Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems

DOI10.1007/BF01211485zbMath0825.93319OpenAlexW2136628844WikidataQ59814481 ScholiaQ59814481MaRDI QIDQ1340093

Richard M. Murray

Publication date: 28 November 1995

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01211485

Mathematics Subject Classification ID

Automated systems (robots, etc.) in control theory (93C85) Control of mechanical systems (70Q05) Nonholonomic systems related to the dynamics of a system of particles (70F25)

Related Items (19)

Engel theorem through singularities ⋮ The step-2 nilpotent \((n,n(n+1)/2)\) sub-Riemannian geometry ⋮ Adaptive robust control of nonholonomic systems with stochastic disturbances ⋮ Non-holonomic control systems: from steering to stabilization with sinusoids ⋮ Theoretical analysis for a class of rheonomous affine constraints on configuration manifolds. I: Fundamental properties and integrability/nonintegrability conditions ⋮ Design of differentially flat planar space robots and their planning and control ⋮ Any (controllable) driftless system with 3 inputs and 5 states is flat ⋮ Robust adaptive neuro-fuzzy control of uncertain nonholonomic systems ⋮ Mathematical modelling and theoretical analysis of nonholonomic kinematic systems with a class of rheonomous affine constraints ⋮ Abnormal curves on the Goursat systems of \(\mathbb{R}^{n}\) ⋮ Kumpera-Ruiz algebras in Goursat flags are optimal in small lengths ⋮ A flat triangular form for nonlinear systems with two inputs: necessary and sufficient conditions ⋮ Design and analysis of a spherical mobile robot ⋮ Geometric approach to Goursat flags ⋮ Paraconformal structures and differential equations ⋮ Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness ⋮ A structurally flat triangular form based on the extended chained form ⋮ Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8 ⋮ Chained form approximation of a driftless system. Application to the exponential stabilization of the general N-trailer system

Cites Work

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• Distributions and the Lie Algebras their Bases Can Generate
• Nonholonomic motion planning: steering using sinusoids
• The GS algorithm for exact linearization to Brunovsky normal form
• Control and stabilization of nonholonomic dynamic systems

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