An introduction to motion planning under multirate digital control

Monaco, S.; Normand‐Cyrot, D.

doi:10.1109/cdc.1992.371122

Cited by 100 publications

(49 citation statements)

References 10 publications

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“…This method was originally proposed by Monaco and Normand-Cyrot [30] and was inspired by multirate digital control. It is most easily understood in the context of nonholonomic motion planning simply as piecewise constant inputs.…”

Section: B Piecewise Constant Inputsmentioning

confidence: 99%

Trajectory generation for the N-trailer problem using Goursat normal form

Tilbury

Murray

Sastry³

1995

IEEE Trans. Automat. Contr.

223

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Section: B Piecewise Constant Inputsmentioning

confidence: 99%

Trajectory generation for the N-trailer problem using Goursat normal form

Tilbury

Murray

Sastry³

1995

IEEE Trans. Automat. Contr.

223

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“…For such systems, the reachability problem has been already clarified in the literature (see e.g. [12][13][14][15]). On the other hand, if Q and U are assumed to be discrete sets, then the system essentially represents a sequential machine (automaton).…”

Section: Nonholonomic Behaviours In Nonsmooth Systemsmentioning

confidence: 99%

Discrete and Hybrid Nonholonomy

Bicchi

Marigo

Piccoli

2004

Hybrid Systems: Computation and Control

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Abstract. In this paper we consider the generalization of the classical notion of nonholonomy of smooth constraints in analytical mechanics, to a substantially wider set of systems, allowing for discrete and hybrid (mixed continuous and discrete) configurations and transitions. We show that the general notion of nonholonomy can be captured by the definition of two different types of nonholonomic behaviours, which we call internal and external, respectively. Examples are reported of systems exhibiting either the former only, or the latter only, or both. For some classes of systems, we provide equivalent or sufficient characterizations of such definitions, which allow for practical tests.

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“…The jth input will be of the following form: u"t) = ukk fort E [ t k , tk+l). When the chained form equations are integrated using these input values, the final state can be expressed in terms of the inputs and the initial state as where the matrices A3 are assured to be nonsingular whenever the first input U& is nonzero [12]. Similarly to the previous section, if the first input does come out to be zero from (27), then a slight modification of this method is necessary.…”

Section: B Piecewise Constant Inputsmentioning

confidence: 99%

“…This steering method was originally inspired by multirate digital control [12], but is most easily understood in terms of motion planning simply as piecewise constant inputs. The first input uo is chosen to be constant over the entire trajectory.…”

Section: B Piecewise Constant Inputsmentioning

confidence: 99%

A multisteering trailer system: conversion into chained form using dynamic feedback

Tilbury

Sørdalen

Bushnell

et al. 1995

IEEE Trans. Robot. Automat.

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Abstract-This paper examines the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, liked together with rigid bars. The state space and kinematic equations of the system are defined, and it is shown how these kinematic equations may be converted into a multiinput chained form. The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization; some of these methods are discussed here. Dynamic state feedback is used to convert the system to this multiinput chained form. It is shown how the dynamic state feedback that is used in this paper corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers.Two different example systems are also presented, along with simulation results for a parallel-parking maneuver.

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An introduction to motion planning under multirate digital control

Cited by 100 publications

References 10 publications

Trajectory generation for the N-trailer problem using Goursat normal form

Trajectory generation for the N-trailer problem using Goursat normal form

Discrete and Hybrid Nonholonomy

A multisteering trailer system: conversion into chained form using dynamic feedback

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