RFID-Based Mobile Robot Trajectory Tracking and Point Stabilization Through On-line Neighboring Optimal Control

Abstract

In this manuscript, we propose an on-line trajectorytracking algorithm for nonholonomic Differential-Drive Mobile Robots (DDMRs) in the presence of possibly large parametric and measurement uncertainties. Most mobile robot tracking techniques that depend on reference RF beacons rely on approximating line-of-sight (LOS) distances between these beacons and the robot. The approximation of LOS is mostly performed using Received Signal Strength (RSS) measurements of signals propagating between the robot and RF beacons. However, accurate mapping between RSS measurements and LOS distance remains a significant challenge and is almost impossible to achieve in an indoor reverberant environment. This paper contributes to the development of a neighboring optimal control strategy where the two major control tasks, trajectory tracking and point stabilization, are solved and treated as a unified manner using RSS measurements emitted from Radio Frequency IDentification (RFID) tags. The proposed control scheme is divided into two cascaded phases. The first phase provides the robot's nominal control inputs (speeds) and its trajectory using full-state feedback. In the second phase, we design the neighboring optimal controller, where RSS measurements are used to better estimate the robot's pose by employing an optimal filter. Simulation and experimental results are presented to demonstrate the performance of the proposed optimal feedback controller for solving the stabilization and trajectory tracking problems using a DDMR. Keywords Mobile robot navigation · RFID systems · optimal control · trajectory tracking · robot stabilization · nonholonomic systems. Frequently Used Symbols K(t)Feedback control gain at time t H K Hamiltonian's gradient with respect to K s Number of RFID tags in the environment ψ Costate variable (Lagrange multiplier)Robot's actual and desired pose at time t q j t ∈ R 3 jth tag position in 3D space t 0 ,t f Initial and final time instantsRobot's control input vector at time t ξ (t) Robot's actuator noise at time t ζ (t)Measurement noise vector at time t (·) o , (·) ε , (·) ad Optimal, perturb, admissible value of (·) L Lebesgue measurable function space ν T dJ(·) Gateaux (directional) derivative of J in direction ν 1 Introduction

Linear time-invariant feedback operator for mobile robot trajectory tracking

“…The main differences between the current work and our previously relevant published articles (see [25], [26], [22], [23], [24]) are the following. In [25], [26], both time-varying and time-invariant feedback laws are established but they are tailored towards solving the tracking problems of semilinear dynamic systems only, which are not applicable for nonlinear affine systems (differential drive mobile robots, for example) as in the current work.…”

“…1. Following [23], let u L and u R , respectively, be the robot's left and right wheel angular velocities. The robot's position is the midpoint of the wheelbase of length l connecting the two lateral wheels along their axis.…”

“…The controller parameters (similar to the feedback gain parameters in our current work) are iteratively determined by adopting several tuning methodologies proposed by the authors in [18], [19], [20], [21]. Recently, linear time-varying feedback laws in cooperation with optimal control theory are extensively used by Miah and Gueaieb, see [22], [23], [24] for solving both trajectory tracking and regulation problems of wheeled mobile robots in a unified manner. Here we extend these ideas for the case when the feedback operator is linear in state and is time-invariant, which provides a partial solution to the tracking and stabilization problems of nonholonomic mobile robots as pointed out by the Brockett's conditions in [2].…”

“…In [25], [26], both time-varying and time-invariant feedback laws are established but they are tailored towards solving the tracking problems of semilinear dynamic systems only, which are not applicable for nonlinear affine systems (differential drive mobile robots, for example) as in the current work. This issue is then overcome in our recent work [22], [23], [24] by developing measurement feedback laws, where the feedback operator is time-varying as opposed to the proposed feedback operator which is timeinvariant.…”

Nonlinear Control for Tracking and Obstacle Avoidance of a Wheeled Mobile Robot With Nonholonomic Constraint

“…Adaptive sliding mode control has been used to deal with the model uncertainty in wheeled mobile robots [7]. A radio frequency identification-based control method has also been proposed for a mobile robot [8], [9]. Moreover, wheeled mobile robots often encounter obstacles when working in complex environment [10].…”