This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system’s dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize the system’s dynamic model using dynamic feedback linearization, a subclass of differential flatness. It is demonstrated that this property considerably simplifies motion planning and the development of controller. Simulation results are presented in the paper, which show that the developed controller has the desirable performance with exponential stability.

This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system’s dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize the system’s dynamic model using dynamic feedback linearization, a subclass of differential flatness. It is demonstrated that this property considerably simplifies motion planning and the development of controller. Simulation results are presented in the paper, which show that the developed controller has the desirable performance with exponential stability.

The kinematics, dynamics, and control of a unicycle moving without slipping on a plane has been extensively studied in the literature of nonholonomic mechanical systems. However, since planar motion can be seen as a limiting case of the motion on a sphere, we focus our analysis on the more general spherical case. This paper introduces a novel approach to path planning for a unicycle rolling on a sphere while satisfying the non-slipping constraint. Our method is based on a simple yet effective idea: first, we model the system as a linear time-varying dynamic system. Then, leveraging the fact that certain such systems can be integrated under specific algebraic conditions, we derive a closed-form expression for the control variables. This formulation includes three free parameters, which can be tuned to generate a path connecting any two configurations of the unicycle. Notably, our approach requires no prior knowledge of nonholonomic system analysis, making it accessible to a broader audience.

The control of vehicles towing trailers is of significant interest to industry due to their wide-ranging applications across various sectors. Trailers play essential roles in logistics, mining, and other fields. This study focuses on the control of a dumper with a trailer specifically used for the monitoring of terrain stability in mining operations. The trailer is equipped with a radar system for detecting potential ground shifts that could jeopardize fieldwork safety. While numerous studies have addressed the control of Ackerman vehicles and trailers, this dumper presents a unique challenge due to its rear-axle steering mechanism. Due to this configuration, which has not been extensively studied in the literature, although the differential flatness of the system is proven, computation of the flat outputs leads to a system of partial differential equations that cannot be solved analytically. For this reason, this paper examines partial feedback linearization to facilitate control and proposes a solution for trajectory tracking that also stabilizes jack-knifing tendencies between the vehicle and trailer. The designed control system was successfully validated in a virtual environment.

This paper studies the differential flatness of the six-degree-of-freedom (6-DOF) model of an Unmanned Surface Vessel (USV), for which no definitive result has previously been established due to complex hydrodynamic couplings. We prove thatthe general USV model is differentially flat by decomposing it into a four-degree-of-freedom subsystem, referred to as the core system, which is flat by pure prolongation, together with an endogenous dynamic extension. This result follows from a systematic application of a recently developed algorithm implemented by the authors in Matlab.The full model inherits the flat outputs of the core system independently of the specific values of the hydrodynamic parameters.