Formation Control of Non-Holonomic Mobile Robots Moving on Slippery Surfaces

2020 ◽  
Author(s):  
Violet Mwaffo ◽  
Pietro De Lellis ◽  
Sean Humbert
Keyword(s):  
Formation Control ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Robotic Systems ◽  
Control Input ◽  
Stochastic Disturbances ◽  
Driving Speed ◽  
Control Schemes ◽  
Mean Square Convergence ◽  
Double Integrator

Abstract In this work, we analyze the decentralized formation control problem for a class of multi-robotic systems evolving on slippery surfaces. Grounded on experimental data of robots moving on a gravel surface inducing slippery, we show that a deterministic model cannot capture the uncertainties resulting from the kinematics of the robots while, instead, a model incorporating stochastic noise is capable of emulating such perturbations on wheel driving speed and turn rate. To account for these uncertainties, we consider a second order non-holonomic unicycle model to capture the full dynamics of individual vehicles where both actuation force and torque are subject to stochastic disturbances. Upon reducing the input-output dynamics of individual robot to a stochastic double integrator, we investigate the effects of these perturbations on the control input using concepts from stochastic stability theory and through numerical simulations. We demonstrated the applicability of the proposed scheme for formation control notably by providing sufficient conditions for exponential mean square convergence and we numerically determined the range of noise intensities for which team of robots can achieve formation stabilization. The promising findings from this work are expected to aid the design of robust control schemes for formation control of non-holonomic robots on off-road or un-paved surfaces.

scholarly journals SDP-Based Robust Formation-Containment Coordination of Swarm Robotic Systems with Input Saturation

2021 ◽  
Vol 102 (1) ◽  
Author(s):  
Kefan Wu ◽  
Junyan Hu ◽  
Barry Lennox ◽  
Farshad Arvin
Keyword(s):  
Formation Control ◽  
Controller Design ◽  
Input Saturation ◽  
Reference Signal ◽  
Robotic Systems ◽  
Time Data ◽  
Containment Control ◽  
Potential Applications ◽  
Hardware Platforms ◽  
Double Integrator

AbstractThere are many potential applications of swarm robotic systems in real-world scenarios. In this paper, formation-containment controller design for single-integrator and double-integrator swarm robotic systems with input saturation is investigated. The swarm system contains two types of robots—leaders and followers. A novel control protocol and an implementation algorithm are proposed that enable the leaders to achieve the desired formation via semidefinite programming (SDP) techniques. The followers then converge into the convex hull formed by the leaders simultaneously. In contrast to conventional consensus-based formation control methods, the relative formation reference signal is not required in the real-time data transmission, which provides greater feasibility for implementation on hardware platforms. The effectiveness of the proposed formation-containment control algorithm is demonstrated with both numerical simulations and experiments using real robots that utilize the miniature mobile robot, Mona.

Nonlinear Stochastic Feedback Controllers for Vibratory Energy Harvesters With Power Flow Constraints

2011 ◽  
Author(s):  
Ian L. Cassidy ◽  
Jeffrey T. Scruggs ◽  
Sam Behrens
Keyword(s):  
Power Generation ◽  
Power Flow ◽  
Flow Direction ◽  
Average Power ◽  
Control Input ◽  
Stochastic Disturbances ◽  
Feedback Controllers ◽  
Energy Harvesters ◽  
System States ◽  
Feedback Laws

This study addresses the formulation of feedback controllers for stochastically-excited vibratory energy harvesters. Maximizing power generation from stochastic disturbances can be accomplished using LQG control theory, with the transducer current treated as the control input. For the case where the power flow direction is unconstrained, an electronic drive capable of extracting as well as delivering power to the transducer is required to implement the optimal controller. It is demonstrated that for stochastic disturbances characterized by second-order, bandpass-filtered white noise, energy harvesters can be passively tuned such that optimal stationary power generation only requires half of the system states for feedback in the active circuit. However, there are many applications where the implementation of a bi-directional power electronic drive is infeasible, due to the higher parasitic losses they must sustain. If the electronics are designed to be capable of only single-directional power flow (i.e., where the electronics are incapable of power injection), then these parasitics can be reduced significantly, which makes single-directional converters more appropriate at smaller power scales. The constraint on the directionality of power flow imposes a constraint on the feedback laws that can be implemented with such converters. In this paper, we present a sub-optimal nonlinear control design technique for this class of problems, which exhibits an analytically computable upper bound on average power generation.

scholarly journals A Survey of Formation Control for Multiple Mobile Robotic Systems

2020 ◽  
pp. 1515-1520
Author(s):  
Lintle Tsiu ◽  
Elisha Didam Markus
Keyword(s):  
Formation Control ◽  
Robotic Systems

scholarly journals Intermittent Time-Varying Formation Control for High-Order Networked Agents Subject to Discontinuous Communications

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Lixin Wang ◽  
Zhe Luo ◽  
Xiaoqiang Li ◽  
Xinsan Li ◽  
Xiaogang Yang
Keyword(s):  
Formation Control ◽  
Linear Matrix ◽  
Control Input ◽  
Intermittent Control ◽  
Movement Trajectory ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Communication Time ◽  
Theoretical Results ◽  
Formation Design

This paper investigates the leaderless and leader-follower time-varying formation design and analysis problems for a group of networked agents subject to discontinuous communications. Firstly, a leaderless time-varying formation control protocol is proposed via the intermittent control strategy, where the control input of each agent is constructed by the distributed local state information and formation instructions in the communication time unit, but it is zero in the noncommunication time unit. Then, an explicit formulation of the formation center function is determined to describe the formation movement trajectory of the whole networked agents. Leaderless time-varying formation design and analysis with discontinuous communications are given in the form of linear matrix inequalities. Moreover, the main results of the leaderless cases are extended to the leader-follower cases. Finally, two numerical examples are provided to illustrate the theoretical results of leaderless and leader-follower cases, respectively.

scholarly journals Position Domain Synchronization Control For Robotic Manipulators

2021 ◽  
Author(s):  
Vangjel Pano
Keyword(s):  
Time Domain ◽  
Robotic Manipulators ◽  
Synchronization Control ◽  
Control Law ◽  
Control Input ◽  
Contour Tracking ◽  
Hybrid Controller ◽  
Reference Motion ◽  
Control Scheme ◽  
Control Schemes

Developed in this thesis is a new control law focusing on the improvement of contour tracking of robotic manipulators. The new control scheme is a hybrid controller based on position domain control (PDC) and position synchronization control (PSC). On PDC, the system’s dynamics are transformed from time domain to position domain via a one-to-one mapping and the position of the master axis motion is used as reference instead of time. The elimination of the reference motion from the control input improves contouring performance relative to time domain controllers. Conversely, PSC seeks to reduce the error of the systems by diminishing the synchronization error between each agent of the system. The new control law utilizes the aforementioned techniques to maximize the contour performance. The Lyapunov method was used to prove the proposed controller’s stability. The new control law was compared to existing control schemes via simulations of linear and nonlinear contours, and was shown to provide good tracking and contouring performances.

scholarly journals On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Time Delay ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Algorithm ◽  
Directed Network ◽  
Consensus Protocol ◽  
Special Cases ◽  
Coupling Time ◽  
Almost All ◽  
Double Integrator

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

Bearing-based formation control of networked robotic systems with parametric uncertainties

2018 ◽  
Vol 306 ◽  
pp. 234-245 ◽  
Author(s):  
Xiaolei Li ◽  
Xiaoyuan Luo ◽  
Jiange Wang ◽  
Yakun Zhu ◽  
Xinping Guan
Keyword(s):  
Formation Control ◽  
Robotic Systems ◽  
Parametric Uncertainties

A stability analysis on a smoking model with stochastic perturbation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anwar Zeb ◽  
Sunil Kumar ◽  
Almaz Tesfay ◽  
Anil Kumar
Keyword(s):  
Stochastic Model ◽  
Stochastic System ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Reproductive Number ◽  
Content Type ◽  
Model Form ◽  
The World ◽  
Dynamic Stochastic

Purpose The purpose of this paper is to investigate the effects of irregular unsettling on the smoking model in form of the stochastic model as in the deterministic model these effects are neglected for simplicity. Design/methodology/approach In this research, the authors investigate a stochastic smoking system in which the contact rate is perturbed by Lévy noise to control the trend of smoking. First, present the formulation of the stochastic model and study the dynamics of the deterministic model. Then the global positive solution of the stochastic system is discussed. Further, extinction and the persistence of the proposed system are presented on the base of the reproductive number. Findings The authors discuss the dynamics of the deterministic smoking model form and further present the existence and uniqueness of non-negative global solutions for the stochastic system. Some previous study’s mentioned in the Introduction can be improved with the help of obtaining results, graphically present in this manuscript. In this regard, the authors present the sufficient conditions for the extinction of smoking for reproductive number is less than 1. Research limitations/implications In this work, the authors investigated the dynamic stochastic smoking model with non-Gaussian noise. The authors discussed the dynamics of the deterministic smoking model form and further showed for the stochastic system the existence and uniqueness of the non-negative global solution. Some previous study’s mentioned in the Introduction can be improved with the help of obtained results, clearly shown graphically in this manuscript. In this regard, the authors presented the sufficient conditions for the extinction of smoking, if <1, which can help in the control of smoking. Motivated from this research soon, the authors will extent the results to propose new mathematical models for the smoking epidemic in the form of fractional stochastic modeling. Especially, will investigate the effective strategies for control smoking throughout the world. Originality/value This study is helpful in the control of smoking throughout the world.

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