Maciej Marcin Michałek

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

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.

Trajectory tracking for a mobile robot with skid-slip compensation in the vector-field-orientation control system

Trajectory tracking for a mobile robot with skid-slip compensation in the vector-field-orientation control system The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The paper includes a control law design description, stability and convergence analysis of a closed-loop system, and practical verification of the proposed control concept. The experimental results illustrate control quality obtained on a laboratory setup equipped with vision feedback, where the Kalman filter algorithm was used in order to practically estimate skid-slip components.

Feedback control framework for car-like robots using the unicycle controllers

The paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots-limited and unlimited ones-are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

Non-minimum-phase property of N-trailer kinematics resulting from off-axle interconnections

Off-axle interconnections between segments of N-trailer vehicles may imply specific oscillatory behaviour of trailers during vehicle manoeuvres. The paper reveals that this kind of oscillations is a direct consequence of the non-minimum-phase property of vehicle kinematics resulting from application of off-axle interconnections between vehicle segments. First we show the non-minimum-phase property for dynamics of a single pair of interconnected segments, and then how it propagates along the N-trailers equipped with arbitrary number of off-axle interconnections. By referring to available results for linear systems, we locally analyse linearly approximated vehicle kinematics around selected steady-motion conditions. We focus on the time-response effects like undershooting, zero-crossing, and overshooting caused by off-axle interconnections. We show how the number and type of interconnections influence the non-minimum-phase effects. Numerical results obtained for three-trailer kinematics validate theoretical considerations providing some quantitative view of the problem. Short discussion has been provided on the possible control-level consequences resulting from the non-minimum-phase property of N-trailers.

Motion planning and feedback control for a unicycle in a way point following task: The VFO approach

Motion planning and feedback control for a unicycle in a way point following task: The VFO approach This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of way-points which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.

Tracking Control Strategy for the Standard N-trailer Mobile Robot – A Geometrically Motivated Approach

The paper is devoted to a novel feedback control strategy for the standard N-trailer robot kinematics expected to perform a tracking task for feasible reference trajectories. The control method proposed results from solely geometrical features of the vehicle kinematics formulated in a cascaded-form, and especially from the way the velocity components propagate along a vehicle kinematic chain. The control strategy is derived for the original vehicle configuration space not involving any model transformations or approximations. Formal considerations are examined by simulation results of backward tracking maneuvers for a 3-trailer vehicle.

Vector-Field-Orientation Tracking Control for a Mobile Vehicle Disturbed by the Skid-Slip Phenomena

The paper is devoted to the trajectory tracking control task for a differentially-driven vehicle moving on a plane surface under conditions of the persistent skid-slip phenomena. The Vector Field(s) Orientation (VFO) control strategy, presented originally for undisturbed case in Michałek and Kozłowski (IEEE Trans Control Syst Technol 18(1):45–65, 2010), has been reformulated here to the new disturbed motion conditions. The extension of the VFO strategy relies on introduction of the nonlinear skid-slip influence compensator in the feed-forward loop, which in practical implementation involves the real-time estimation of the skid-slip velocities and their time-derivatives. The approach considers the skid-slip effects solely on the kinematic level avoiding the need of modeling a complicated phenomenon of the wheels-ground interaction. Theoretical analysis shows the asymptotic tracking ability for the position trajectory with boundedness of the orientation error. Experimental results included in the paper reveal substantial tracking quality improvement resulting from the utilization of the proposed skid-slip influence compensator.

The Concept of Passive Control Assistance for Docking Maneuvers With N-Trailer Vehicles

We present a concept of passive control-assistance system, which can help a human driver in precise maneuvers with a tractor-trailer vehicle in the task of docking with the last trailer. The novel approach is developed for truly N-trailer vehicles comprising a car-like tractor and arbitrary number of on-axle or off-axle hitched trailers. Passivity of the proposed assistance system results from the fact that it does not interact directly with a vehicle, but acts solely as an advisor suggesting control action to a human operator through a passive human-machine interface. The key role in the concept plays the cascaded Vector-Field-Orientation feedback control law responsible for computation of the efficient control strategy for a driver based on a feedback from a current vehicle configuration. The passive assistance system has been functionally compared with an alternative active control assistance proposed in the literature. This paper reports the results of experimental tests conducted with a laboratory-scale vehicle, which illustrate efficacy of the cooperation between a driver and a control assistant in the task of backward docking with three trailers.

Experimental verification of SMC with moving switching lines applied to hoisting crane vertical motion control

In this paper we propose sliding mode control strategies for the point-to-point motion control of a hoisting crane. The strategies employ time-varying switching lines (characterized by a constant angle of inclination) which move either with a constant deceleration or a constant velocity to the origin of the error state space. An appropriate design of these switching lines results in non-oscillatory convergence of the regulation error in the closed-loop system. Parameters of the lines are selected optimally in the sense of two criteria, i.e. integral absolute error (IAE) and integral of the time multiplied by the absolute error (ITAE). Furthermore, the velocity and acceleration constraints are explicitly taken into account in the optimization process. Theoretical considerations are verified by experimental tests conducted on a laboratory scale hoisting crane.

Cascaded VFO Control for Non-Standard N-Trailer Robots

Articulated mobile robots consisting of a tractor and passively off-hooked trailers belong to a class of highly nonlinear, nonholonomic, structurally unstable, differentially non-flat, and underactuated dynamic systems. Due to the mentioned properties of their kinematics, motion control problems related to N-trailer robots (N-trailers) are non-trivial and challenging. Cascaded control strategy presented in this paper provides unified solution to the set-point and trajectory tracking control tasks for articulated robots equipped with arbitrary number of passively off-axle hitched trailers. Practically useful features of the proposed controller come from its high scalability and from application of the Vector-Field-Orientation (VFO) controller in the outer loop, which ensures fast errors convergence and simplicity of control implementation and tuning. Control input limitations of the robot are directly taken into account by utilization of a simple velocity scaling procedure which preserves an instantaneous motion curvature of a tractor. Description and theoretical substantiation of the concept are followed by the results of experimental validation tests conducted with usage of a 3-trailer semi-autonomous vehicle.