Contact Status Optimization of Multibody Dynamic Systems Using Dual Variable Transformation

2014 ◽  
Author(s):  
Carlotta Mummolo ◽  
Luigi Mangialardi ◽  
Joo H. Kim
Keyword(s):  
Contact Force ◽  
Dynamic Systems ◽  
Contact Point ◽  
A Priori ◽  
Iterative Solution ◽  
Contact Forces ◽  
Analytical Relationship ◽  
Sqp Algorithm ◽  
Predictive Algorithm ◽  
Classical Formulation

Generating the motion of redundant systems under general constraints within an optimization framework is a problem not yet solved, as there is, so far, a lack of completely predictive methods that concurrently solve for the optimal trajectory and the contact status induced by the given constraints. A novel approach for optimal motion planning of multibody systems with contacts is developed, based on a Sequential Quadratic Programming (SQP) algorithm for Nonlinear Programming (NLP). The objective is to detect and optimize the contact status and the relative contact force within the optimization sequential problem, while simultaneously optimizing a trajectory. The novelty is to seek for the contact information within the iterative solution of the SQP algorithm and use this information to sequentially update the resulting contact force in the system’s dynamic model. This is possible by looking at the analytical relationship between the dual variables resulting from the constrained NLP and the Lagrange multipliers that represent the contact forces in the classical formulation of constrained dynamic systems. This approach will result in a fully predictive algorithm that doesn’t require any a priori knowledge on the contact status (e.g., time of contact, point of contact, etc.) or contact force magnitude. A preliminary formulation is presented, as well as numerical experiments on simple planar manipulators, as demonstration of concepts.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Solution Process ◽  
Solution Space ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components ◽  
The Relationship

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them for simplifying the solution process, and then the static equilibrium equations are applied to find certain contact force components and the relationship between the others. Using the friction cone equation at each foot contact point and the known contact force components, the problem is transformed into a geometrical one to find the ranges of contact forces and the relationship between them that satisfy the friction constraint. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the whole solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Optimal Contact Force Distribution for Multi-Limbed Robots

2005 ◽  
Vol 128 (3) ◽  
pp. 566-573 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
New Strategy ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The incremental strategy of opening up the friction cones is aided by using the “force space graph” which indicates where the solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Pre-Optimization of Asymmetrical Underplatform Dampers

2016 ◽  
Author(s):  
Chiara Gastaldi ◽  
Muzio M. Gola
Keyword(s):  
Contact Surface ◽  
Contact Stiffness ◽  
Contact Point ◽  
A Priori ◽  
Element Model ◽  
Contact Forces ◽  
Friction Coefficients ◽  
Lift Off ◽  
Lower Limits ◽  
Underplatform Damper

The numerical coupled optimization of an underplatform damper is the exploration of its dynamics through a finite element model which includes both the damper and the blades. This is an effective approach if the initial damper mass and geometry have been previously selected in such a way that those parameter combinations leading to undesirable damper behavior (i.e. contact point lift-off, jamming, excessive contact forces) are ruled out a priori. This can be obtained through a pre-optimization where, after choosing the damper type the following main steps are followed: 1. ensure that damper jamming is avoided through an appropriate choice of platform angles, in function of the friction coefficients; 2. ensure that damper lift-off is avoided through an appropriate choice of the shape and position of the damper-platform flat contact surface and the position of the damper mass center; 3. set upper and lower limits to the value of damper-platform contact forces (as a multiple of the damper centrifugal force), the first being related to friction and wear problems, the second to the very existence of bilateral contacts; 4. check the model, and in particular the values of friction coefficients and contact stiffness, against experimental results. Once the above knowledge concerning the most desirable damper shape has been gathered an effective coupled-optimization can safely be performed. This is done by finding the most effective match between the damper size/mass and the bladed disk through a non-linear dynamic calculation (not examined in this paper). The outcome of both the pre-optimization and the coupled optimization are strongly dependent on the assumed values of friction coefficients, which depend on the contact surface type (then, different for the left and right side of the damper) and the contact pressure. The paper capitalizes on already developed tools, presented in previous ASME papers, such as the test rig developed by the AERMEC lab to draw the appropriate values of contact parameters, the numerical model representing the stand-alone dynamics of the damper between the platforms and the automatic random sampling tuning procedure. The purpose of the paper is to illustrate the procedure through the analysis of a family of rigid bar dampers with a curved-flat cross section.

Visualization of the Contact Force Solution Space for Multi-Limbed Robots

2005 ◽  
Vol 128 (1) ◽  
pp. 295-302 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Solution Space ◽  
Entire Solution ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them, and then the static equilibrium equations are applied. Using the friction cone equation at each foot contact point, the problem is then transformed into a geometrical one. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the entire solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Nonintrusive Measurement of Contact Forces During Vibration Dominated Impacts

2004 ◽  
Vol 126 (3) ◽  
pp. 489-497 ◽  
Author(s):  
Satwinder Jit Singh ◽  
Anindya Chatterjee
Keyword(s):  
Contact Force ◽  
Tikhonov Regularization ◽  
Strain Gauge ◽  
Initial Conditions ◽  
Contact Point ◽  
Electrical Contact ◽  
Contact Forces ◽  
Force Estimation ◽  
Contact Duration ◽  
Gauge Data

Impact force estimation is done indirectly through, e.g., strain measurements away from the contact point, because inserting a force transducer between the contacting objects changes the force. Most prior contact force measurements involved a single contact interval. Here we study transverse impacts of a slender beam and a clamped-free plate; contact occurs more than once within one impact. Strain gauge data, electrical contact detection, and a dynamic model of the beam are used to estimate the contact force. The problem of force estimation from strain gauge data is ill-posed, and Tikhonov regularization fails initially. A reduced-order model is then developed using symmetry, and better initial conditions are estimated using a Kalman filter. Subsequently, Tikhonov regularization gives excellent force estimates, empirically supported by the contact duration measurements. Two other methods that explicitly use the contact duration measurements are also given. The first uses Tikhonov regularization within each contact interval, followed by Kalman filtering during noncontact to get initial conditions for the next contact. The second uses truncated Fourier sine series in each contact interval and is, computationally, the simplest. All three methods provide consistent force estimates. Our work complements recent work by Inoue and coworkers where the impulse response of the colliding object was measured separately using a Hopkinson bar, and electrical contact was not monitored.

scholarly journals A Study on the Effect of the Contact Point and the Contact Force of a Glass Fiber under End-Face Polishing Process

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Ying-Chien Tsai ◽  
Guang-Miao Huang ◽  
Shin-Wei Cheng ◽  
Cheng-An Hsu ◽  
Innchyn Her
Keyword(s):  
Mathematical Model ◽  
Glass Fiber ◽  
Contact Force ◽  
Contact Point ◽  
Coupling Efficiency ◽  
Single Mode ◽  
Contact Forces ◽  
Initial Contact ◽  
Fiber Core ◽  
The Mathematical Model

The offset between the center lines of the polished end-face and the fiber core has a significant effect on coupling efficiency. The initial contact point and the contact force are two of the most important parameters that induce the offset. This study proposes an image assistant method to find the initial contact point and a mathematical model to estimate the contact force when fabricating the double-variable-curvature end-face of single mode glass fiber. The repeatability of finding the initial contact point via the vision assistant program is 0.3 μm. Based on the assumption of a large deflection, a mathematical model is developed to study the relationship between the contact force and the displacement of the lapping film. In order to verify the feasibility of the mathematical model, experiments, as well as DEFORM simulations, are carried out. The results show that the contact forces are alomst linearly proportional to the feed amounts of the lapping film and the errors are less than 9%. By using the method developed in this study, the offset between the grinding end-face and the center line of the fiber core is within 0.15 to 0.35 μm.

scholarly journals Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement

2022 ◽  
Vol 43 (1) ◽  
pp. 93-112
Author(s):  
Kaiming Zhang ◽  
Xudong Zheng ◽  
Zhang Chen ◽  
Bin Liang ◽  
Tianshu Wang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Friction Force ◽  
Contact Force ◽  
Contact Point ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Force Model ◽  
Lagrange Equations ◽  
Stick Slip ◽  
Normal Contact

AbstractThe non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

A Contact Force Solution for Non-Colliding Contact Dynamics Simulation

2006 ◽  
Author(s):  
Inna Sharf ◽  
Yuning Zhang
Keyword(s):  
Rigid Body ◽  
Contact Force ◽  
Contact Point ◽  
Closed Form Solution ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Friction Forces ◽  
Contact Points

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop a novel approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for three test cases: 1) a thin rod sliding down a stationary wedge; 2) a cube rotating off the stationary wedge under application of an external moment and 3) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the proposed formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

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