Kinematic Models of Doubly Generalized N-trailer Systems

Abstract

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.

Trailer-Maneuverability in N-Trailer Structures

“…One concludes that an analysis of the trailer-mobility ellipsoid (18) is equivalent to an analysis of the ellipse represented by (22). Thus, eigenvalues and eigenvectors of matrix (21) determine, respectively, dimensions and an inclination of the trailer-mobility ellipse in the space of velocities…”

“…A practical meaning of the singularity M N = 0 can be also explained by referring to an instantaneous motion curvature of the N th trailer. According to the geometrical interpretation of measure (24), the singularity M N = 0 corresponds to a situation where the ellipse (22) degenerates to a finite-length line segment in the space U N of velocities…”

“…We are going to illustrate the general result represented by (22), with matrix (21), using some special (yet popular) examples of articulated structures, for which the results of numerical computations can be graphically visualized or which are even analytically tractable. Moreover, we reveal some underlying relations between kinematic parameters of N-trailers and properties of a trailer-mobility ellipse.…”

“…Since the first introduction of the fundamental manipulability analysis for serial robot manipulators in [3] (see also [4], [5]), the problems of motion capability and dexterity/agility have been investigated (in the fundamental meaning) for numerous mechanical and robotic systems, like: general constrained multibody systems [6], underactuated robots and devices [7], singlebody wheeled mobile robots [8], mobile manipulators [1], [9], multi-fingered devices [10], continuum robots [11], [12], redundant parallel mechanisms [13], or leader-follower networks [14]. Despite a common usage of the N-trailer structures, and in spite of numerous detailed study concerning their various properties (see, e.g., [15]- [22]), any generic trailer-maneuverability analysis has not been proposed for this kind of multi-body vehicles thus far (some analyses have been made for the tracks with trailers, as in [23], but they address a character/quality of motion in some particular scenarios rather than a generic capability of motion).…”

Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

“…A large number of contemporary and practically important robots can be described as nonholonomic systems. Despite different sources of nonholonomy and nonholonomic manipulators, wheel mobile robots [1] and free-floating space robots [2] belong to this class. Even when modeled at the kinematic level, nonholonomic systems are difficult to control because the number of controls is smaller than the dimension of their configuration spaces.…”