tasks ◽  
Serial Manipulators ◽  
Six Degrees Of Freedom ◽  
Kinematic Inversion ◽  
Resolution Scheme ◽  
Robotic Tasks

This paper introduces the concept of functional redundancy of serial manipulators, and presents a new resolution scheme to solve such redundant robotic tasks requiring less than six degrees-of-freedom. Instead of projecting the secondary task onto the null space of the Jacobian matrix in order to take advantage of the redundancy, the twist of end-effector is directly decomposes into two orthogonal subspaces where the main and secondary tasks lie, respectively. The algorithm has shown to be computationally efficient and well suited to solve functionally-redundant robotic tasks, such as arc-welding.

Dynamic Analysis and Parametric Excitation of a Multi-Span Beam Structure Coupled With a Sequence of Moving Rigid Bodies

2018 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Beam Structure ◽  
Assumed Mode Method ◽  
Mode Method

Dynamic analysis of a multi-span beam structure carrying moving rigid bodies is essentially important in various engineering applications. With many rigid bodies having different speeds and varying inter-distances, number of degrees of freedom of the coupled beam-moving rigid body system is time-varying and the beam-rigid body interaction is thus complicated. Developed in this paper is a method of extended solution domain (ESD) that resolves the issue of time-varying number of degrees and delivers a consistent mathematical model for the coupled system. The governing equation of the coupled system is derived with generalized assumed mode method through use of exact eigenfunctions and solved via numerical integration. Numerical simulation shows the accuracy and efficiency of the proposed method. Moreover, a preliminary study on parametric resonance on a beam structure with 10 rigid bodies provides guidance for future development of conditions on parametric resonance induced by moving rigid bodies, which can be useful for operation of certain coupled structure systems.

scholarly journals Multi-Camera-Based Universal Measurement Method for 6-DOF of Rigid Bodies in World Coordinate System

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5547 ◽  
Author(s):  
Zuoxi Zhao ◽  
Yuchang Zhu ◽  
Yuanhong Li ◽  
Zhi Qiu ◽  
Yangfan Luo ◽  
...  
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
High Speed ◽  
Measurement Method ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Least Square ◽  
Matrix Analysis ◽  
Average Error ◽  
World Coordinate System

The measurement of six-degrees-of-freedom (6-DOF) of rigid bodies plays an important role in many industries, but it often requires the use of professional instruments and software, or has limitations on the shape of measured objects. In this paper, a 6-DOF measurement method based on multi-camera is proposed, which is accomplished using at least two ordinary cameras and is made available for most morphological rigid bodies. First, multi-camera calibration based on Zhang Zhengyou’s calibration method is introduced. In addition to the intrinsic and extrinsic parameters of cameras, the pose relationship between the camera coordinate system and the world coordinate system can also be obtained. Secondly, the 6-DOF calculation model of proposed method is gradually analyzed by the matrix analysis method. With the help of control points arranged on the rigid body, the 6-DOF of the rigid body can be calculated by the least square method. Finally, the Phantom 3D high-speed photogrammetry system (P3HPS) with an accuracy of 0.1 mm/m was used to evaluate this method. The experiment results show that the average error of the rotational degrees of freedom (DOF) measurement is less than 1.1 deg, and the average error of the movement DOF measurement is less than 0.007 m. In conclusion, the accuracy of the proposed method meets the requirements.

Chrono: A Parallel Physics Library for Rigid-Body, Flexible-Body, and Fluid Dynamics

2013 ◽  
Author(s):  
Toby Heyn ◽  
Hammad Mazhar ◽  
Arman Pazouki ◽  
Daniel Melanz ◽  
Andrew Seidl ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Gpu Computing ◽  
Rigid Bodies ◽  
Flexible Body ◽  
Simulation Engine ◽  
Physics Simulation ◽  
Flexible Body Dynamics

This contribution discusses a multi-physics simulation engine, called Chrono, that relies heavily on parallel computing. Chrono aims at simulating the dynamics of systems containing rigid bodies, flexible (compliant) bodies, and fluid-rigid body interaction. To this end, it relies on five modules: equation formulation (modeling), equation solution (simulation), collision detection support, domain decomposition for parallel computing, and post-processing analysis with emphasis on high quality rendering/visualization. For each component we point out how parallel CPU and/or GPU computing have been leveraged to allow for the simulation of applications with millions of degrees of freedom such as rover dynamics on granular terrain, fluid-structure interaction problems, or large-scale flexible body dynamics with friction and contact for applications in polymer analysis.

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