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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

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Introduction The aim of this research is to develop a robot-assistive training approach for the disabled individuals with impaired upper limb functions. People with impaired upper limb function can regain their motor functionality undergoing intense rehabilitation exercises. With increasing number of disabled individuals, we face deficiency in the number of expert therapists. One promising remedy could be the use of robotic assistive devices. Method To instruct and demonstrate rehabilitation exercise, this research used NAO robot. A library of recommended rehabilitation exercises involving shoulder (i.e., abduction/adduction, vertical flexion/extension, and internal/external rotation), and elbow (i.e., flexion/extension) joint movements was formed in Choregraphe (graphical programming interface). For this purpose, a kinematic model of human upper-extremity was developed based on modified Denavit-Hartenberg notations. Result In experiments, NAO robot gave voice instruction and was maneuvered to cooperate and demonstrate the exercises from the library. NAO also plays some complex game with the subject that represents a multi-joint movement's exercise, which was also included in the library. Conclusions Experimental results with healthy participants reveal that the NAO robot can successfully instruct and demonstrate upper-extremity rehabilitation exercises for single and multi-joint movements. It implies a technical development of cooperative rehabilitation system for which target group will be individuals with upper limb impairment.

Most mobile robot navigation 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, to date, relying on RSS measurements for approximating LOS distance remains a significant challenge. Accurate mapping between RSS measurements and LOS distance is almost impossible to achieve in an indoor reverberant environment. In this paper, we design a partially-observed feedback controller for a differential drive mobile robot (DDMR) where the feedback signal is in the form of noisy RSS measurements emitted from radio frequency identification (RFID) tags placed in the environment. The proposed controller does not require an accurate mapping between the LOS distance and the RSS measurements from RFID tags. In addition, it takes into account the robot's actuator (speed) constraints. Unlike many other previously devised solutions, the proposed control scheme does not require the linearization of the nonlinear DDMR model. The performance of this method is demonstrated through both numerical simulations and real-time experiments.

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