On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass

Abstract

This paper addresses the trajectory tracking control design of an omnidirectional mobile robot with a center of mass displaced from the geometrical center of the robot platform. Due to the high maneuverability provided by omniwheels, such robots are widely used in industry to transport loads in narrow spaces. As a rule, the center of mass of the load does not coincide with the geometric center of the robot platform. This makes the trajectory tracking control problem of a robot with a displaced center of mass relevant. In this paper, two controllers are constructed that solve the problem of global trajectory tracking control of the robot. The controllers are designed based on the Lyapunov function method. The main difficulty in applying the Lyapunov function method for the trajectory tracking control problem of the robot is that the time derivative of the Lyapunov function is not definite negative, but only semidefinite negative. Moreover, the LaSalle invariance principle is not applicable in this case since the closed-loop system is a nonautonomous system of differential equations. In this paper, it is shown that the quasi-invariance principle for nonautonomous systems of differential equations is much convenient for the asymptotic stability analysis of the closed-loop system. Firstly, we construct an unbounded state feedback controller such as proportional-derivative term plus feedforward. As a result, the global uniform asymptotic stability property of the origin of the closed-loop system has been proved. Secondly, we find that, if the damping forces of the robot are large enough, then the saturated position output feedback controller solves the global trajectory tracking control problem without velocity measurements. The effectiveness of the proposed controllers has been verified through simulation tests. Namely, a comparative analysis of the bounded controller obtained and the well-known "PD+" like control scheme is carried out. It is shown that the approach proposed in this paper saves energy for control inputs. A. S. Andreev, O. A. PeregudovaBesides, a comparative analysis of the bounded controller and its analogue constructed earlier in a cylindrical phase space is carried out. It is shown that the controller provides lower values for the root mean square error of the position and velocity of the closed-loop system.

Điều Khiển Trượt Pid Robot Di Động Đa Hướng

“…Mỗi bánh xe được gắn trực tiếp với trục động cơ của nó nên động cơ và bánh xe có cùng tâm quay [4]. Hiện nay, robot này được nhiều nhà khoa học quan tâm nghiên cứu và công bố, tiêu biểu như: chiến lược điều khiển mô hình tham chiếu [1], học sâu tăng cường [2], bộ điều khiển PI [4], đánh giá sự chính xác độ bám quỹ đạo của robot như trợ lý riêng [5], thuật toán PID trong [6] để tính toán kết nối 3 động cơ DC của robot tạo nền tảng giúp robot di chuyển nhanh với một góc bất kỳ, bộ điều khiển lớp biên và PD+ thông thường [7], điều khiển bám quỹ đạo mô hình ước lượng của hệ nơ-ron mờ thích nghi [8], điều khiển bám quỹ đạo tiệm cận toàn cục với vận tốc biên [9].…”

Adaptive Backstepping Control for Mecanum‐Wheeled Omnidirectional Vehicle Using Neural Networks

“…1 shows the relationship between the robot velocity in the world frame and the angular velocity of i th wheel. Let 3,4) are world frame, body frame and wheel frames, respectively. For simplicity, we define q = [x y φ] T , θ = θ 1 θ 2 θ 3 θ 4 T , and…”

“…Recently, omnidirectional mobile robots have attracted much attention. Owing to their excellent maneuverability and superior agile capability to move toward any position with zero turning radius, omnidirectional mobile robots have been widely applied in various fields, such as hospitals, warehouses and sheltered workshops for disabled people, and so on [1][2][3]. Among various types of omnidirectional mobile robots, the mecanum-wheeled omnidirectional vehicle (MWOV) is one of them.…”

Dynamics-Based Piecewise Constant Control of an Omnivehicle

“…The majority of papers investigating omnivehicles can be divided into two vast groups: those concerning the assembly of real prototypes and enhancement of their maneuverability (for example, [7][8][9][10], see also [3]) and those studying the ways of control on the prescribed trajectories (for example, [11][12][13][14][15][16]). The analysis of their dynamics helps enhance the properties of the prototypes and the controllers.…”

“…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.…”