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Loworder controllability and kinematic reductions for affine connection control systems
 SIAM Journal on Control and Optimization
"... Abstract. Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, loworder controllability results are given for the class of mechanical control systems. Second, a precise connection is made between those mechanical systems which are dynami ..."
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Cited by 22 (6 self)
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Abstract. Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, loworder 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., have velocities as inputs). Interestingly and surprisingly, these two subjects are characterised and linked by a certain intrinsic vectorvalued quadratic form that can be associated to an affine connection control system.
Geometric Local Controllability: SecondOrder Conditions
 in Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, Dec. 2002, Institute of Electrical and Electronics Engineers
, 2002
"... In a geometric point of view, a nonlinear control system, a#ne in the controls, is thought of as an a#ne subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from this point of view, one should describe those properties of the a#ne subbundle that eithe ..."
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Cited by 13 (5 self)
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In a geometric point of view, a nonlinear control system, a#ne in the controls, is thought of as an a#ne subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from this point of view, one should describe those properties of the a#ne subbundle that either ensure or prohibit local controllability. In this paper, secondorder conditions of this nature are provided. The techniques involve a fusion of wellestablished analytical methods with di#erential geometric ideas. 1.
Legless Locomotion: Models and Experimental Demonstration
 In Proceedings of the IEEE International Conference on Robotics and Automation
, 2004
"... Abstract — We show through experiment and simulation that a highcentered roundbodied legged robot can locomote by generating outofphase motions of reaction masses attached to its legs. These leg motions create body attitude oscillations which, when coupled with the slipfree contact constraints, ..."
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Cited by 7 (7 self)
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Abstract — We show through experiment and simulation that a highcentered roundbodied legged robot can locomote by generating outofphase motions of reaction masses attached to its legs. These leg motions create body attitude oscillations which, when coupled with the slipfree contact constraints, locomote the robot. By varying the mean position of the leg oscillations, the robot can move in different directions in the plane. We also present some simplified models, where body attitude dynamics and contact kinematics are decoupled, to explain this form of legless locomotion.
Geometric Control Theory and its Application to Underwater Vehicles
, 2008
"... (Department of Mathematics) The proposed research is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of marine science. In particular, we apply geometric methods to solve the motion planning problem for underwater vehicles. ..."
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Cited by 6 (4 self)
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(Department of Mathematics) The proposed research is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of marine science. In particular, we apply geometric methods to solve the motion planning problem for underwater vehicles. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. The work presented here is based on this recent progress with the objective to develop efficient tools for scientists and engineers in ocean research. On one hand, the underwater vehicle presents an ideal platform to extend known theory to mechanical systems which include dissipative and potential forces. And, on the other hand, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for concrete applications. 1 Goals, Objectives and Impact RESEARCH GOAL 1.1. It is a goal of this research to combine mathematics and ocean engineering through the application of differential geometry to the motion planning problem for underwater vehicles.
A catalog of inversekinematics planners for underactuated systems on matrix lie groups
 In IROS
, 2003
"... Abstract — This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (lowdimensional) combinatorial selection and inversekinematics problems. We present a catalog of solutions for all underactuat ..."
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Cited by 6 (2 self)
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Abstract — This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (lowdimensional) combinatorial selection and inversekinematics problems. We present a catalog of solutions for all underactuated systems on SE(2), SO(3) and SE(2) × R classified according to their controllability properties. I.
Kinematic Reduction and Planning using Symmetry for a Variable Inertia Mechanical System
 In IEEE/RSJ International Conference on Intelligent Robots and Systems
, 2004
"... Abstract — Motivated by finding locomotion primitives for a legged robot, we present controllability results and kinematic reduction for a variable inertia mechanical system. We show that the mechanical system is configuration controllable and use the symmetry resulting from angular momentum conserv ..."
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Cited by 6 (6 self)
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Abstract — Motivated by finding locomotion primitives for a legged robot, we present controllability results and kinematic reduction for a variable inertia mechanical system. We show that the mechanical system is configuration controllable and use the symmetry resulting from angular momentum conservation to develop a kinematic representation of the mechanical system. We also show through simulation how plans for the kinematic representation can be implemented on the full dynamical mechanical system. Our hope is that this technique will lead us to a general procedure for solving the gait synthesis problem. I.
On the factorization of trajectory lifting maps
, 2005
"... Trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques. Well known systems theoretic concepts such as differential flatness or more recent ones such as bisimulations can be also understood through the trajectory lifting maps they ..."
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Cited by 1 (0 self)
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Trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques. Well known systems theoretic concepts such as differential flatness or more recent ones such as bisimulations can be also understood through the trajectory lifting maps they define. In this paper we initiate a study of trajectory preserving and lifting maps between affine control systems. Our main result shows that any trajectory lifting map between two singleinput control affine systems can be locally factored as the composition of two special trajectory lifting maps: a projection onto a quotient system followed by a differentially flat output with respect to another control system.
Kinematic Reducibility of Multiple Model Systems
"... This paper considers the relationship between second order multiple model systems and first order multiple model systems. Such a relationship is important to, among other things, studying path planning for mechanical control systems. This is largely due to the fact that the computational complexity ..."
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This paper considers the relationship between second order multiple model systems and first order multiple model systems. Such a relationship is important to, among other things, studying path planning for mechanical control systems. This is largely due to the fact that the computational complexity of a path planning problem rapidly increases with the dimension of the state space, implying that being able to reduce a path planning problem from TQ to Q can be helpful. Not surprisingly, the necessary and sufficient condition for such a reduction is that each model constituting a multiple model control system be reducible. We present an extensive example in order to illustrate how these results can provide insight into the control of some specific physical systems.
SIAM Journal on Control and Optimization
, 2005
"... Loworder controllability and kinematic reductions for affine connection control systems ..."
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Loworder controllability and kinematic reductions for affine connection control systems
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"... An approximate decoupled dynamics and kinematics analysis of legless locomotion ..."
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An approximate decoupled dynamics and kinematics analysis of legless locomotion