Kinematic Models of Doubly Generalized N-trailer Systems
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In this paper a Pfaff matrix for doubly generalized N-trailer systems is derived when not only lateral, as in generalized N-trailer systems, but also longitudinal constraints are respected. Based on the matrix, kinematic models are presented for doubly generalized N-trailer systems parameterized with a vector composed of codes of active constraints at each axle. For all constraints active, a closed-form formula for kinematics is derived while for other models – a recursive one is proposed. It is shown how to construct analytically a null space for two types of possible Pfaff matrices and some examples are provided to illustrate introduced formulas. The kinematic models can be used either to test algorithms of motion planning (control) for a broad class of easy parameterizable models or to design or verify wheeled systems.
KeywordsModel Kinematics Generalized N-trailer Nonholonomic systems
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