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Passive Decomposition and Control of Nonholonomic Mechanical Systems

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1 Author(s)
Dongjun Lee ; Dept. of Mech., Aerosp. & Biomedi cal Eng., Univ. of Tennessee, Knoxville, TN, USA

We propose nonholonomic passive decomposition, which enables us to decompose the Lagrange-D'Alembert dynamics of multiple (or a single) nonholonomic mechanical systems with a formation-specifying (holonomic) map h into 1) shape system, describing the dynamics of h(q) (i.e., formation aspect), where q ∈ ℜn is the systems' configuration; 2) locked system, describing the systems' motion on the level set of h with the formation aspect h(q) being fixed (i.e., maneuver aspect); 3) quotient system, whose nonzero motion perturbs both the formation and maneuver aspects simultaneously; and 4) energetically conservative inertia-induced coupling among them. All the locked, shape, and quotient systems individually inherit Lagrangian dynamics-like structure and passivity, which facilitate their control design/analysis. Canceling out the coupling, regulating the quotient system, and controlling the locked and shape systems individually, we can drive the formation and maneuver aspects simultaneously and separately. Notions of formation/maneuver decoupled controllability are introduced to address limitations imposed by the nonholonomic constraint, along with passivity-based formation/maneuver control design examples. Numerical simulations are performed to illustrate the theory. Extension to kinematic nonholonomic systems is also presented.

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Robotics, IEEE Transactions on  (Volume:27 ,  Issue: 1 )