A Two-Point Boundary-Value Approach for Planning Manipulation Tasks

Song, Peng; Kumar, Vijay; Pang, Jong-Shi

doi:10.15607/rss.2005.i.017

Cited by 6 publications

(8 citation statements)

References 21 publications

(33 reference statements)

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“…Combining Proposition 3 and Lemmas 4 and 5, we obtain the following result, which brings us one step closer to the main existence and uniqueness for the discretetime boundary value problem. (q h,0 , ν h,0 , δ h,0 ), a unique discrete-time trajectory (14) exists satisfying (16) for every j = 0, 1, . .…”

Section: Preliminary Analysismentioning

confidence: 99%

“…positive scalarsμ, h 0 , and ψ x exist such that for every vector μ > 0 satisfying max and every pair (q h,0 , δ h,0 ) satisfying (12), a discrete-time trajectory (14) exists satisfying (16) for every j = 0, 1, . .…”

Section: Boundary-value Analysis Proposition 7 Allows Us To Employ Tmentioning

confidence: 99%

“…This paper addresses neither the numerical implementation nor the order of convergence of the time-stepping methods. For details on practical implementation and computational results, see [16,18]; see also [4] for a part-insertion application of a boundary-value planar rigid-body problem. The order of convergence analysis for frictional contact problems is a very difficult topic, even for initial-value problems.…”

mentioning

confidence: 99%

“…The numerical experiments in [17] employed the complementarity solver path [7], which produced satisfactory results. Despite such practical experience, which is somewhat limited, there is an urgent need for the development of some robust algorithms for solving (16) along with a rigorous proof of applicability.…”

mentioning

confidence: 99%

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Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems

Pang¹,

Kumar²,

Song³

2005

SIAM J. Numer. Anal.

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Beginning with a proof of the existence of a discrete-time trajectory, this paper establishes the convergence of a time-stepping method for solving continuous-time, boundary-value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions. Our investigation complements the analysis of the initial-value rigid-body model with one frictional contact encountering inelastic impacts by Stewart [Arch. Ration. Mech. Anal., 145 (1998), pp. 215-260] and the recent analysis by Anitescu [Optimization-Based Simulation for Nonsmooth Rigid Multibody Dynamics, Argonne National Laboratory, Argonne, IL, 2004] using the framework of measure differential inclusions. In contrast to the measure-theoretic approach of these authors, we follow a differential variational approach and address a broader class of problems with multiple elastic or inelastic impacts. Applicable to both initial and affine boundary-value problems, our main convergence result pertains to the case where the compliance in the normal direction is decoupled from the compliance in the tangential directions and where the friction coefficients are sufficiently small. Disciplines Engineering | Mechanical Engineering Comments

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Section: Preliminary Analysismentioning

confidence: 99%

Section: Boundary-value Analysis Proposition 7 Allows Us To Employ Tmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems

Pang¹,

Kumar²,

Song³

2005

SIAM J. Numer. Anal.

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“…Not surprisingly, many of the important problems that could yield to closed-form analysis have been solved and studied thoroughly. Problems characterized by intermittent contact is one particularly important type of robotics problems for which research must rely on simulation techniques [1][2][3][4][5][6]. Evidence of the need for simulation is the recent trend of robotics researchers studying grasping, assembly, and dexterous manipulation problems using Open Dynamic Engine (ODE) [7].…”

Section: Introductionmentioning

confidence: 99%

Sources of Error in a Simulation of Rigid Parts on a Vibrating Rigid Plate

Berard

Nguyen

Anderson

et al. 2010

Journal of Computational and Nonlinear Dynamics

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We present a simulation study of an important rigid-body contact problem. The system in question is composed of a rigid plate and a single rigid body (or particle). The plate follows a prescribed periodic motion of small amplitude and high frequency, such that the net force applied to the part appears to be from a time-independent, position-dependent velocity field in the plane of the plate. Theoretical results obtained by Vose et al. were found to be in good agreement with simulation results obtained with the Stewart–Trinkle time-stepping method. In addition, simulations were found to agree with the qualitative experimental results of Vose et al. After such verification of the simulation method, additional numerical studies were done that would have been impossible to carry out analytically. Specifically, we were able to demonstrate the convergence of the method with decreasing step size (as predicted theoretically by Stewart). Further analytical and numerical studies will be carried out in the future to develop and select robust simulation methods that best satisfy the speed and accuracy requirements of different applications. With the accuracy of our time-stepper verified for this system, we were able to study the inverse problem of designing new plate motions to generate a desired part motion. This is done through an optimization framework, where a simulation of the part interacting with the plate (including the full dynamics of the system) is performed, and based on the results of the simulation the motion of the plate is modified. The learned (by simulation) plate motion was experimentally run on the device, and without any tuning (of the simulation parameters or device parameters) our learned plate motion produced the desired part motion.

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Design, modeling, and constraint-compliant control of an autonomous morphing surface for omnidirectional object conveyance

2021

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In this paper, we conceptualize, analyze, and assemble a prototype adaptive surface system capable of morphing its geometric configuration using an array of linear actuators to impose omnidirectional movement of objects that lie on the surface. The principal focus and contribution of this paper is the derivation of feedback control protocols–for regulating the actuators’ length in order to accomplish the object conveyance task–that scale with the number of actuators and the nonlinear kinematic constraints of the morphing surface. Simulations and experimental results demonstrate the advantages of distributed manipulation over static-shaped feeders.

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A Two-Point Boundary-Value Approach for Planning Manipulation Tasks

Cited by 6 publications

References 21 publications

Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems

Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems

Sources of Error in a Simulation of Rigid Parts on a Vibrating Rigid Plate

Design, modeling, and constraint-compliant control of an autonomous morphing surface for omnidirectional object conveyance

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