Application of laconic forms of the equations of motion in the dynamics of nonholonomic mobile robots

Zobova, A. A.

doi:10.20537/nd1104003

Cited by 8 publications

(8 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the moments of forces i applied to the wheel axes have the form i ¼ o i , where i is independent of v and o, then equation 5admits the singular invariant measure. 18…”

Section: An Omniwheel Mobile Robotmentioning

confidence: 99%

Experimental investigations of a highly maneuverable mobile omniwheel robot

Kilin

Božek

Karavaev

et al. 2017

International Journal of Advanced Robotic Systems

View full text Add to dashboard Cite

In this article, a dynamical model for controlling an omniwheel mobile robot is presented. The proposed model is used to construct an algorithm for calculating control actions for trajectories characterizing the high maneuverability of the mobile robot. A description is given for a prototype of the highly maneuverable robot with four omniwheels, for which an algorithm for setting the coefficients of the PID controller is considered. Experiments on the motion of the robot were conducted at different angles, and the orientation of the platform was preserved. The experimental results are analyzed and statistically assessed.

show abstract

“…If the moments of forces i applied to the wheel axes have the form i ¼ o i , where i is independent of v and o, then equation 5admits the singular invariant measure. 18…”

Section: An Omniwheel Mobile Robotmentioning

confidence: 99%

Experimental investigations of a highly maneuverable mobile omniwheel robot

Kilin

Božek

Karavaev

et al. 2017

International Journal of Advanced Robotic Systems

View full text Add to dashboard Cite

show abstract

“…The simplest dynamical model of the omnivehicle is based on the no-slip constraints of wheels: the omniwheel is modeled as a rigid disk which does not slip in the direction of the contact roller axis (so the dynamics of the rollers is neglected). Different methods are used to derive equations that govern the dynamics of the vehicle (for example, analysis of the reaction force [11,17], Lagrange's multipliers method [6,12,14], Chaplygin's equations [18], Ferrers' equations [19], the Appel -Gibbs method [15,20,21], and Tatarinov's laconic equations [22,23]). All of them give three ordinary differential equations that determine the change of the center of mass velocity and angular velocity due to controls.…”

Section: Introductionmentioning

confidence: 99%

Dynamics-Based Piecewise Constant Control of an Omnivehicle

Moiseev¹,

Zobova²

2022

Nelin. Dinam.

View full text Add to dashboard Cite

show abstract

“…Dynamics of a vehicle with parallel wheels (Fig. 1c) was studied in papers [2], [3]. It also has been shown in [2], [3] that Tatarinov laconic method [4] is rather useful to derive dynamic equations of an omni-vehicle, so we also use this method in our paper.…”

Section: Introductionmentioning

confidence: 99%

“…1c) was studied in papers [2], [3]. It also has been shown in [2], [3] that Tatarinov laconic method [4] is rather useful to derive dynamic equations of an omni-vehicle, so we also use this method in our paper. Martynenko et al [5] studied omni-vehicle dynamics under control.…”

Section: Introductionmentioning

confidence: 99%

Dynamics-Based Piecewise Constant Control of Omni-Vehicle

Moiseev

Zobova

2021

Preprint

View full text Add to dashboard Cite

In this paper, we consider the dynamics of a mobile vehicle moving under control on a perfectly rough horizontal plane. The vehicle consists of a horizontal platform and three omni-wheels that can rotate independently. An omni-wheel has freely rotating rollers on its rim [1]. We use its simplest model: an omni-wheel on a perfectly rough plane is modelled as a rigid disk with a constraint that its contact point velocity directed perpendicular to the disk's plane. The vehicle is controlled by three direct current motors in wheels' axes. Two terms model torques generated by motors: the rst one is proportional to the voltage, the second one is proportional to the value of the angular velocity of a wheel (counter-electromotive force). We study constant voltage dynamics and boundary-value problems for arbitrary initial and nal mass center coordinates, course angles and their derivatives using a piecewise constant control with one switching point. This problem is reduced to a system of algebraic equations for some specific (symmetric) vehicle model. We numerically model the system and analyze the possibility of optimization. For another vehicle configuration, we get the solution as numerical parametric continuation starting from the solution for the symmetric vehicle.

show abstract

Application of laconic forms of the equations of motion in the dynamics of nonholonomic mobile robots

Cited by 8 publications

References 2 publications

Experimental investigations of a highly maneuverable mobile omniwheel robot

Experimental investigations of a highly maneuverable mobile omniwheel robot

Dynamics-Based Piecewise Constant Control of an Omnivehicle

Dynamics-Based Piecewise Constant Control of Omni-Vehicle

Contact Info

Product

Resources

About