Planar tree-like structures consisting of rigid links with rotational joints are considered. These models can be used to describe the dynamics of planar biped robots, in particular during the single support phase. Another simple structure of this type is the so-called acrobot. In both cases, the base joint is unactuated while motors are available at all other joints. As a result, motion planning and control of such systems remain challenging tasks. It is shown that flatness-based methods can be helpful to their solution if time scaling is taken into account. To this end the known concept of orbital flatness has to be extended. Moreover, controlled time scaling turns out to provide a helpful additional degree of freedom.Motion planning and feedback design are briefly discussed.
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