Application of the VFO method to set-point control for theN-trailer vehicle with off-axle hitching

Abstract

In this article the cascaded set-point feedback controller has been proposed for kinematics of the articulated mobile vehicle equipped with arbitrary number of off-axle hitched trailers. The concept results from geometrical features of the vehicle model, and from application of the Vector-Field-Orientation method in the outer loop of the cascaded controller. Solution presented in this article is formulated in the original configuration space of the vehicle not involving any auxiliary state or input transformation. It guarantees convergence of the last vehicle segment to the prescribed neighbourhood of a desired posture along with approximate straightening of a vehicle kinematic chain during approaching the destination. Practical limits of the control input amplitudes have been taken into account during the control law derivation by the application of a simple on-line scaling procedure to the nominally computed control functions. Results of numerical simulations illustrate effectiveness of the method for a 3-trailer vehicle.

Cascaded VFO Control for Non-Standard N-Trailer Robots

“…Limitations allow preventing the effect of vehicle folding in particular joints, which has to be avoided in most practical cases (due to mechanical constraints imposed on admissible joint angles). The issue of vehicle folding has been treated in details in [15]. The general rule of σ selection (to avoid the folding effect) is to satisfy equality…”

“…For the set-point control task decision factor σ can be freely chosen by a designer for almost all initial conditions e(0) (cf. [15]). …”

“…It is also possible to write the N-trailer kinematics in an alternative closed form as a driftless nonholonomic system (cf. [15])…”

“…Kinematic relations between velocities of neighboring segments can be written in the matrix forms [15] …”

“…According to the type of interconnection between the vehicle segments (on-axle or off-axle) one distinguishes three kinds of tractor-trailer vehicles: Standard N-Trailers (SNT) where all the hitching joints are situated at the midpoint of a preceding segment axle [10,12], non-Standard N-Trailers (nSNT) where all the joints are mounted off the axle of a preceding segment [15], and General N-Trailers (GNT) with the mixed locations of particular hitching points-on and off the axles [1]. Highly nonlinear nature of N-trailer kinematics, the presence of nonholonomic constraints, structural instability of joint-angle subsystem, and nonminimum-phase properties resulting from off-axle interconnections [16] all make the motion control tasks of N-trailers the non-trivial and challenging problems.…”