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42
Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments
 International Journal of Robotics Research
, 1998
"... We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedo ..."
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Cited by 31 (14 self)
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We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedom of the part. The extra motion freedoms of the part are exhibited as rolling, slipping, and free flight.
Optimal Gait Selection for Nonholonomic Locomotion Systems
, 2000
"... This paper addresses the optimal control and selection of gaits in a class of nonholonomic locomotion systems that exhibit group symmetries. We study optimal gaits for the snakeboard, a representative example of this class of systems. We employ Lagrangian reduction techniques to simplify the optimal ..."
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Cited by 31 (8 self)
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This paper addresses the optimal control and selection of gaits in a class of nonholonomic locomotion systems that exhibit group symmetries. We study optimal gaits for the snakeboard, a representative example of this class of systems. We employ Lagrangian reduction techniques to simplify the optimal control problem and describe a general framework and an algorithm to obtain numerical solutions to this problem. This work employs optimal control techniques to study the optimality of gaits and issues involving gait transitions. The general framework provided in this paper can easily be applied to other examples of biological and robotic locomotion. KEY WORDSoptimal control, robotic locomotion, geometric mechanics, locomotive gaits 1.
Stability and drift of underwater vehicle dynamics: mechanical systems with rigid motion symmetry
 Physica D
, 1997
"... This paper develops the stability theory of relative equilibria for mechanical systems with symmetry. It is especially concerned with systems that have a noncompact symmetry group, such as the group of Euclidean motions, and with relative equilibria for such symmetry groups. For these systems with r ..."
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Cited by 27 (8 self)
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This paper develops the stability theory of relative equilibria for mechanical systems with symmetry. It is especially concerned with systems that have a noncompact symmetry group, such as the group of Euclidean motions, and with relative equilibria for such symmetry groups. For these systems with rigid motion symmetry, one gets stability but possibly with drift in certain rotational as well as translational directions. Motivated by questions on stability of underwater vehicle dynamics, it is of particular interest that, in some cases, we can allow the relative equilibria to have nongeneric values of their momentum. The results are proved by combining theorems of Patrick with the technique of reduction by stages. This theory is then applied to underwater vehicle dynamics. The stability of specific relative equilibria for the underwater vehicle is studied. For example, we find conditions for Liapunov stability of the steadily rising and possibly spinning, bottomheavy vehicle, which corresponds to a relative equilibrium with nongeneric momentum. The results of this paper should prove
Nonlinear Control of Mechanical Systems: A Riemannian Geometry Approach
, 1998
"... Nonlinear control of mechanical systems is a challenging discipline that lies at the intersection between control theory and geometric mechanics. This thesis sheds new light on this interplay while investigating motion control problems for Lagrangian systems. Both stability and motion planning aspec ..."
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Cited by 24 (0 self)
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Nonlinear control of mechanical systems is a challenging discipline that lies at the intersection between control theory and geometric mechanics. This thesis sheds new light on this interplay while investigating motion control problems for Lagrangian systems. Both stability and motion planning aspects are treated within a unified framework that accounts for a large class of devices such as robotic manipulators, autonomous vehicles and locomotion systems. One distinguishing feature of mechanical systems is the number of control forces. For systems with as many input forces as degrees of freedom, many control problems are tractable. One contribution of this thesis is a set of trajectory tracking controllers designed via the notions of configuration and velocity error. The proposed approach includes as special cases a variety of results on joint and workspace control of manipulators as well as on attitude and position control of vehicles. Whenever fewer input forces are available than deg...
Nonprehensile Robotic Manipulation: Controllability and Planning
, 1997
"... the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra ..."
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Cited by 23 (5 self)
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the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra actuators; the expectation derived from a good model can minimize sensing requirements. Despite this, most robot systems attempt to dominate or nullify task mechanics, rather than exploit them. There has been little e ort to understand the manipulation capabilities of even the simplest robots under more complete mechanics models. This thesis addresses that knowledge de cit by studying graspless or nonprehensile manipulation. Nonprehensile manipulation exploits task mechanics to achieve a goal state without grasping, allowing simple mechanisms to accomplish complex tasks. With nonprehensile manipulation, a robot can manipulate objects too large or heavy to be grasped and lifted, and a lowdegreeoffreedom robot can control more degreesoffreedom of an object by allowing relative motion between the object and the manipulator. Two key problems are determining controllability of and motion planning for
Nonlinear Control of Mechanical Systems: A Lagrangian Perspective
, 1997
"... . Recent advances in geometric mechanics, motivated in large part by applications in control theory, have introduced new tools for understanding and utilizing the structure present in mechanical systems. In particular, the use of geometric methods for analyzing Lagrangian systems with both symmetr ..."
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Cited by 22 (4 self)
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. Recent advances in geometric mechanics, motivated in large part by applications in control theory, have introduced new tools for understanding and utilizing the structure present in mechanical systems. In particular, the use of geometric methods for analyzing Lagrangian systems with both symmetries and nonintegrable (or nonholonomic) constraints has led to a unified formulation of the dynamics that has important implications for a wide class of mechanical control systems. This paper presents a survey of recent results in this area, focusing on the relationships between geometric phases, controllability, and curvature, and the role of trajectory generation in nonlinear controller synthesis. Examples are drawn from robotics and flight control systems, with an emphasis on motion control problems. Key Words. Geometric mechanics, nonlinear control, Lagrangian dynamics, motion control. 1. INTRODUCTION Mechanical systems form an important class of nonlinear control systems that h...
Optimal gaits for dynamic robotic locomotion
 International Journal of Robotic Research
, 2001
"... This paper addresses the optimal control and selection of gaits in a class of dynamic locomotion systems that exhibit group symmetries. We study nearoptimal gaits for an underwater eellike robot, though the tools and analysis can be applied more broadly to a large family of nonlinear control syste ..."
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Cited by 19 (2 self)
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This paper addresses the optimal control and selection of gaits in a class of dynamic locomotion systems that exhibit group symmetries. We study nearoptimal gaits for an underwater eellike robot, though the tools and analysis can be applied more broadly to a large family of nonlinear control systems with drift. The approximate solutions to the optimal control problem are found using a truncated basis of cyclic input functions. This generates feasible paths that approach the optimal one as the number of basis functions is increased. We describe an algorithm to obtain numerical solutions to this problem and present simulation results that demonstrate the types of solutions that can be achieved. Comparisons are made with experimental data using the REEL II robot platform. 1
Oscillations, SE(2)snakes and motion control
 In IEEE Conf. Decision and Control
, 1995
"... This paper is concerned with the problem of motion generation via cyclic variations in selected degrees of freedom (usually referred to as shape variables) in mechanical systems subject to nonholonomic constraints (here the classical one of a disk rolling without sliding on a at surface). In earlier ..."
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Cited by 16 (0 self)
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This paper is concerned with the problem of motion generation via cyclic variations in selected degrees of freedom (usually referred to as shape variables) in mechanical systems subject to nonholonomic constraints (here the classical one of a disk rolling without sliding on a at surface). In earlier work, we identi ed an interesting class of such problems arising in the setting of Lie groups, and investigated these under a hypothesis on constraints, that naturally led to a purely kinematic approach. In the present work, the hypothesis on constraints does not hold, and as a consequence, it is necessary to take into account certain dynamical phenomena. Speci cally we concern ourselves with the group SE(2) of rigid motions in the plane and a concrete mechanical realization dubbed the SE(2){snake. In a restricted version, it is also known as the Roller Racer (a patented toy). Based on the work of Bloch, Krishnaprasad, Marsden and Murray, one recognizes in the example of this paper a balance law called the momentum equation, which is a direct consequence of the interaction of the SE(2){symmetry of the problem with the constraints. The systematic use of this type of balance law results in certain structures in the example of this paper. We exploit these structures to demonstrate that the single shape freedom in this problem can be cyclically varied to produce a rich variety of motions of the SE(2){ snake. In their study of the Snakeboard, a patented modication of the skateboard that also admits the group SE(2) as a symmetry group, Lewis, Ostrowski, Burdick and Murray, exploited the same typeofbalance law as the one discussed here to generate motions. A key di erence however is that, in the presentpaper,we have only one control variable and thus controllability considerations become somewhat more delicate. In the present paper, we give a self{contained treatment of the geometry, mechanics and motion control of the Roller Racer. 1.
Computing Reduced Equations for Robotic Systems with Constraints and Symmetries
, 1998
"... : This paper develops easily computable methods for deriving the reduced equations for mechanical systems with Lie group symmetries. These types of systems occur frequently in robotics, and are found generically in robotic locomotion, wheeled mobile robots, and satellites or underwater vehicles with ..."
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Cited by 16 (0 self)
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: This paper develops easily computable methods for deriving the reduced equations for mechanical systems with Lie group symmetries. These types of systems occur frequently in robotics, and are found generically in robotic locomotion, wheeled mobile robots, and satellites or underwater vehicles with robotic arms. Results are presented for two important cases: the unconstrained case, for both body and spatial representations, and the constrained (mixed kinematic and dynamic) case. In each case, the dynamic equations for these nonholonomic mechanical systems are given, and illustrated by the appropriate calculations for an example system. A primary result of this paper is to show that the spectrum of possible constraints ranging from no constraints to fully constrained systems can be expressed within a single unifying principle for calculating the reduced equations. In this process, the structure of the reduced Lagrangian directly reveals two useful components in the reduction proces...
Gait Kinematics for a Serpentine Robot
 In Proc. IEEE Int. Conf. on Rob. and Autom
, 1996
"... : This paper considers the problem of serpentine, or snakelike, locomotion from the perspective of geometric mechanics. A particular model, which is similar to Hirose's Active Cord Mechanism (ACM), is analyzed. Using the kinematic constraints, we develop a connection, which describes the net motion ..."
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Cited by 14 (1 self)
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: This paper considers the problem of serpentine, or snakelike, locomotion from the perspective of geometric mechanics. A particular model, which is similar to Hirose's Active Cord Mechanism (ACM), is analyzed. Using the kinematic constraints, we develop a connection, which describes the net motion of the machine as a function of variations in the mechanism 's shape variables. We present simulation results demonstrating three types of locomotive gaits, one of which bears an obvious resemblance to the serpentine motion of a snake. We also show how these algorithms can be used to optimize certain inputs given the particular choice of physical parameters for a snake robot. 1. Introduction Most mobile robots are wheeled vehicles, since wheels provide the simplest means for robotic mobility. The assumption that these wheels do not slip provides nonholonomic kinematic constraints on a vehicle 's motion. These kinematic nonholonomic systems have been extensively studied in the literature. F...