Nilpotentization of the Kinematics of the N-Trailer System at Singular Points and Motion Planning Through the Singular Locus
نویسنده
چکیده
We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering the two-trailer system in a neighborhood of singular configurations. We show also that the n-trailer system is a universal local model for all Goursat structures and that all Goursat structures are locally nilpotentizable.
منابع مشابه
Generalized Helices and Singular Points
In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.
متن کاملAPPLICATION OF THE SINGULAR BOUNDARY VALUE PROBLEM FOR INVESTIGATION OF PISTON DYNAMICS UNDER POLYTROPIC EXPANSION PROCESS
In this paper a mathematical simulation of a simplified internal combustion engine is presented. To contribute engine kinematics and its geometry, simple relations are derived for constrained motions. The equation of motion for the piston forms a singular boundary value problem. The uniqueness of the solution was studied in the Banach space. For solving governing equations an iterative numerica...
متن کاملTrajectory Tracking Weeled Mobile Robot Using Backstepping Method with Connection off Axle Trailer
The connection of the tractor to the inactive trailer or motor vehicle causes a motion control problem when turning in the screw, forward or backward movements and high speeds. This is due to the inactive trailer being controlled by the tracking using a physical link that is not affected by the movement. Trailers usually take tracks under these conditions. This phenomenon is called Jack Knife. ...
متن کاملSingular constrained linear systems
In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کامل