Seong-Min Lee

From the numerical simulation and experimental validation, the feasibility and efficiency of the proposed control systems for the SMP is demonstrated. The analysis of human factors can be applied to build the control and operation system of the motion platform with people.

Introduction Introduction

Motivation

In this research, a new motion platform, here called SMP, was developed to provide unconstrained three-DOF rotation and three-DOF translation. In addition, the effectiveness of the unrestricted rotation capability in moving platforms is assessed by human factors.

Figure 1.1. Application of spherical driven platforms in various industries. (a) Vehicle [1]

Background

Thus, human factors should be analyzed according to the operation of the motion platform, and the human factors according to motion range should be evaluated to validate the use of the proposed platform.

Figure 1.2. Existing motion platforms and comparison of characteristics. (a) Serial motion platform [6]

Research Objectives

Philosophy of the Proposed Research

We are motivated by exploring the human factors in the operation of SMP, and this helps to apply SMP to a better virtual reality.

Organization of Thesis

Publication

Journals
Conferences

Overview

Although the parallel mechanism, in general, offers a small range of motion compared to the serial mechanism due to geometrical design constraints, limiting the acceleration, the Stewart platform provides better range of motion with six DOF. Different mechanisms based on the parallel platform, such as parallel cable driving [ 22 ], the new geometric approach [ 23 ], and other mechanisms have been proposed to overcome the range of motion limitations.

Figure 2.1. Comparison of spherical driving mechanisms. (a) Spherical wheel. (b) Mecanum wheel [9]

Spherical Motion Platform I Based on Three Spherical Wheels Wheels

Mechanical Structure and Design
Spherical Wheel Mechanism
Kinematic Model
Dynamic Model

H is the height of the center of the cockpit from the center of the small sphere in (2.5). The angular velocity of the cockpit Ω in (2.7) is expressed as the sum of two components.

Figure 2.2. Design and mechanical structures of multi-DOF spherical motion platform I

Spherical Motion Platform II Based on Four Spherical Wheels Wheels

Mechanical Structure and Design
Compliant Spherical Wheel Mechanism
Kinematic Model
Dynamic Model

The location of the small balls and the cockpit are defined for the motion analysis by geometric relation. Rotation of the cockpit is driven by four motors through four small balls to the cockpit ball taking into account the slip mode.

Figure 2.6. Design and mechanical structures of SMP II. (a) Geometric structure

Geometric Stability

For the SMP II, the position of the cabin is always located within the quadrangle consisting of P1, P2, P3 and P4 with minimum distance between ki. a) Comparison of SMP I and II. b) Case study of geometrical stability for SMP I.

Active Driving Control

Kinematic Control for Four Rolling Contacts

It is considered that the cabin sphere loses contact with the 4th small sphere as an illustration.

Slip Estimation for Rotational Motion

When the sliding motion occurs partially as 0 < λi< 1, the actuator input in (2.79) can be calculated using the estimated sliding ratio ˆλ. When the sliding motion occurs, the actuator input is calculated using the estimated sliding ratio, λˆ in (2.79), which reduces the abrasion of the wheel and sphere simultaneously.

Numerical Simulation and Experimental Validation

Validation for SMP I
Validation for SMP II

Errors could be compensated by feedback control for cockpit orientation and position. The orientation of the SMP II is shown from the prototype with four SPWs as shown in the figure. Errors can be compensated for by CL controls for cockpit orientation and position.

Figure 2.11. Open-loop control system for numerical simulation.

Overview

The orientation of Atlas' cockpit sphere can be determined using certain markers and cameras, as shown in Figure. The center of gravity of the cockpit sphere is thus estimated from the weight distribution using a load cell with measurement of the distributed mass on each rolling contact, and then gravity. torque due to mass eccentricity is determined. From the slip motion estimation result, it is also validated that the unbalanced weight of the cockpit causes the center of gravity to shift, which reduces the control performance.

Figure 3.1. Researches for measuring rotation of sphere. (a) Spherical wheel motor [41]

Orientation Sensor for Orientation Measurement

Kinematic Analysis for Optical Sensors
Orientation Sensor With Compliant Mechanism
Sensor Fusion With Kalman Filter

The rotary motion of the cabin can be measured by n optical sensors with 2n inputs on the Xi and Yi axes. Three joints and four springs make the same gap from the optical sensor to the cabin surface at all relative positions of the cabin sphere. As a result, the cockpit orientation can be estimated by both the IMU and the optical sensors minimizing the accumulation error and maximizing the robustness of the optical sensor.

Figure 3.2. Optical sensor for cockpit orientation measurement. (a) Top view. (b) Side view

Loadcell Sensor for Balanced Weight Distribution

The performance of the sensor depends on a sampling rate of measurement, and thus a discrete model must be analyzed as in (3.29). R = E[wwT] is a covariance matrix for w[υTa oT T] where υa and υo are measurement noise of accelerometer and optical sensor, respectively. In (3.34), Mi represents the weight distribution of the cabin sphere measured from the load cells, and it is calculated by weight from the load cells and the position of the stages.

Figure 3.4. Sensing system with loadcell to measure mass distribution. (a) Schematic design

Experimental Validation

Validation Using Small-Scale SMP II
Validation Using Full-Scale SMP II
Estimation of Center of Gravity

The experimental results show that the angular velocity of the cockpit can be measured with three optical sensors. Then, the experimental results show that it is not sufficient to measure and estimate the angular velocity of the cockpit using only one optical sensor. The results indicate that the optical sensor data can be used to estimate the orientation of the cockpit.

Figure 3.5. Experimental setup for optical sensors. (a) Top view. (b) Side view.

Overview

Thus, SMP [3], [10] with a spherical cabin, has been developed in contrast to existing motion simulators. Additionally, disturbance observer-based (DOB) control [55] has been developed to estimate and compensate for matching uncertainties such as dynamic uncertainties. Finite-time tracking control was also achieved by the Stewart motion platform despite uncertain dynamic models.

Robust Control for Kinematic and Dynamic Uncertainties

Mathematical Model
Tracking Control Design

The kinematic equations of the SMP can be derived from a rotation of the driving wheels and a relative position of the linear stages. The control system is designed based on the following assumption regarding the uncertainties as well as unexpected disturbances of the SMP. The cabin sphere tracking errors reach the sliding surface σ, and the sliding motion occurs with σσ 0 within finite time T1.

Fig. 4.2 shows a control system to improve the accuracy of the SMP control due to the uncertainties in (4.1) and (4.5)

Robust Adaptive Control For Uncertainties

Therefore, it is proved that the CL system is asymptotically stable and the tracking error converges to 0 under the kinematic and dynamic uncertainties after t > max (T0, T1). Furthermore, for the case of ||σ|| ≤ ε, σ is still bounded, according to [63], where the adaptation law governsˆ. It is noted that, in practice, the presented adaptation laws are continuously increasing and these cannot be applied in SMP control, causing large noise due to ||σ|| ≠ 0.

Numerical Simulation and Experimental Validation

Validation of DOB-SMC Using SMP I
Validation of Adaptive SMC Using SMP II

The experimental results show that the orientation and position tracking performance of the DOB-SMC is better than that of the PID and I-SMC, even in the presence of uncertainties comparable to the numerical simulation. The tracking performance is demonstrated from the results for the trajectory using DOB-SMC within 1.3° of eMax. 4.16(a) and (b) show the comparison of the trajectory tracking performance of the PID controller and the SMC.

Figure 4.4. Actual scaled SMP with full cockpit sphere. (a) SMP. (b) Inside of the cockpit

Overview

In addition, tracking control systems have been developed to compensate for time delay using predicted reference for a wireless network system [90] and path preview for autonomous vehicles [91]. It cannot further converge the tracking error to zero in the case of a large time delay. In this section, the prediction-based preview controller (PPC) for the motion platform is developed to handle the time delay as well as the disturbance.

Problem Formulation

Motion Platform With Input delay
Reference Trajectory

The control input u = [J]–1U generated inside the cockpit is transmitted to the motion controller using wireless communication as shown in the figure. Ba = [0n×n In×n]T is the perturbation matrix and dn represents the time-varying external perturbations and is assumed to be d (r+1) times continuous differentiable. A motion cue is generated from the motion of the platform corresponding to the reference trajectory.

Fig. 5.1(b) represents the structure for motion platform operation. The operator inside the cockpit controls a vehicle with visual and motion stimuli

State Prediction With Time delay

Analysis
Numerical Simulation

Note that in [77, Proposition 2], the convergence for the constant xr was only demonstrated, and it may decrease the effectiveness of the proposed controller for practical applications. 5.2(b) implies that the proposed air traffic controller ensures delayed convergence, and it is limited in the applicability of the air traffic controller to the time-varying trajectory. Thus, the results and [77, Proposition 2] cannot guarantee the convergence of the engine speed ω to the time-varying desired speed ωr. a) Trajectory of Wpˆ.(b).

Table 5.1. List of Specifications of Mechanical Parameters.

Prediction-Based Preview Control

State Prediction Based on Finite Spectrum Assignment
Prediction-Based Preview Controller Design

First, it is discussed that the constant reference range xd is limited in various industrial applications. It is then ensured that the error e(t) in (5.19) is bounded according to the boundedness of ev(t) when. As a result, without delay effect, the convergence of the state x is ultimately verified to the desired trajectory xd according to ed(∞) = 0.

Numerical Simulation and Experimental Validation

Numerical Simulation

Note that the tracking error only depends on the DOB errors and the predictors for future disturbances and trajectory. In addition, Table 5.3 shows the tracking results of θ and ψ for the controllers, which verify whether the SP mitigates the disturbance d better despite the time delay than the existing methods. Then, given convergence, ev(t) is guaranteed to tend to zero according to Proposition 5.3 for a time-varying reference trajectory.

Table 5.2. List of Specifications of Mechanical and Control Parameters for Numerical Simulation

Overview

A sensory conflict theory was developed to explain that SS is caused by conflicts between signals from different sensory systems [93]. However, SS still occurred due to a false indication caused by limited ranges of motion and control error despite MC. A Stewart platform [21] has been commonly used in the motion simulator capable of six DOFs motion, but it has limited motion ranges.

Experimental Setup

Spherical Motion Platform for Flight Simulator

In other words, the conflicts also arise from the mismatch between current perception and past experience. Also note that the body frame is xbybzb at the CR of the cockpit sphere, since the cockpit is designed to seat the human as close to the center as possible to reduce the unwanted gyro effect, as shown in Fig. The rotation and translation of the cockpit sphere is also measured from an IMU sensor, and the results are fed into the control system.

Figure 6.1. Flight simulation using the spherical motion platform.

Motion Cueing Algorithm for Motion Simulator

Conventional Washout Algorithm
Modified Washout Algorithm for Spherical Motion Platform
Limitation of Conventional Washout Algorithm

So, for the rotational movement, range limit and high-pass filter are unnecessary, and this shows that the SMP has the ability to reproduce the rotational movement. Moreover, the SMP has better performance for tilt coordination due to the larger workspace of rotational motion compared to the conventional motion simulator. The algorithms are limited to specific motion simulators (only parallel motion simulators that in and furthermore, the high computational burden of the model predictive controls limits practical implementation.

Table 6.1. Human Perception Threshold for Rotational and Translational Motion [124]

Evaluation of Sense of Reality According to Motion Range

Participants and Procedures

Therefore, the experiment is performed with a scale gain of 0.25 for safety as the scale difference does not significantly affect motion sickness.

Evaluation of Motion Sickness

Result of Subjective and Objective Measurements
Correlation Between Physiological Responses and Simulator Sickness Rating
Conclusion and Discussion

In general, the EDA of the moving group is smaller than the EDA of the non-moving group. The BVP of the exercise group was higher than that of the no-exercise group when the difference was significant. The TEMP of the exercise group is thus lower compared to the no-exercise group when there are significant differences between the two groups.

Figure 6.4. Simulator Sickness Questionnaire scores of the no-motion and motion groups

Accomplishments and Contributions

The experimental results proved the better position tracking and orientation control performance of the proposed controllers regardless of the dynamic uncertainties and kinematic uncertainties compared to the conventional controllers. PPC was introduced to compensate for the time lag and disturbance effects in SMP operation. Numerical simulation and experimental results verified the feasibility of the proposed controller for application in the motion platform.

Future Works

Son, “Design and motion control improvement for a spherical wheel-based motion platform,” IEEE/ASME Trans. Shintemirov, “Constrained orientation control of a spherical parallel manipulator via online convex optimization,” IEEE/ASME Trans. Son, “Sliding mode control with multi-sensor fusion for spherical motion platform orientation,” IEEE Int.