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This paper considers modeling and control of a planar flexible two-link telescoping manipulator. The telescoping interface between the deploying and non-deploying portions of the links is discussed in detail. The equations of motion are derived using Lagrange's equation and constrained using a projection method that eliminates the need to compute Lagrange multipliers explicitly. Passivity-based control of the telescoping manipulator is also investigated. It is shown that several passive input-output maps exist. In particular, by a suitable redefinition of the inputs and outputs, a modified tip-based control is made possible. The model is validated through numerical simulation, and the tip-based control is compared with joint-based control. Simulation results show that tip-based control has better closed-loop performance compared with joint-based control.

The motion equations of a rolling flexible spherical shell are derived using a Lagrangian formulation. The motion equations developed capture the nonholonomic nature of the flexible sphere rolling without slip on a flat surface. The free vibrations of the spherical shell are modeled using the Rayleigh-Ritz discretization method. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the spherical shell on its trajectory.

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