Rolling Constraints Research Articles

Motion Planning for Rolling-Based Locomotion

The basic motivation of this paper is to study locomotion on a hemisphere. To understand the problem we resort to a simplified quasi-static model in which the locomotion object is represented by a mass point. In this formulation, the driving principle is based on controlling the position of the center of mass of the object, exploiting non-holonomic rolling constraint to propel the hemisphere. The principle is tested under simulation using two motion planning algorithms. The simulation results show the possibility of steering the loocmotion system to the desired configurations by moving the center of mass through multiple generalized figure eights on the main hemisphere plane.

Computational Intelligence-Based Process Optimization for Tandem Cold Rolling

The requirements for the manufacturers of steel have been increased in many respects in recent years. Harsh competition among manufacturers demands a continuous reduction of production costs and improvement of product quality. The work presented herein describes maximizing rolling mill throughput and minimizing processing costs and crop losses by computational intelligence-based process modeling and optimization. In this article, an intelligent searching mechanism is introduced to optimize the rolling schedule by assessing rolling constraints and the combined cost function of tension, shape, and power distribution. The optimization results have been compared with current rolling practices based on empirical models. It is shown that the proposed model can significantly reduce the power distribution cost, maximize the safe level of strip tension, and obtain good strip shape. The proposed model is generic for complex engineering problem optimization, and is capable of multiple-objective problem solving.

The Pseudo-Rigid Rolling Coin

A pseudo-rigid coin is a thin disk that can deform only to the extent of undergoing an arbitrary affine deformation in its own plane. The coupling of the classical rolling problem with this deformability, albeit limited, may shed light on such phenomena as the production of noise by a twirling dish. From the point of view of analytical dynamics, one of the interesting features of this problem is that the rolling constraint turns out to be nonholonomic even in the case of motion on a straight line in a vertical plane. After the analytical formulation of the general problem, explicit solutions are obtained for special shape-preserving motions. For more general motions, numerical studies are carried out for various initial conditions.

Supersymmetric standard model of inflation with extra dimensions

We embed the supersymmetric standard model of hybrid inflation based on the next-to-minimal superpotential term $\ensuremath{\lambda}{\mathrm{NH}}_{u}{H}_{d}$ supplemented by an inflaton term $\ensuremath{\kappa}\ensuremath{\varphi}{N}^{2}$ into an extra-dimensional framework, in which all the Higgs fields and singlets live in the bulk, while all the matter fields live on the brane. All the parameters of the effective 4D model can then be naturally understood in terms of a fundamental (``string'') scale ${M}_{*}\ensuremath{\sim}{10}^{13}\mathrm{GeV}$ and a brane supersymmetry breaking scale ${10}^{8}\mathrm{GeV},$ of the same order as the height of the inflaton potential during inflation. In particular, the very small Yukawa couplings $\ensuremath{\lambda}\ensuremath{\sim}\ensuremath{\kappa}\ensuremath{\sim}{10}^{\ensuremath{-}10},$ necessary for the model to solve the strong CP problem and to generate the correct effective $\ensuremath{\mu}$ term after inflation, can be naturally understood in terms of volume suppression factors. The brane scalar masses are naturally of order a TeV while the bulk inflaton mass is naturally in the MeV range sufficient to satisfy the slow roll constraints. Curvature perturbations are generated after inflation from the isocurvature perturbations of the supersymmetric Higgs field as discussed in a companion paper.

Monte Carlo reconstruction of the inflationary potential

We present Monte Carlo reconstruction, a new method for ``inverting'' observational data to constrain the form of the scalar field potential responsible for inflation. This stochastic technique is based on the flow equation formalism and has distinct advantages over reconstruction methods based on a Taylor expansion of the potential. The primary ansatz required for Monte Carlo reconstruction is simply that inflation is driven by a single scalar field. We also require a very mild slow roll constraint, which can be made arbitrarily weak since Monte Carlo reconstruction is implemented at arbitrary order in the slow roll expansion. While our method cannot evade fundamental limits on the accuracy of reconstruction, it can be simply and consistently applied to poor data sets, and it takes advantage of the attractor properties of single-field inflation models to constrain the potential outside the small region directly probed by observations. We show examples of Monte Carlo reconstruction for data sets similar to that expected from the Planck satellite, and for a hypothetical measurement with a factor of five better parameter discrimination than the Planck satellite.

Kinematic Creep in a Continuously Variable Transmission: Traction Drive Mechanics for Cobots

Two continuously variable transmissions are examined, one that relates a pair of linear speeds and another that relates a pair of angular speeds. These devices are elemental in the design of cobots, a new class of robot that creates virtual guiding surfaces to aid a human operator in assembly tasks. Both of these transmissions are traction drive mechanisms that rely on the support of either lateral or longitudinal forces across rolling contacts with spin. When a rolling contact between elastic bodies or even between rigid bodies in spin is called upon to transmit a tractive force, kinematic creep develops, expressing a departure from the intended rolling constraint. Creep in turn gives rise to nonideal properties in a cobot’s virtual guiding surfaces. This paper develops simple models of the two transmissions by expressing the relative velocity field in the contact patch between rolling bodies in terms of creep and spin. Coulomb friction laws are applied in a quasi-static analysis to produce complete force-motion models. These models may be used to evaluate a cobot’s ability to support forces against its virtual guiding surfaces.

Toward a heuristic optimum design of rolling schedules for tandem cold rolling mills

Scheduling for tandem cold mills refers to the determination of inter-stand gauges, tensions and speeds of a specified product. Optimal schedules should result in maximized throughput and minimized operating cost. This paper presents a genetic algorithm based optimization procedure for the scheduling of tandem cold rolling mills. The optimization procedure initiates searching from a logical staring point — an empirical rolling schedule — and ends with an optimum cost. Cost functions are constructed to heuristically direct the genetic algorithm’s searching, based on the consideration of power distribution, tension, strip flatness and rolling constraints. Numerical experiments have shown that the proposed method is more promising than those based on semi-empirical formulae. The results generated from a case study show that the proposed approach could significantly improve empirically derived settings for the tandem cold rolling mills.

A unified approach to non-holonomic dynamics

Dynamical problems subject to non-linear non-holonomic constraints are analyzed using the differential variational principles of Jourdain (JVP) and Gauss (GVP). In contrast with linear non-holonomic constraints which arise from passive contact or rolling constraints, non-linear non-holonomic constraints (NNHC) arise in problems where the constraints are actively imposed, such as control or servo-constraints, consideration of some first integrals as kinetic side conditions, or mathematical constraints without regard to their physical realizability. To date, such problems have been treated by various ad hoc and unrelated methods in a fragmented manner, without a unifying idea running through the various methods of approach. In the present paper, it is shown that by applying the JVP to velocity constraints, and the GVP to acceleration constraints, dynamical problems subject to NNHC can be handled in a uniform way. Both the method of constraint embedding (elimination of variations) and constraint adjoining (use of Lagrange multipliers) are used in analyzing the behavior of the dynamical system subject to NNHC.

On the Modeling of Friction and Rolling in Flexible Multi-Body Systems

This paper is concerned with the dynamic analysis of flexible, nonlinear multi-body systems undergoing contact involving friction and rolling. A continuous friction law is used to model the friction forces between contacting bodies. This avoids the numerical problems associated with the discontinuity inherent to Coulomb's friction law and eliminates the need for different sets of equations modeling sliding and rolling as distinct phenomena. On the other hand, continuous friction laws eliminate specific physical phenomena implied by Coulomb's friction law. The condition of vanishing relative velocity between two contacting bodies is not possible: sticking or rolling are replaced by creeping with a small relative velocity. Discrete events such as transition from slipping to rolling or rolling to slipping are eliminated, together with the high frequency phenomena they are likely to cause. The computational issues associated with the continuous friction law and with the enforcement of the non-holonomic rolling constraint are addressed in this paper. This work is developed within the framework of energy preserving and decaying time integration schemes that provide unconditional stability for nonlinear, flexible multi-body systems undergoing contact involving friction and rolling.

An Active Sensing-based Control Algorithm for the Scrollic Gripper

This paper proposes an algorithm for the scrollic (synchronously closing with rolling constraints) gripper based on active sensing about the displacement of its joints, in order to control the trajectory of objects grasped outside the workspace. The gripper has fingers composed of two cylinders in parallel, the translation and rotation of which are independently driven. This characteristic gives a dynamic decoupled behavior to the gripper, and makes it compliant to open during a close motion, or to rotate against the actuated direction, when forced by the inwards movement of the object. The algorithm presents a high level of tolerance concerning uncertainties about the object's position, weight and shape. The kinematics, design concept and control algorithm of the gripper are discussed in detail.

The energy-momentum method for the stability of non-holonomic systems

In this paper, we analyze the stability of relative equilibria of non-holonomic systems (that is, mechanical systems with non-integrable constraints such as rolling constraints). In the absence of external dissipation, such systems conserve energy, but nonetheless can exhibit both neutrally stable and asymptotically stable, as well as linearly unstable relative equilibria. To carry out the stability analysis, we use a generalization of the energy-momentum method combined with the Lyapunov-Malkin theorem and the center manifold theorem. While this approach is consistent with the energy-momentum method for holonomic systems, it extends it in substantial ways. The theory is illustrated with several examples, including the rolling disk, the roller racer and the rattleback top

Control algorithm for the scrollic gripper based on intrinsic sensory information

—This paper proposes a control algorithm for the scrollic (synchronously closing with rolling constraints) gripper in order to control the trajectory of an object grasped outside the workspace toward the center of the gripper. The gripper has fingers composed of two cylinders in parallel, the translation and rotation of which are independently driven by direct-drive motors. The algorithm is based on sensory information about angular displacements of the cylindrical fingers, i.e. rollers. In fact, the object has direct affects on the rollers and the displacements are actively collected by rotary encoders. That is, contact sense not by tactile sensors but by intrinsic angular sensors is utilized. The algorithm yields the gripper to reduce a dynamic decoupled behavior and makes it compliant not only to close but also to open during a close motion. The algorithm presents a high level of tolerance concerning uncertainties about the object's position, orientation, size, shape and weight. The kinematics, the design concept and the control algorithm of the gripper are shown. Also, these are verified by grasp demonstrations.

２板間に挟まれて運動する剛球の位置制御

In this paper, we consider a position control of a rigid ball which is held between two parallel plates. The kinematic constraint of the system is rolling constraint which is a nonholonomic constraint. Thus, the system becomes drift-less nonlinear system. As Brockett showed, the equilibrium of such systems can not be stabilized with any continuous static state feedbacks even though the system is controllable in the sense of nonlinear. We applied a control strategy which is transforming this system into time-state control form by coordinate transformation and input transformation. By the simulation, we will show that we can stabilize both ball and the plate at the goal point.

Trajectory generation for the N-trailer problem using Goursat normal form

Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the design of a 'scrollic' gripper for firm 3D grasping

A parallel-jaw gripper is a very useful tool for robot manipulation tasks due to its simple mechanism and control. This fact limits the range of successful grasps it can undergo, and also makes it unfeasible under uncertainties. Thus, it is desirable to improve its dexterity and manipulability. In this paper, we propose a new design of a two-fingered parallel gripper that utilizes rolling at the contacts for object repositioning and reorientation, aimed at effective firm grasps. We name it the scrollic gripper, an acronym for synchronously closing with rolling constraints. At first, the background to utilize the rolling constraints is described. Then, grasping and manipulation of the gripper are discussed. In grasp acquisition, we propose a quality function for evaluating grasp stability. The sophisticated hardware and functioning for the scrollic gripper consist, basically, on implementation of an additional degree-of-freedom to the conventional parallel-jaw gripper, leading to grasp acquisition and secu...

NONLINEAR MODELING OF COMPLEX MECHANICAL SYSTEMS

This article provides an introduction to a technique for formulating nonlinear models of mechanical systems composed of interconnected and constrained rigid body systems such as those encountered in vehicle technology, biomechanics, spacecraft design and robotics. The approach is based on an algorithm developed by Kane to treat nonholonomic systems, for example systems with rolling constraints. The algorithm is interpreted geometrically in terms of tangent vectors to the instantaneous configuration manifold embedded in the space of nonconstrained motions for the system. The level and style of the presentation is intended to be understood by scientifically literate readers with minimal knowledge in mechanics beyond the introductory level. Examples also show how computer algebra can be used to reduce the effort required for treating complex systems. An annotated reference list, which includes a discussion of computer software, is also provided.

Control of Mechanical Systems With Rolling Constraints

There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified ap proach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system. We then dis cuss the input-output linearization and zero dynamics of the system. This approach is applied to the dynamic control of mo bile robots. Two types of control algorithms for mobile robots are investigated: trajectory tracking and path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotic input-output stability and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performance of trajectory-tracking and path-following algo rithms.

An analysis of angular momentum in the discus throw

Recent advances in computational technology have dramatically increased the use of muscle-driven simulation to study accelerations produced by muscles during gait. Accelerations computed from muscle-driven simulations are sensitive to the model used to represent contact between the foot and ground. A foot-ground contact model must be able to calculate ground reaction forces and moments that are consistent with experimentally measured ground reaction forces and moments. We show here that a rolling constraint can model foot-ground contact and reproduce measured ground reaction forces and moments in an induced acceleration analysis of muscle-driven simulations of walking, running, and crouch gait. We also illustrate that a point constraint and a weld constraint used to model foot-ground contact in previous studies produce inaccurate reaction moments and lead to contradictory interpretations of muscle function. To enable others to use and test these different constraint types (i.e., rolling, point, and weld constraints) we have included them as part of an induced acceleration analysis in OpenSim, a freely-available biomechanics simulation package.

Modular Mobile Robot Design

Decentralised kinematics and control for modular wheeled mobile robots are developed and the results of an implentaion are shown. The inverse kinematics is developed from basics theory of planar motion. The forward kinematics is solved by the use of a non-linear least squares estimator. The controller tracks deviations from the path and from the rigid body / rolling constraints

Motion of two rigid bodies with rolling constraint

The motion of two rigid bodies under rolling constraint is considered. In particular, the following two problems are addressed: (1) given the geometry of the rigid bodies, determine the existence of an admissible path between two contact configurations; and (2) assuming that an admissible path exists, find such a path. First, the configuration space of contact is defined, and the differential equations governing the rolling constraint are derived. Then, a generalized version of Frobenius's theorem, known as Chow's theorem, for determining the existence of motion is applied. Finally, an algorithm is proposed that generates a desired path with one of the objects being flat. Potential applications of this study include adjusting grasp configurations of a multifingered robot hand without slipping, contour following without dissipation or wear by the end-effector of a manipulator, and wheeled mobile robotics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>