Geometric control of mechanical systems

By Francesco Bullo, Andrew D. Lewis. 2004

955 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2a6744e7a6805d107804e163fd49dc0b0c8eed3e

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In Control and Systems Engineering

Citations in the corpus

Discrete mechanics and optimal control for constrained systems (2010, background): “Actuation of the joint connection itself by joint forces s(J ) ∈Rr ) effects both bodies, where according to ‘action equals reaction’, the resulting generalized forces on the bodies are equal, but opposite in sign, see, for example, [43].”
Planning algorithms (2006, background): “Proofs of the Frobenius theorem appear in numerous differential geometry and control theory books [135, 158, 481, 848].”
Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control (2016, background): “17 of [5] it is shown that this assumption is not coordinate-invariant nor is it related to stabilisability of the system.”
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006, methodology): “Holonomically constrained mechanical systems, such as linkages and rigid bodies, admit canonical Lagrangian and Hamiltonian descriptions [151].”
The Magnus expansion and some of its applications (2008, methodology): “To characterize the controllability of linear systems of the form x′(t) = A(t)x(t) +B(t)u(t) (363) is a relatively simple task thanks to an algebraic criterion known as the Kalman rank condition [33,129].”
Flapping flight for biomimetic robotic insects: part II-flight control design (2006, methodology): “Recently, averaging theory and high-frequency periodic control has been successfully paired with tools from geometric control theory [31], [32] for trajectory tracking and approximate stabilization of fish and snake-like vehicles [33]–[39].”
Geometric tracking control of a quadrotor UAV on SE(3) (2010, methodology): “the region where the rotation angle between R and Rd is less than 180◦ [ 14 ].”
Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load (2013, neutral): “…τ 0 ( 〈W1, M̂〉+W2 · fRe3 ) dt = 0, (4) wheref is the thrust magnitude,M is the moment vector, andW1 = RT δR, W2 = δxQ = δxL − lδq are variational vector fields [11], with the infinitesimal variations satisfying [6], [2], [7] δq = ξ × q, ξ ∈ R3 s.t. ξ · q = 0 δq̇ = ξ̇ × q + ξ × q̇ δR = Rη̂, η ∈…”
Nonholonomic Mechanics and Control (2004, background): “A forthcoming monograph by Bullo and Lewis [2] also uses a differential geometric framework to study the control of “simple””
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems (2011, positive): “The equations of motion have the standard form (e.g. [8]): where the map (cid:98) · : R 3 → so (3) is deﬁned by while the control matrix is deﬁned as .”