scholarly journals An Asymptotically Optimal NMPC Core for Multi Degrees of Freedom Rigid Bodies

2012 ◽  
Vol 45 (17) ◽  
pp. 207-212
Author(s):  
Chyon Hae Kim ◽  
Shimon Sugawara ◽  
Shigeki Sugano
Keyword(s):  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Asymptotically Optimal

scholarly journals An Efficient Contact Model for the Simulation of Cargo Airdrop Extraction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong
Keyword(s):  
Degrees Of Freedom ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Dynamics ◽  
Moving Frame ◽  
Contact Friction ◽  
Practical Implementation ◽  
Contact Formulation ◽  
Efficient Code ◽  
Extraction Phase

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.

scholarly journals Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Beth Boardman ◽  
Troy Harden ◽  
Sonia Martínez
Keyword(s):  
Degrees Of Freedom ◽  
Metric Spaces ◽  
Dynamic Environments ◽  
Random Trees ◽  
Asymptotically Optimal ◽  
Euclidean Metric ◽  
The Third ◽  
Dubins Vehicle ◽  
Improved Performance ◽  
Dubins Vehicles

Three algorithms that improve the performance of the asymptotically optimal Rapidly exploring Random Tree (RRT*) are presented in this paper. First, we introduce the Goal Tree (GT) algorithm for motion planning in dynamic environments where unexpected obstacles appear sporadically. The GT reuses the previous RRT* by pruning the affected area and then extending the tree by drawing samples from a shadow set. The shadow is the subset of the free configuration space containing all configurations that have geodesics ending at the goal and are in conflict with the new obstacle. Smaller, well defined, sampling regions are considered for Euclidean metric spaces and Dubins' vehicles. Next, the Focused-Refinement (FR) algorithm, which samples with some probability around the first path found by an RRT*, is defined. The third improvement is the Grandparent-Connection (GP) algorithm, which attempts to connect an added vertex directly to its grandparent vertex instead of parent. The GT and GP algorithms are both proven to be asymptotically optimal. Finally, the three algorithms are simulated and compared for a Euclidean metric robot, a Dubins' vehicle, and a seven degrees-of-freedom manipulator.

Generalized Abbe Principle: Position Error Propagation in Machine Elements

1996 ◽  
Author(s):  
Joseph Pegna
Keyword(s):  
Error Propagation ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Statistical Characterization ◽  
Physical Limit ◽  
Potential Applications ◽  
Machine Elements ◽  
Tolerance Verification ◽  
Precision Machines

Abstract In the quest for ever finer levels of technology integration, mechanical linkages reach their precision limits at about 5micrometers per meter of workspace. Beyond this physical limit, all six dimensional degrees of freedom need to be precisely ascertained to account for mechanical imperfections. This paper substantiates Wu’s vision of “precision machines without precision machinery.” A formulation and statistical characterization of position and orientation error propagation in rigid bodies are presented for two extreme models of measurement. It is shown that error distribution is uniquely dependent upon the design of the measurement plan. The theoretical foundations presented were evolved in the course of designing precision machinery. Other potential applications include: fixture design, metrology, and geometric tolerance verification.

Theory and Method of Dynamic Modeling for Multilayer Vibration Isolation System

2000 ◽  
Author(s):  
Liao Dao-Xun ◽  
Lu Yong-Zhong ◽  
Huang Xiao-Cheng
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Vibration Isolation ◽  
Rigid Bodies ◽  
Design Calculation ◽  
Isolation System ◽  
Dry Land ◽  
Vibration Isolation System ◽  
Six Degrees Of Freedom ◽  
Floating Raft

Abstract The multilayer vibration isolation system has been widely applied to isolate vibration in dynamic devices of ships, high-speed vehicles forging hammer and precise instruments. The paper is based on the coordinate transformation of space general motion for mass blocks (rigid bodies) and Lagrangian equation of multilayer vibration isolation system. It gives a strict mathematical derivation on the differential equation of the motion for the system with six degrees of freedom of relative motion between mass blocks (including base). The equations are different from the same kind of equations in the reference literatures. It can be used in the floating raft of ships in order to isolates vibration and decrease noise, also used in design calculation of the multilayer vibration isolation for dynamic machines and precise instruments on the dry land.

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.

scholarly journals Complex Bogie Modeling Incorporating Advanced Friction Wedge Components

2009 ◽  
Author(s):  
Brian Sperry ◽  
Corina Sandu ◽  
Brent Ballew
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Model Simulation ◽  
Surface Friction ◽  
Rigid Bodies ◽  
Operating Conditions ◽  
Normal Operation ◽  
Contact Points ◽  
Modeling Software ◽  
Simulation Results

This research focuses on the dynamic behavior of the three-piece bogie that supports the freight train car bodies. While the system is relatively simple, in that there are very few parts involved, the behavior of the bogie is somewhat more complex. Our research focuses primarily on the behavior of the friction wedges under different operating conditions that are seen under normal operation. The Railway Technologies Laboratory (RTL) at Virginia Tech has been developing a model to better capture the dynamic behavior of friction wedges using 3-D modeling software. In previous years, a quarter-truck model, and half-truck variably damped model have been developed using MathWorks MATLAB®. This year, research has focused on the development of a half-truck variably damped model with a new (curved surface) friction wedge, and a half-truck constantly damped model, both using the MATLAB® based software program. Currently a full-truck variably damped model has been created using LMS Virtual.Lab. This software allows for a model that is more easily created and modified, as well as allowing for a much shorter simulation time, which became a necessity as more contact points, and more complex inputs were needed to increase the accuracy of the simulation results. The new model consists of seven rigid bodies: the bolster, two sideframes, and four wedges. We have also implemented full spring nests on each sideframe, where in previous models equivalent spring forces were used. The model allows six degrees-of-freedom for the wedges and bolster: lateral, longitudinal, and vertical translations, as well as pitch, roll, and yaw. The sideframes are constrained to two degrees-of-freedom: vertical and longitudinal translations. The inputs to the model are vertical and longitudinal translations or forces on the sideframes, which can be set completely independent of each other. The model simulation results have been compared with results from NUCARS®, an industrially-used train modeling software developed by the Transportation Technology Center, Inc. (TTCI), a wholly owned subsidiary of the Association of American Railroads (AAR), for similar inputs, as well as experimental data from warping tests performed at TTCI.

Validation of a Novel 3D-Printed Instrumented Spatial Linkage That Measures Changes in the Rotational Axes of the Tibiofemoral Joint

2013 ◽  
Author(s):  
Daniel P. Bonny ◽  
S. M. Howell ◽  
M. L. Hull
Keyword(s):  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Anatomic Landmarks ◽  
Tibiofemoral Joint ◽  
Six Degrees Of Freedom ◽  
Revolute Joints ◽  
Flexion Extension ◽  
3D Printed ◽  
Total Knee ◽  
Position And Orientation

The two kinematic axes of the tibiofemoral joint, the flexion-extension (F-E) and longitudinal rotation (LR) axes [1], are unrelated to the anatomic landmarks often used to align prostheses during total knee arthroplasty (TKA) [1, 2]. As a result, conventional TKA changes the position and orientation of the joint line, thus changing the position and orientation of the F-E and LR axes and consequently the kinematics of the knee. However, the extent to which TKA changes these axes is unknown. An instrument that can measure the locations of and any changes to these axes is an instrumented spatial linkage (ISL), a series of six instrumented revolute joints that can measure the six degrees of freedom of motion (DOF) between two rigid bodies without constraining motion. Previously, we computationally determined how best to design and use an ISL such that rotational and translational errors in locating the F-E and LR axes were minimized [3]. However, this ISL was not constructed and therefore its ability to measure changes in the axes has not been validated. Therefore the objective was to construct the ISL and quantify the errors in measuring changes in position and orientation of the F-E axis.

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.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

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