scholarly journals Observer-Based Time-Variant Spacing Policy for a Platoon of Non-Holonomic Mobile Robots

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3824
Author(s):  
Martín Velasco-Villa ◽  
Raúl Dalí Cruz-Morales ◽  
Alejandro Rodriguez-Angeles ◽  
Carlos A. Domínguez-Ortega
Keyword(s):  
Mobile Robots ◽  
Lyapunov Theory ◽  
Time Varying ◽  
External Disturbances ◽  
Virtual Reference ◽  
Navigation Strategy ◽  
Time Gap ◽  
A Chain ◽  
Bounded Input ◽  
Posture Tracking

This paper presents a navigation strategy for a platoon of n non-holonomic mobile robots with a time-varying spacing policy between each pair of successive robots at the platoon, such that a safe trailing distance is maintained at any speed, avoiding the robots getting too close to each other. It is intended that all the vehicles in the formation follow the trajectory described by the leader robot, which is generated by bounded input velocities. To establish a chain formation among the vehicles, it is required that, for each pair of successive vehicles, the (i+1)-th one follows the trajectory executed by the former i-th one, with a delay of τ(t) units of time. An observer is proposed to estimate the trajectory, velocities, and positions of the i-th vehicle, delayed τ(t) units of time, consequently generating the desired path for the (i+1)-th vehicle, avoiding numerical approximations of the velocities, rendering robustness against noise and corrupted or missing data as well as to external disturbances. Besides the time-varying gap, a constant-time gap is used to get a secure trailing distance between each two successive robots. The presented platoon formation strategy is analyzed and proven by using Lyapunov theory, concluding asymptotic convergence for the posture tracking between the (i+1)-th robot and the virtual reference provided by the observer that corresponds to the i-th robot. The strategy is evaluated by numerical simulations and real-time experiments.

Tracking Control of an Uncertain MEMS Resonator via Adaptive Terminal Sliding Mode Control

2013 ◽  
Vol 302 ◽  
pp. 665-670
Author(s):  
Chi Ching Yang ◽  
Rong Hao Guo
Keyword(s):  
Sliding Mode ◽  
Reference Signal ◽  
Sufficient Conditions ◽  
Adaptive Controller ◽  
Lyapunov Theory ◽  
Time Varying ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Mems Resonator ◽  
System Uncertainties

The purpose of this study is to develop the adaptive terminal sliding mode scheme to control a MEMS resonator with a six-powered potential function for tracking a given reference signal in the presence of system uncertainties and external disturbances. The proposed adaptive controller includes the time-varying feedback gains can tackle the nonlinear dynamics without directly eliminating. Meanwhile, these time-varying feedback gains are adaptively updated according to the suitable updated rules without the known bounds of system uncertainties and external disturbances. Some sufficient conditions to guarantee the stability based on Lyapunov theory and numerical simulations are performed to demonstrate the effectiveness of the presented scheme.

Finite-time control of uncertain time-varying systems in p-normal form

2020 ◽  
Author(s):  
Kanya Rattanamongkhonkun ◽  
Radom Pongvuthithum ◽  
Chulin Likasiri
Keyword(s):  
Normal Form ◽  
Finite Time ◽  
Control Law ◽  
Time Varying ◽  
Time Control ◽  
Special Cases ◽  
Time Varying Systems ◽  
A Chain ◽  
Uncertain Time ◽  
Power Integrator

Abstract This paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well defined. Furthermore, all states converge to zero in finite time.

scholarly journals New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3811
Author(s):  
Katarzyna Adamiak ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Continuous Time ◽  
Sliding Mode ◽  
Representative Point ◽  
Time Varying ◽  
Sliding Surface ◽  
External Disturbances ◽  
Mode Control ◽  
Switching Type ◽  
Time Systems

This study considers the problem of energetical efficiency in switching type sliding mode control of discrete-time systems. The aim of this work is to reduce the quasi-sliding mode band-width and, as follows, the necessary control input, through an application of a new type of time-varying sliding hyperplane in quasi-sliding mode control of sampled time systems. Although time-varying sliding hyperplanes are well known to provide insensitivity to matched external disturbances and uncertainties of the model in the whole range of motion for continuous-time systems, their application in the discrete-time case has never been studied in detail. Therefore, this paper proposes a sliding surface, which crosses the system’s representative point at the initial step and then shifts in the state space according to the pre-generated demand profile of the sliding variable. Next, a controller for a real perturbed plant is designed so that it drives the system’s representative point to its reference position on the sliding plane in each step. Therefore, the impact of external disturbances on the system’s trajectory is minimized, which leads to a reduction of the necessary control effort. Moreover, thanks to a new reaching law applied in the reference profile generator, the sliding surface shift in each step is strictly limited and a switching type of motion occurs. Finally, under the assumption of boundedness and smoothness of continuous-time disturbance, a compensation scheme is added. It is proved that this control strategy reduces the quasi-sliding mode band-width from O(T) to O(T3) order from the very beginning of the regulation process. Moreover, it is shown that the maximum state variable errors become of O(T3) order as well. These achievements directly reduce the energy consumption in the closed-loop system, which is nowadays one of the crucial factors in control engineering.

scholarly journals Motion Planning for a Chain of Mobile Robots Using A* and Potential Field

Robotics ◽  
2018 ◽  
Vol 7 (2) ◽  
pp. 20 ◽  
Author(s):  
A poorva ◽  
Rahul Gautam ◽  
Rahul Kala
Keyword(s):  
Motion Planning ◽  
Mobile Robots ◽  
Potential Field ◽  
A Chain

Fractional robust finite time control of four-wheel-steering mobile robots subject to serious time-varying perturbations

2022 ◽  
Vol 169 ◽  
pp. 104634
Author(s):  
Liquan Jiang ◽  
Shuting Wang ◽  
Yuanlong Xie ◽  
Sheng Quan Xie ◽  
Shiqi Zheng ◽  
...  
Keyword(s):  
Mobile Robots ◽  
Finite Time ◽  
Time Varying ◽  
Time Control

Mixed H∞ and Passivity Performance Analysis of Interfered Digital Filters with Markovian Jumping Parameters and Delays

2021 ◽  
pp. 2250003
Author(s):  
Mani Kant Kumar
Keyword(s):  
Performance Analysis ◽  
Performance Index ◽  
Digital Filters ◽  
Matrix Decomposition ◽  
Lyapunov Theory ◽  
Markovian Jumping Parameters ◽  
Unified Framework ◽  
External Disturbances ◽  
Markovian Jumping ◽  
Stochastically Stable

This paper deals with the problem of mixed [Formula: see text] and passivity performance analysis of digital filters subject to Markovian jumping parameters, external disturbances, time delays and bounds of the nonlinearity functions. By employing Lyapunov theory and matrix decomposition technique, a novel sufficient condition is established. The proposed criterion ensures that the underlying system is stochastically stable and satisfies a mixed [Formula: see text] and passivity performance index simultaneously. The obtained criterion can also be employed to solve the [Formula: see text] problem or the passivity problem in a unified framework. Moreover, the problem is formulated to obtain optimal mixed [Formula: see text] and passivity performance index of the interfered digital filters. The effectiveness and superiority of our proposed results are illustrated by three examples.

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