A complementarity approach to a quasistatic multi-rigid-body contact problem

Pang, Jong-Shi; Trinkle, Jeff; Lo, Grace

doi:10.1007/bf00249053

Cited by 30 publications

(28 citation statements)

References 5 publications

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“…Most (Mason 1986;Peshkin and Sanderson 1988;Alexander and Maddocks 1993;Lynch and Mason 1996) have investigated the planar motion of a sliding workpiece moving in response to a position controlled "pusher" (e.g., fence or finger). Planar quasi-static motion of a body interacting with multiple contacts has also been studied (Trinkle and Zeng 1995;Pang, Trinkle, and Lo 1996). These papers focus on effective means of considering the finite number of possible motion responses (slide, roll, separate) at each of the multiple points of contact for the case where a rigid body is acted on by known external forces and torques when contacting constraining bodies that are motionor effort-controlled.…”

Section: Rigid Body Mechanicsmentioning

confidence: 99%

Spatial Compliant Motion of a Rigid Body Constrained by a Frictional Contact

Huang

Schimmels

2003

int j robot res

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In this paper, we study the quasi-static motion of an elastically suspended, unilaterally constrained rigid body. The motion of the rigid body is determined, in part, by the position controlled motion of its support base and by the behavior of the elastic suspension that couples the part to the support. The motion is also determined, in part, by contact with a frictional surface that both couples the rigid body to the unilateral constraint and generates a friction force. The unknown friction force, however, is determined in part by the unknown direction of the rigid-body motion. We derive an analytically solvable set of equations that simultaneously determines both the friction force and the resulting rigid-body motion.We also address the issues of whether a solution to these equations exists and whether the obtained solution is unique. We show that, for any passive compliant system in which the nominal motion imposes contact, a solution to the set of motion equations always exists. We also show that, for any passive system with an upper bounded friction coefficient, the solution is unique. Two sufficient conditions that guarantee the uniqueness of the solution are presented.

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Section: Rigid Body Mechanicsmentioning

confidence: 99%

Spatial Compliant Motion of a Rigid Body Constrained by a Frictional Contact

Huang

Schimmels

2003

int j robot res

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“…The approaches from the rigid body dynamics literature are perhaps more applicable to these problems, as they concern themselves with moving bodies and therefore must include some treatment of the MDP. However, due to the difficulty in solving the resulting problems [35,2,23] they are either computationally infeasible [50,37] or make approximating assumptions [51,45,3,4,48,49,15,43,38] in order to allow for real-time simulation. Others make no convergence guarantees [5,6,18] or are only guaranteed to converge for small friction coefficients [46].…”

Section: Virtual Motionmentioning

confidence: 99%

Accurate Energetic Constraints for Passive Grasp Stability Analysis

Haas-Heger

Ciocarlie

2020

IEEE Trans. Robot.

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Passive reaction effects in grasp stability analysis occur when the contact forces and joint torques applied by a grasp change in response to external disturbances applied to the grasped object. For example, nonbackdrivable actuators (e.g. highly geared servos) will passively resist external disturbances without an actively applied command; for numerous robot hands using such motors, these effects can be highly beneficial as they increase grasp resistance without requiring active control. We introduce a grasp stability analysis method that can model these effects, and, for a given grasp, distinguish between disturbances that will be passively resisted and those that will not. We find that, in order to achieve this, the grasp model must include accurate energetic constraints. One way to achieve this is to consider the Maximum Dissipation Principle (MDP), a part of the Coulomb friction model that is rarely used in grasp stability analysis. However, the MDP constraints are non-convex, and difficult to solve efficiently. We thus introduce a convex relaxation method, along with an algorithm that successively refines this relaxation locally in order to obtain solutions to arbitrary accuracy efficiently. Our resulting algorithm can determine if a grasp is passively stable, solve for equilibrium contact forces and compute optimal actuator commands for stability. Its implementation is publicly available as part of the open-source GraspIt! simulator.

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“…Mathematical programming techniques used for solving the latter problems include linear complementarity methods, sequential quadratic programming algorithms, Newton methods for generalized equations, and B-differentiable equations. One recent area of applications of frictional contact problems occurs in robotics research; see [11,12,151,153,161,177,198] and [145, section 14.1].…”

Section: Contact Mechanics Problemsmentioning

confidence: 99%

Engineering and Economic Applications of Complementarity Problems

Ferris¹,

1997

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Abstract. This paper gives an extensive documentation of applications of finite-dimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.

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A complementarity approach to a quasistatic multi-rigid-body contact problem

Cited by 30 publications

References 5 publications

Spatial Compliant Motion of a Rigid Body Constrained by a Frictional Contact

Spatial Compliant Motion of a Rigid Body Constrained by a Frictional Contact

Accurate Energetic Constraints for Passive Grasp Stability Analysis

Engineering and Economic Applications of Complementarity Problems

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