Rational Interpolation of Car Motions

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
J. M. Selig
Keyword(s):  
Final Section ◽  
Rational Interpolation ◽  
Polynomial Functions ◽  
Optimal Motion ◽  
Kinematic Constraint ◽  
Differential Constraint ◽  
Kinematic Constraints ◽  
Cayley Map ◽  
Polynomial Curve ◽  
Rigid Body Motions

This work introduces a general approach to the interpolation of the rigid-body motions of cars by rational motions. A key feature of the approach is that the motions produced automatically satisfy the kinematic constraints imposed by the car wheels, that is, cars cannot instantaneously translate sideways. This is achieved by using a Cayley map to project a polynomial curve in the Lie algebra se(2) to SE(2) the group of rigid displacements in the plane. The differential constraint on se(2), which expresses the kinematic constraint on the car, is easily solved for one coordinate if the other two are given, in this case as polynomial functions. In this way, families of motions obeying the constraint can be found. Several families are found here and examples of their use are shown. It is shown how rest-to-rest motions can be generated in this way and also how these motions can be joined so that the motion is continuous and differentiable across the join. A final section discusses the optimization of these motions. For some cost functions, the optimal motions are known but can be rather impractical to use. By optimizing over a family of motions which satisfy the boundary conditions for the motion, it is shown that rational motions can be found simply and are close to the overall optimal motion.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

Energy-Optimal Motion Trajectory of an Omni-Directional Mecanum-Wheeled Robot via Polynomial Functions

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1400-1414
Author(s):  
Li Xie ◽  
Karl Stol ◽  
Weiliang Xu
Keyword(s):  
Energy Consumption ◽  
Polynomial Functions ◽  
Heavy Duty ◽  
Optimal Motion ◽  
Wheeled Robots ◽  
Motion Trajectories ◽  
Decision Variables ◽  
Robotic Motion ◽  
Wheeled Robot ◽  
Mecanum Wheel

SUMMARYThe Mecanum wheel is one of the practical omni-directional wheel designs in industry, especially for heavy-duty tasks in a confined floor. An issue with Mecanum-wheeled robots is inefficient use of energy. In this study, the robotic motion trajectories are optimized to minimize the energy consumption, where a robotic path is expressed in polynomial functions passing through a given set of via points, and a genetic algorithm is used to find the polynomial’s coefficients being decision variables. To attempt a further reduction in the energy consumption, the via points are also taken as decision variables for the optimization. Both simulations and experiments are conducted, and the results show that the optimized trajectories result in a significant reduction in energy consumption, which can be further lowered when the via points become decision variables. It is also found that the higher the order of the polynomials the larger the reduction in the energy consumption.

Use of critical state representations of sand in the method of stress characteristics

1987 ◽  
Vol 24 (3) ◽  
pp. 441-446 ◽  
Author(s):  
M. G. Jefferies ◽  
K. Been
Keyword(s):  
Bearing Capacity ◽  
Key Words ◽  
Critical State ◽  
Method Of Characteristics ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
The Method Of Characteristics ◽  
State Stress

The limitations of critical state representations of sand behaviour are discussed and it is shown that stress dilatancy is an implicit part of a critical state framework. It is then argued that dilatancy leads to underestimates of bearing capacity factors in the method of characteristics. Kinematic constraints should also be considered in such calculations. Both dilatancy and kinematic constraint may be introduced into a stress characteristics approach while preserving critical state characterization of sand, using the technique known as the method of associated fields. Key words: bearing capacity, critical state, stress dilatancy, method of characteristics.

Rational Motion Interpolation Under Kinematic Constraints of Planar 6R Closed Chain

2007 ◽  
Author(s):  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Rational Interpolation ◽  
Geometric Constraints ◽  
Rational Curve ◽  
Constrained Motion ◽  
Extreme Position ◽  
Kinematic Constraints ◽  
Closed Chain ◽  
Curve Interpolation

This paper deals with the problem of synthesizing planar rational motions under the kinematic constraints of planar 6R closed chain. It follows our previous work on the synthesis of rational motions under the kinematic constraints of planar open chains. Planar quaternions are used to represent planar displacements. In this way, the problem of rational motion interpolation is transformed into that of rational curve interpolation, and the kinematic constraints of a planar 6R closed chain are transformed into geometric constraints for the rational interpolation. An algorithm for the constrained motion interpolation is developed that detects an extreme position on the rational motion that violates the kinematic constraints. This position is then modified so that it is in compliance with the kinematic constraints and is added to the list of positions to be interpolated. By restricting the kinematic constraints to 5R and 4R closed chains, the algorithm is also applicable to the problem of synthesizing planar rational motions for 5R and 4R closed chains.

scholarly journals SINS/OD fault-tolerant navigation algorithm based on tracked vehicle kinematic constraints

2018 ◽  
Vol 198 ◽  
pp. 01001
Author(s):  
Xiaqing Tang ◽  
Zepeng Sun ◽  
Huan Zhang ◽  
Meng Wu
Keyword(s):  
Fault Tolerant ◽  
Detection Algorithm ◽  
Integrated Navigation ◽  
Tracked Vehicle ◽  
Kinematic Constraint ◽  
Simulation Experiments ◽  
Kinematic Constraints ◽  
Navigation Algorithm ◽  
The Difference ◽  
Constraint Model

In this paper, for the problem that the accuracy declining of the SINS/OD navigation caused by the sliding and idling during the process of turning and straight running, and stopping output of the odometer, a kinematic constraint model of the tracked vehicle is established. The sliding and idling during the process of turning are compensated. In the filtering process, the difference of the displacement increment is used as the observed quantity, and a two-layer fault detection algorithm is used to detect the output fault of the odometer. The simulation experiments show that the SINS/OD integrated navigation algorithm assisted by the kinematic constraints of the tracked vehicle can detect the output fault of the odometer accurately and perform fault-tolerant navigation, which greatly improves the positioning accuracy after the odometer failure.

scholarly journals A Discussion of Low-Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Dan Negrut ◽  
Laurent O. Jay ◽  
Naresh Khude
Keyword(s):  
Numerical Experiments ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Real Life ◽  
Flexible Multibody Dynamics ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Integration Formulas ◽  
Impact Phenomena ◽  
Low Order

The premise of this work is that the presence of high stiffness and/or frictional contact/impact phenomena limits the effective use of high order integration formulas when numerically investigating the time evolution of real-life mechanical systems. Producing a numerical solution relies most often on low-order integration formulas of which the paper investigates three alternatives: Newmark, HHT, and order 2 BDFs. Using these methods, a first set of three algorithms is obtained as the outcome of a direct index-3 discretization approach that considers the equations of motion of a multibody system along with the position kinematic constraints. The second batch of three algorithms draws on the HHT and BDF integration formulas and considers, in addition to the equations of motion, both the position and velocity kinematic constraint equations. Numerical experiments are carried out to compare the algorithms in terms of several metrics: (a) order of convergence, (b) energy preservation, (c) velocity kinematic constraint drift, and (d) efficiency. The numerical experiments draw on a set of three mechanical systems: a rigid slider-crank, a slider-crank with a flexible body, and a seven body mechanism. The algorithms investigated show good performance in relation to the asymptotic behavior of the integration error and, with one exception, result in comparable CPU simulation times with a small premium being paid for enforcing the velocity kinematic constraints.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies—Part 1: Characterization and Prediction of the Kinematic Constraint Changes

1991 ◽  
Vol 113 (1) ◽  
pp. 70-76 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part 1. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforessen changes in topology. Part 2 presents the implementation of the characterizations into a simulation strategy and presents examples.

MARS — Its Tenth Anniversary of Operation and its Future

1980 ◽  
Vol 19 (03) ◽  
pp. 125-132
Author(s):  
G. S. Lodwick ◽  
C. R. Wickizer ◽  
E. Dickhaus
Keyword(s):  
Conceptual Development ◽  
Administrative Support ◽  
Final Section ◽  
Economic Benefits ◽  
Hospital Environment ◽  
Computer Scientist ◽  
University Of Missouri ◽  
Complete Bibliography ◽  
The University ◽  
Economic Considerations

The Missouri Automated Radiology System recently passed its tenth year of clinical operation at the University of Missouri. This article presents the views of a radiologist who has been instrumental in the conceptual development and administrative support of MARS for most of this period, an economist who evaluated MARS from 1972 to 1974 as part of her doctoral dissertation, and a computer scientist who has worked for two years in the development of a Standard MUMPS version of MARS. The first section provides a historical perspective. The second deals with economic considerations of the present MARS system, and suggests those improvements which offer the greatest economic benefits. The final section discusses the new approaches employed in the latest version of MARS, as well as areas for further application in the overall radiology and hospital environment. A complete bibliography on MARS is provided for further reading.

Introduction

2018 ◽  
Author(s):  
Peter Hopkins
Keyword(s):  
Final Section ◽  
Short Note ◽  
Current Situation ◽  
Research Projects ◽  
Everyday Lives ◽  
Early Settlement ◽  
The Everyday ◽  
Initial Research

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.

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