Nonholonomic Motion Planning Using Trigonometric Switch Inputs

Li, L.

doi:10.2507/ijsimm16(1)co5

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…A logistic train consist of a tractor and a certain number of towed trailers. The tractor towing a set of trailers usually has a classic Ackermann steering system or a rear-wheel differential drive [12][13][14][15]. Ackermann steering system involves one or two steering wheels at the front.…”

Section: Introductionmentioning

confidence: 99%

Kinematic Model of a Logistic Train with a Double Ackermann Steering System

Paszkowiak¹,

Bartkowiak²,

Pelic³

2021

Int. j. simul. model.

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The demand for fast, economic and high load capacity intralogistics transport is a growing trend. One of the recent solution is a logistic train, which consists of a tractor and a certain number of towed trailers. It is essential that the trailer follows the track of the preceding unit as it allows reduction of shopfloor area dedicated for transport. A perfectly suited steering system for this application is the double Ackermann system. In this study, the kinematic model of the tractor with n trailers was developed based on the Jacobian matrix. The tractor model was adapted to drive along a given trajectory using a PD controller. The simulation studies confirmed that the PD controller is sufficient to control the trajectory for developed kinematic model. The obtained results showed that the trailers with the double Ackermann steering system follow a similar path, which is the most convenient for narrow turn ride. The developed kinematic model can be used for the fast path planning and the design of transportation routes in manufacturing areas. The expanded model with an advanced control system can be used to control a real logistic train.

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Section: Introductionmentioning

confidence: 99%

Kinematic Model of a Logistic Train with a Double Ackermann Steering System

Paszkowiak¹,

Bartkowiak²,

Pelic³

2021

Int. j. simul. model.

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“…Pontryagin Maximum Principle in variational form was employed in Reference [33] to obtain a convergent sequence of controls for optimal motions of general non-holonomic systems with state and input constraints. New methods to non-holonomic path planning are given in Reference [34], which proposed to steer the non-holonomic mobile robot without additional constraints via rotation and linear translation using trigonometric switch inputs, a generic APF-based method via deforming a feasible path of non-holonomic systems (e.g., a mobile robot with trailers) without the violating non-holonomic constraint [35], and the ones based on partial differential equations other than the Laplace's Equation coined by References [7,24], which applied a parabolic partial differential equation, and Reference [29], which used the Navier-Stokes equation of viscous flow for path planning. It is noted that HPF is interpreted in heat conduction, instead of hydrodynamics, in a recent work [28] with a demonstration of a real-time mobile robot navigation experiment.…”

Section: Introductionmentioning

confidence: 99%

A Real-Time Hydrodynamic-Based Obstacle Avoidance System for Non-holonomic Mobile Robots with Curvature Constraints

Kuo¹,

Wang²,

Chou³

et al. 2018

Applied Sciences

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The harmonic potential field of an incompressible nonviscous fluid governed by the Laplace’s Equation has shown its potential for being beneficial to autonomous unmanned vehicles to generate smooth, natural-looking, and predictable paths for obstacle avoidance. The streamlines generated by the boundary value problem of the Laplace’s Equation have explicit, easily computable, or analytic vector fields as the path tangent or robot heading specification without the waypoints and higher order path characteristics. We implemented an obstacle avoidance approach with a focus on curvature constraint for a non-holonomic mobile robot regarded as a particle using curvature-constrained streamlines and streamline changing via pure pursuit. First, we use the potential flow field around a circle to derive three primitive curvature-constrained paths to avoid single obstacles. Furthermore, the pure pursuit controller is implemented to achieve a smooth transition between the streamline paths in the environment with multiple obstacles. In addition to comparative simulations, a proof of concept experiment implemented on a two-wheel driving mobile robot with range sensors validates the practical usefulness of the integrated system that is able to navigate smoothly and safely among multiple cylinder obstacles. The computational requirement of the obstacle avoidance system takes advantage of an a priori selection of fast computing primitive streamline paths, thus, making the system able to generate online a feasible path with a lower maximum curvature that does not violate the curvature constraint.

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Motion planning and stabilization of nonholonomic systems using gradient flow approximations

Grushkovskaya,

Zuyev

2023

Nonlinear Dyn

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Nonlinear control-affine systems described by ordinary differential equations with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems under the bracket-generating condition. This methodology is based on the approximation of a gradient-like dynamics by trajectories of the designed closed-loop system. As an intermediate outcome, we characterize the asymptotic behavior of solutions of the considered class of nonlinear control systems with oscillating inputs under rather general assumptions on the generating potential function. These results are applied to examples of nonholonomic trajectory tracking and obstacle avoidance.

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Nonholonomic Motion Planning Using Trigonometric Switch Inputs

Cited by 3 publications

References 16 publications

Kinematic Model of a Logistic Train with a Double Ackermann Steering System

Kinematic Model of a Logistic Train with a Double Ackermann Steering System

A Real-Time Hydrodynamic-Based Obstacle Avoidance System for Non-holonomic Mobile Robots with Curvature Constraints

Motion planning and stabilization of nonholonomic systems using gradient flow approximations

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