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We obtain an intrinsic vector-valued symmetric bilinear form that can be associate with an underactuated simple mechanical control system. We determine properties of the form which serve as necessary conditions for driving underactuated simple mechanical control systems to rest. We also determine properties of the form that serve as sufficient conditions… (More)

Analysis and control of underactuated mechanical systems in the nonzero velocity setting remains a challenging problem. In this paper, we demonstrate the utility of a recently developed alternative representation of the equations of motion for this large class of nonlinear control systems. The alternative representation gives rise to an intrinisic symmetric… (More)

We provide a constructive global discontinuous control law with state dependent switches for a class of under-actuated nonlinear mechanical robotic systems that will drive the system to an arbitrarily small neighborhood of rest from all initial configurations and velocities in arbitrarily small time. Because all physical mobile robotic systems are… (More)

This paper presents the definition of a new type of dynamic singularity for robotic manipulators. It is applicable to all underactuated robotic systems that can be described by Lagrange's equations where the Lagrangian is the kinetic minus potential energy. The approach is to decompose the velocity at every point in the configuration space into velocity… (More)

Analysis and control of underactuated mechanical systems in the nonzero velocity setting remains a challenging problem. In this paper, we demonstrate the utility of a recently developed alternative representation of the equations of motion for this large class of nonlinear control systems. The alternative representation gives rise to an intrinisic symmetric… (More)

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