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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 derived. This condition involves an object that we call the symmetric product. Of particular interest is… (More)

Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE Abstract We apply some recently… (More)

In this paper, we provide controllability tests and motion control algorithms for under-actuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space. Local controllability… (More)

Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, low-order controllability results are given for the class of mechanical control systems. Second, a precise connection is made between those mechanical systems which are dynamic (i.e., have forces as inputs) and those which are kinematic (i.e.,… (More)

— The snakeboard is shown to possess two de-coupling vector fields, and to be kinematically controllable. Accordingly, the problem of steering the snakeboard from a given configuration at rest to a desired configuration at rest is posed as a constrained static nonlinear inversion problem. An explicit algorithmic solution to the problem is provided, and its… (More)

Analysis and simulations are performed for a simpliied 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 diiculty lies primarily in the way in which the… (More)

Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order control variations, a specific method for generating such variations is proposed. The theory is applied to a number of nontrivial examples.

This paper studies the mechanics of undu-latory locomotion. This type of locomotion is generated by a coupling of internal shape changes to external non-holonomic constraints. Employing methods from geometric mechanics, we use the dynamic symmetries and kine-matic constraints to develop a specialized form of the dynamic equations which govern undulatory… (More)

Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such explicit and fixed parameterisation by control is commonplace in control theory, leading to definitions,… (More)