Nonlinear control of planar multibody systems in shape space

Sreenath, N.

doi:10.1007/bf02134010

Cited by 37 publications

(21 citation statements)

References 17 publications

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“…(12) and (14) in section 2.2 with Eqs. (18) and (19) in section 2.3. We have seen in section 2.3 that these two systems have structurally identical kinematical equations and constraints but the nature of their constraints are different.…”

Section: Kmentioning

confidence: 99%

“…An easier way out is to test the integrability of the constraint imposed by the pseudoinverse control. 18 We can use Eqs. (7) and (8) to test the integrability of the pseudoinverse constraint In Eq.(40).…”

Section: An Ordinarily Redundant Terrestrial Manipulatormentioning

confidence: 99%

“…While the problem of reorienting a space multibody system using internal motion has been studied by a number of researchers 110]1, [11], [131, [18], 1211, [231, etc., an important problem that has not been addressed so far is the repeatability problem in space manipulators. The motion of the end-effector of a space manipulator is related to the joint motions through the "generalized Jacobian" 119] by eliminating the dependence of the end-effector motion on the chaunge of orientation of the space vehicle.…”

Section: Introductionmentioning

confidence: 99%

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Repeatability in Redundant Manipulator Systems

Mukherjee¹

1994

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Approved for public release; distribution is unlimited Nonholonomic mechanical system, motion planning, configuration space, I repeatability, pseudoinverse control, free-flying space manipulator, holonomic loops A•srrAcr (Continue on reverse i necessary and identify by block number)Terrestrial manipulators with more DOF than the dimension of the workspace and space manipulators with as many manipulator DOF as the dimension of the workspace are both redundant systems. An interesting problem of such redundant systems has been the repeatability problem due to the presence of nonholonomic constraints. We show in this paper, contrary to the existing belief, that integrability of the nonholonomic constraints is not a necessary condition for the repeatability of the configuration variables. There exist certain trajectories in the independent configuration variable space that are like "holonomic loops! along which the redundant manipulators exhibit repeatable motion. In this paper we present a simple method based on optimization techniques for designing repeatable trajectories for free-flying space manipulators and terrestrial manipulators under pseudoinverse control. Terrestrial manipulators with more dof than the dimension of the workspace and space manipulators with as many manipulator dof as the dimension of the workspace are both redundant systems. An interesting problem of such redundant systems has been the repeatability problem due to the presence of nonholonomic constraints. We show in this paper, contrary to the existing belief, that integrability of the nonholonomic constraints is not a necessary condition for the repeatability of the configuration variables. There exist certain trajectories in the independent configuration variable space that are like "holonomic loops" along which the redundant manipulators exhibit repeatable motion. In this paper we present a simple method based on optimization techniques for designing repeatable trajectories for free-flying space manipulators and terrestrial redundant manipulators under pseudoinverse control.

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Section: Kmentioning

confidence: 99%

Section: An Ordinarily Redundant Terrestrial Manipulatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Repeatability in Redundant Manipulator Systems

Mukherjee¹

1994

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“…We call them first-order systems according to (Murray et al [1994]), though they are also called differently (Khaneja and Brockett [1999]). Attitude control of 3-D spacecraft using shape changes (Sreenath [1992]) is known as a typical example of first-order systems. The author also proposed a new actual example of this class, called trident snake robot (Ishikawa [2004]), which is a wheeled planar mobile robot with three snake-like branches.…”

Section: Introductionmentioning

confidence: 99%

Switched Feedback Control for a class of First-order Nonholonomic Driftless Systems

Ishikawa

2008

IFAC Proceedings Volumes

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This paper is concerned with stabilizing feedback control for a class of nonholonomic driftless systems, whose controllability Lie algebra rank condition is satisfied by up to firstorder Lie brackets. We propose a switched feedback law which drives all the initial states to the origin with bounded control inputs (as opposed unbounded, division-by-zero-type discontinuous control). The discontinuity of the feedback law takes place on a subspace defined by the 'parallelism' condition for the base and the fiber vectors in R 3 (or simply q × φ = 0 ). We also show that the complement of this discontinuity region is homotopic to SO(3) which is also isomorphic to S 2 × S. The proposed control law is examined by numerical simulations.

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“…The joints are controlled by internal (angular momentum preserving) actuators, e.g., by direct drive motors. A number of control problems for a multi[ink with zero angular momentum has been considered in the literature; see, e.g., [I]-[3], [ii], [15], [17]- [20], [22]. The interest in these problems has been motivated, in part, by space robotics applications [1]- [3], springboard diver dynamics [4], [8], and the falling cat phenomenon [7], [16].…”

mentioning

confidence: 99%

New results on control of multibody systems which conserve angular momentum

Kolmanovsky

McClamroch

Coppola

1995

Journal of Dynamical and Control Systems

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A planar system of rigid bodies interconnected by one degree of freedom rotational joints is considered. This multibody system is referred to as a multilink, and the rigid bodies are referred to as links. The angular momentum of the multilink is conserved but is not necessarily zero. We show that if the number of links is at least four, then periodic joint motions can make the absolute orientation of a specified base link track exactly a specified function of time whose time derivative is periodic. This result on the use of periodic joint motions for orientation tracking extends previous work [15], [20], [22] on using periodic joint motions for rest-to-rest reorientation. It has interesting physical consequences. Specifically, in the case of non-zero angular momentum periodic joint motions can maintain the orientation of the base link constant. In the case of zero angular momentum periodic joint motions can change the orientation of the base link at a specified angular rate. We also demonstrate that if the multilink consists of at least three links, then for any value of the angular momentum joint motions can reorient the multilink arbitrarily over an arbitrary time interval. This result extends similar results in [15] for zero angular momentum and in [20] that apply for nonzero angular momentum but not for an arbitrary time interval. In terms of their control-theoretic aspects, the problems treated in the paper can be viewed as controllability problems for a class of nonlinear control system with time-dependent drift.

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Nonlinear control of planar multibody systems in shape space

Cited by 37 publications

References 17 publications

Repeatability in Redundant Manipulator Systems

Repeatability in Redundant Manipulator Systems

Switched Feedback Control for a class of First-order Nonholonomic Driftless Systems

New results on control of multibody systems which conserve angular momentum

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