Abstract
The complexity of the control of the road train is due to the pronounced nonlinearities, as well as the instability of the control object during the movement in the backward motion (jackknifing). For the road trains, the location of the towing device behind the tractor's rear axle is quite typical. In this study, a synthesis of control laws for road trains with offset of coupling devices relative to the rear axle of the tractor (off-axle hitching) is proposed. The controllers have been implemented both to ensure a stable circular motion and for rectilinear motion with a given orientation angle, and the behavioral features of this model have been studied on the basis of them. Based on the analysis of the approaches to the synthesis of the laws governing the road train with the coupling out, it was decided to synthesize the required control laws using the Lyapunov function method. Synthesized controllers can be directly used to program the robotic systems of the respective models. It is also possible to use them for the development of the Dubins machine for the investigated model. They can be used to build automatic control systems that would help the driver to drive a car with a trailer while driving backward. In this research, a study was made of the state of the solution of the problem associated with the reverse movement of a road train consisting of a tractor and a semitrailer with a coupling, synthesized laws made it possible to study the features of such model, determined by its linear dimensions. For comparison of the synthesized laws, the analysis of phase portraits of trajectories, angles of folding and control, orientation angles was carried out, and also the analysis of the quality of transient processes with the change in the speed of the road train was performed.
Highlights
Road trains consisting of a tractor and passive semitrailers belong to the class of nonlinear, non-holonomic, structurally unstable dynamic systems
A review of the existing complexes of theoretical and empirical methods is performed, the combination of which makes it possible to study the object with the greatest certainty in order to select the optimal mathematical apparatus for achieving the goal of synthesizing control laws for the reverse motion of a road train with coupling out
A control system has been synthesized for following a road train along a route curve defined by its curvature radius
Summary
Road trains consisting of a tractor and passive semitrailers belong to the class of nonlinear, non-holonomic, structurally unstable (with reverse motion) dynamic systems. The problem of controlling the movement of a road train with a semitrailer under the assumption of non-holonomic constraints (the absence of lateral slippage of the support wheels) is of great theoretical and practical importance Research in this field is stimulated by numerous applied problems. The scalar control action, constrained by the geometric constraint, determines the instantaneous turning radius In this capacity, it is possible to consider the proposed model, and solve for it the task of achieving a given aim. It is possible to note that the direct Lyapunov method has already been successfully applied for the synthesis of a tractor control law with one semitrailer with a hitch in the “on-axle hitching” model [14]. The structure of the script in the internal language of the Maple system has a modular structure: the synthesis of the control law in symbolic form, the recording of the CDS, the input of data, numerical integration, the mapping of phase portraits
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