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185
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 228 (25 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Flatness and defect of nonlinear systems: Introductory theory and examples
 International Journal of Control
, 1995
"... We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is ..."
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Cited by 173 (15 self)
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We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is measured by a nonnegative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems ’ standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of planar curves. The three nonflat examples, the simple, double and variable length pendulums, are borrowed from nonlinear physics. A high frequency control strategy is proposed such that the averaged systems become flat. ∗This work was partially supported by the G.R. “Automatique ” of the CNRS and by the D.R.E.D. of the “Ministère de l’Éducation Nationale”. 1 1
Geometric Phases And Robotic Locomotion
, 1994
"... . Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and wheele ..."
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Cited by 69 (3 self)
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. Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallel parking. In this paper we explore the use of tools from differential geometry to model and analyze this class of locomotion mechanisms in a unified way. In particular, we describe locomotion in terms of the geometric phase associated with a connection on a principal bundle, and address issues such as controllability and choice of gait. We also provide an introduction to the basic mathematical concepts which we require and apply the theory to numerous example systems. 1. Introduction The term "locomotion" refers to autonomous movement from place to place. Robotic locomotion employs a variety of mechanisms. Though most of today's mobile r...
Configuration Controllability of Simple Mechanical Control Systems
 SIAM Journal on Control and Optimization
, 1995
"... In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is also derived. ..."
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Cited by 69 (10 self)
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In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is also derived.
Nonholonomic Mechanics and Locomotion: The Snakeboard Example
 In Proc. IEEE Int. Conf. Robotics and Automation
, 1994
"... Analysis and simulations are performed for a simplified model of a commercially available variant of the skateboard, known as the Snakeboard 1 . Although the model exhibits basic gait patterns seen in a large number of locomotion problems, the analysis tools currently available do not apply to this ..."
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Cited by 59 (25 self)
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Analysis and simulations are performed for a simplified model of a commercially available variant of the skateboard, known as the Snakeboard 1 . Although the model exhibits basic gait patterns seen in a large number of locomotion problems, the analysis tools currently available do not apply to this problem. The difficulty lies primarily in the way in which the nonholonomic constraints enter into the system. As a first step towards understanding systems represented by our model we present the equations of motion and perform some controllability analysis for the snakeboard. We also perform numerical simulations of possible gait patterns which are characteristic of snakeboard locomotion. Introduction This paper investigates a simplified model of a commercially available derivative of a skateboard known as the Snakeboard . The Snakeboard (Figure 1) allows the rider to propel him/herself forward without having to make contact with the ground. This motion is roughly accomplished by coupl...
Trajectory Generation for the NTrailer Problem Using Goursat Normal Form
, 1995
"... In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the probl ..."
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Cited by 58 (9 self)
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In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the problem of rbxing a mobile robot WMI R trailers. We present an algorithm for finding a family of ~WIS~~~OM whicb will convert the system of rolling constraints on the wheels of the robot with n traiten into the GoaFapt canonical form..nRo of these transformations are studied in detail. The Gomt normal form for exterior diffemtial systems is dual to the socalled chainedform for vector fields that bas been studied previously. Consequently, we are able to give the state feedback law aad change o € e00rdinaW tovert the Ntrai4r system id0 chained form. Tllree metbods for for chainedform systems using shrosoidg and polynomiPls aa inputs are presented. The motion prpnnhag strategy Is therefore to the Ntrailer system into Gonrsat form, use this to lind the cboinedform coordinates, plan a path for the corresponding cimkdform system, and then transform the resalting traje.ctory back into the original coordinates. Simulations and h.ames of mode animations of the Ntnder system for parallel parking and backing into a loading dock using this strategy are included.
The Geometric Mechanics of Undulatory Robotic Locomotion
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1996
"... This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion problems have ..."
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Cited by 56 (15 self)
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This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion problems have a natural geometric interpretation as a connection on a principal fiber bundle. The properties of connections lead to simplified results for studying both dynamics and issues of controllability for locomotion systems. We demonstrate the utility of this approach using a novel "Snakeboard" and a multisegmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.
Motion Control of DriftFree, LeftInvariant Systems on Lie Groups
 IEEE Transactions on Automatic Control
, 1995
"... In this paper we address the constructive controllability problem for driftfree, leftinvariant systems on finitedimensional Lie groups with fewer controls than state dimension. We consider small (ffl) amplitude, lowfrequency, periodically timevarying controls and derive average solutions for sys ..."
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Cited by 52 (6 self)
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In this paper we address the constructive controllability problem for driftfree, leftinvariant systems on finitedimensional Lie groups with fewer controls than state dimension. We consider small (ffl) amplitude, lowfrequency, periodically timevarying controls and derive average solutions for system behavior. We show how the pthorder average formula can be used to construct openloop controls for pointtopoint maneuvering of systems that require up to (p \Gamma 1) iterations of Lie brackets to satisfy the Lie algebra controllability rank condition. In the cases p = 2; 3, we give algorithms for constructing these controls as a function of structure constants that define the control authority, i.e., the actuator capability, of the system. The algorithms are based on a geometric interpretation of the average formulas and produce sinusoidal controls that solve the constructive controllability problem with O(ffl ) accuracy in general (exactly if the Lie algebra is nilpotent). The methodology is applicable to a variety of control problems and is illustrated for the motion control problem of an autonomous underwater vehicle with as few as three control inputs.
Exponential Stabilization of Driftless Nonlinear Control Systems
, 1995
"... This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, x = X 1 (x)u 1 + \Delta \Delta \Delta + Xm (x)um ; x 2 R n : Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineer ..."
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Cited by 50 (3 self)
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This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, x = X 1 (x)u 1 + \Delta \Delta \Delta + Xm (x)um ; x 2 R n : Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a nonstandard dilation. Even though the approximation can be given a coordinatefree interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the close...