# Development of a Novel Omnidirectional Treadmill-Based Locomotion Interface Device with Running Capability

^{*}

## Abstract

**:**

^{2}. Moreover, through a pilot test with the proposed locomotion interface device, we verified that the fast directional changes during walking and running with the designed speed adaptation controller do not exceed the acceleration performance of the proposed system. Due to its wide range of movement speeds and acceleration capabilities, and lack of any motion constraints, the proposed locomotion interface device with a novel ODT can be used as a representative platform in various VR environments to enhance the immersive experience.

## 1. Introduction

_{X}vector, while the Y-axis translational motion is generated by rotational actuation of the belt of each segment along $\text{}\overrightarrow{\mathrm{A}}$

_{Y}vector. Thus, the 2D treadmill combines small treadmills assembled orthogonally to create a single, large treadmill. An ODT provides an infinite ground plane by generating independent belt motions along two orthogonal axes (X and Y). In the cases of Cyberwalk [12] and Torus treadmill [14], Y-axis translational motion is generated by individual actuators attached directly to each unit segment. This increases the inertia of the segments; thus, this design requires a very large amount of power to rotate all the segments (X-axis motion). As the weight of each segment is increased, the acceleration performance is greatly reduced.

## 2. LI Device Design for Fast Motion

#### 2.1. Actuation of Unit Segment Belt by Geared Transmission

#### 2.2. Transmission Design for Omnidirectional Motion

_{Y}direction, while the friction on the tooth surface caused by motion in the $\text{}\overrightarrow{\mathrm{A}}$

_{X}direction is reduced by the passive rotation of the toothed rollers, similar to an omni-wheel. The toothed roller for reducing the frictional force is designed by body of rotation of an involute toothed part of a normal geared pulley along the rotational vector $\overrightarrow{N}$ shown in Figure 3b. This rotational vector also represents the axis of the passive rotation of the toothed rollers when segments move along the X-axis.

_{h}= 3.2 mm), tooth width (w

_{h}= 2.76 mm) and input angle of the tooth (λ = 25 deg). Moreover, GOPS design also considers the parameters depended on the number of teeth (Z = 36) such as radius of the pitch circle (r

_{p}= 57.295 mm), total radius (r = 56.375 mm) of the GOPS and the radius of the base circle (r

_{b}= 53.175 mm) because the frontal projection of the GOPS is identical to a normal geared-pulley profile.

_{GOP}) as follows:

_{GOP}represents the number of teeth in one toothed roller. It can also define an appropriate number for n because the number of teeth must be a natural number. All toothed rollers have an index number (i

_{th}) according to the range 1 ≤ i

_{∈ℕ}≤ n, as shown in Figure 4. Odd and even numbers in the toothed roller index (i) make up each separate geared omni-pulley (GOP) (see also Figure 3), and two GOPs are combined to form one GOPS.

_{roller}as the GOPS design parameter, whose range is calculated by the general geared-pulley parameters (p, t

_{h}, etc.) and the GOPS configuration parameter (n) that has already been determined. Due to the shape of the toothed roller, the radius at its end (r

_{roller}) is used to define its size. Moreover, r

_{roller_thick}is defined as the largest radius at the center of the toothed roller, as shown in the right-side image of Figure 4. r

_{roller}has the following range:

_{roller}is calculated to maintain the proper tooth shape, and its maximum size corresponds to the circumcenter point to avoid interference between the arrangements of each toothed roller installed in a GOP. The selected r

_{roller}defines the value of r

_{roller_thick}according to the following relationship:

_{roller}is 10.82 mm, which is selected considering the range of r

_{roller}calculated using Equation (2) (3.6~16.27 mm), and d

_{o}is selected as 28.5 mm to avoid interference between the toothed rollers of the GOPs.

#### 2.3. Realization of Stable Omnidirectional Motion

_{GOP}.

#### 2.4. Design of Actuation System for Desired Performance

^{2}is generated [22]. Thus, the target performance of velocity and acceleration of the ODT were set to 3 m/s and 3 m/s

^{2}, respectively, to simulate running and stopping. To validate the target performance, dynamic analysis was performed using a commercial multibody dynamics software (ADAMS), as shown in Figure 6. To obtain realistic analysis results, the boundary conditions, including the mass and inertia, were set based on 3D modeling, gravity, the initial X-axis drive chain tension (3000 N) and the Coulomb friction due to contact between the segment belt and the Teflon-coated segment structure [19].

^{y}, Motor2

^{y}) actuate the power transmission belts, which in turn drive the gearboxes. The gearboxes actuate timing belts for rotation of the 3 GOP shafts simultaneously as a mechanically coupled power transmission system. The actuation mechanism for the X-axis also uses a distributed power design, in which the four drive chains are mechanically coupled. In Figure 7b, Motor1

^{x}and Motor2

^{x}simultaneously actuate the drive chains by actuating the sprockets.

_{c}

^{i}), where

**v**= [v

_{c}_{c}

^{x}

**v**

_{,}_{c}

^{y}]

**is the desired speed of the active surface, and v**

^{T}_{1}

^{i}and v

_{2}

^{i}correspond to the velocity of each motor, determined via encoder feedback with respect to the X or Y-axis, T

_{c}

_{1}

^{i}and T

_{c}

_{2}

^{i}are the torque values. Synchronization for reducing the difference of each motor’s speed (v

_{v}

^{i}) and torque (v

_{T}

^{i}) in each axis was achieved by proportional-derivative (PD) control, as follow:

_{Pv}and k

_{Dv}are the positive gains of the speed controller. The torque synchronization controller is also implemented using PD control, as follows:

_{Pt}

^{i}and k

_{Dt}

^{i}are the positive gains of the torque synchronization controller, and T

_{c}

_{1}

^{i}and T

_{c}

_{2}

^{i}are the torque values for the control input of C

_{t}

^{i}. To secure control stability of the low-level controller, suitable gains were selected based on the Nyquist criterion by considering the backlash model [19,25]. In terms of the Nyquist criterion, the intersection shows a marginally stable condition, i.e., within 0.4 Hz. Regarding the gain of the controller, the X and Y values were set as; k

_{Pv}

^{i}= 0.1 and 0.5, k

_{Dv}

^{i}= 0.02 and 0.04, k

_{Pt}

^{i}= 0.2 and 0.4, and k

_{Dt}

^{i}= 0.08 and 0.1, respectively.

#### 2.5. Fabricating the ODT and Verifying the Performance

^{2}. In addition, to verify the low-level controller, the velocity and torque transmitted from the motors were also measured.

^{2}, respectively.

## 3. LI Control for Omnidirectional Running

#### 3.1. Design of High-Level Controller

_{d}is the desired position, v

_{w}is the intentional velocity of the user, and v

_{c}and a

_{c}are the treadmill belt velocity and acceleration commands, respectively. In the model shown in Equation (6), v

_{c}is applied to the treadmill servo motors, where its dynamics are compensated by the low-level controller. To avoid sudden variations in belt acceleration, the dynamics are extended using a

_{c}. The final control input (v

_{c}) can be obtained by time-domain integration of a

_{c}. To maintain the user at the center position, the desired position (x

_{d}) is set to zero (i.e., x

_{d}= 0) and saturation is applied to v

_{c}to remove the oscillatory command due to the negative position error when a user does not intend to walk.

^{user}, Y

^{user}). The X

^{user}-axis is set up along the anterior-posterior (AP) direction of the user’s body, and the Y

^{user}-axis is along the medio-lateral (ML) direction. The walking intention (${v}_{w}$), referred to in treadmill coordinates, is converted to ${v}_{w}^{user}$ in the user coordinates. To interface with the walking intention ${v}_{w}^{user}$, the control command ${v}_{c}^{user}={\left[\begin{array}{cc}{v}_{c}^{X,user}& {v}_{c}^{Y,user}\end{array}\right]}^{T}$ is generated by the high-level controller with respect to the user coordinates. Then, this control command is transformed into treadmill coordinates as ${v}_{c}$. According to the adaptive treadmill controller, which can be considered to be a cascade system [28], the linear growth rate of the interconnection term and the convergence property represented by Equation (6) guarantee the stability of the entire system. Thus, the control command (${v}_{c}$) for interfacing with the 2D gait information is derived as follows:

**=**[x

^{user}, y

^{user}]

^{T}represents the position error in the user coordinate system,

**k**$\in {R}^{2\times 2}$ is a diagonal positive constant matrix which determines the convergence rate of the observer output to the true value of ${\widehat{v}}_{w}^{user}$ stably [30], and

_{o}**ξ**is the state of the feed-forward term, Finally, the total control law including the feedback command (${\mathsf{\mu}}^{user}$) in the user coordinate system can be derived as follows:

**α**

_{1}$\in {R}^{2\times 2}$ and

**k**

_{s}$\in {R}^{2\times 2}$ are diagonal positive matrices, β, k

_{a}and α

_{2}$\in R$ are positive constants, and

**q**is the error of the velocity command defined as ${v}_{c}^{user}-{R}_{z,\theta}^{\mathrm{T}}$

**v.**The applied RISE control scheme for the uncertainty compensation reduces position error via a closed-loop system while guaranteeing stability and asymptotic convergence of the position error by the estimation property of the RISE control scheme with the applied observer [22]. Similar procedure of the high-level control design for a user-driven treadmill such as observer-based control is also performed in the other research [30].

^{user}-axis), as shown in Figure 12. Although the user walks straight ahead, the waist shows a swaying motion in the ML direction. The ML motions of a user during walking can affect the treadmill controller by inducing a continuous response. In the study reported in [31], the maximum displacement of the body’s center of mass in ML direction was shown to range from 5.65–8.33 cm. Thus, the dead zone in the ML direction applied in the current work is ±4 cm.

#### 3.2. Performance of Curvature Radius

**v**

_{c}, in the treadmill frame can be approximated as follows:

_{initial}is the initial user orientation angle, and ${v}_{w}^{user}$ is the user’s intended velocity that is assumed to be a positive real value along the X

^{user}-axis (see Figure 12). Therefore, the maximum velocity and acceleration that the ODT can generate relates to the intended velocity and the angular speed of a user as follows (here, θ

_{initial}= 0):

^{user}and Y

^{user}axes. If the intentional user velocity is less than 3 m/s and the proposed ODT has an acceleration limitation of 3 m/s

^{2}, the allowable range of the angular velocity $\dot{\theta}$ of the user, shown in Figure 13a, can be calculated from Equation (11). Given that the intended velocity (${v}_{w,given}^{user}$) is not directly measurable and is instead an estimated value, the user’s travel trajectory ($\overrightarrow{L}$

^{VR}), defined in VR coordinates (X

^{VR}, Y

^{VR}), can be calculated by integrating the

**v**

_{c}into Equation (12), as follows:

^{VR}has arbitrary curved paths in the VR, the curvature radius of $\overrightarrow{L}$

^{VR}can be calculated as follows:

^{2}), as shown in Figure 13b. It should be noted that due to the limited acceleration performance defined in Equation (11), the minimum radius of curvature is dependent on both the user’s speed and the allowable angular velocity.

## 4. Pilot Study Results of Locomotion Interface Device with 2-Dimensional Running

#### 4.1. High-Level Controller Setup for Locomotion Interface

#### 4.2. Running Performance of High-Level Controller

^{2}. Thus, the proposed locomotion interface device can handle about 2.7 times the maximum acceleration achieved when a user changes direction while running at 1.8–2.8 m/s.

_{c}is proportional to the user’s speed and is inversely proportional to the angular velocity of the user.

## 5. Conclusions

^{2}). Thus, the developed locomotion interface with the fast ODT is expected to serve as a representative VR interface device for normal walking and running, with many potential applications. In future works, an intelligent controller will be designed to provide an immersive VR experience by simulating more complex types of locomotion, such as quick turning, side stepping, and backward walking. Furthermore, in the future works, it is planned to conduct User Experience Questionnaire (UEQ) with the more users for a qualitative evaluation of the feeling of the subjects who have an experience of gait interface with the proposed system.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Omnidirectional treadmill (ODT) concept (see Figure 2 for the cross-sectional view), and the geared omni-pulley (GOP)-based actuation scheme of the proposed ODT to generate infinite 2D ground.

**Figure 2.**Cross-sectional view of the Y-axis motion of a 2D treadmill (unit segment): (

**a**) Transversal treadmill actuated directly by an actuator (Torus or Cyberwalk treadmill), (

**b**) Frictional transmission mechanism based on the Omni-wheel via the frame-fixed motor (US army ODT), (

**c**) The proposed mechanism based on gear-driven transmission via a frame-fixed motor.

**Figure 3.**(

**a**) GOPS design including toothed rollers, (

**b**) The front projection of GOPS design with a normal geared-pulley parameter, and GOPS configuration with its geometric analysis.

**Figure 5.**(

**a**) Drive chain of segment treadmills for X-axis motion, (

**b**) Design and operation of the synchronizer mechanism.

**Figure 7.**Mechanically coupled actuation system design: power transmission mechanisms of (

**a**) the Y-axis and (

**b**) the X-axis.

**Figure 9.**The developed ODT using GOP actuation on the active surface, distributed actuation, and the dynamics simulations results.

**Figure 10.**Verification of the performance using a sinusoidal motion command for surface acceleration of 3 m/s

^{2}. (

**a**) Y-axis speed synchronous performance, (

**b**) Y-axis torque synchronous performance, (

**c**) X-axis speed synchronous performance, and (

**d**) X-axis torque synchronous performance.

**Figure 12.**Expansion of high-level LI controller; 2D locomotion control commands and the dead zone in the saturation direction of the motion command in the user coordinates.

**Figure 13.**Performance analysis of the proposed 2D treadmill. (

**a**) The allowable range of angular velocity, given the acceleration limitations of the 2D treadmill and the user velocity, and (

**b**) The minimum radius of curvature based on the performance of the proposed ODT.

**Figure 14.**System configuration and gain parameters of the high-level controller used to evaluate running performance.

**Figure 15.**Pilot study results. (

**a**) The control command ${v}_{c}^{user}$ of the high-level controller, (

**b**) angular velocity θ of the user, (

**c**) velocity command (v

_{c}) and the actual velocity (v) of the active surface in treadmill coordinates (X, Y), (

**d**) magnitude of the acceleration generated by the treadmill, (

**e**) trajectory of the user in virtual reality (VR) coordinates (X

^{VR}, Y

^{VR}), and (

**f**) the radius of curvature r

_{c}of the user.

**Figure 16.**Position errors in time domain and their ellipse fitted graph in the treadmill coordinate.

Item | Specifications | |
---|---|---|

System frame dimensions | 2780 mm × 3310 mm × 640 mm | |

Active surface area | 2.5 m × 2.5 m | |

Unit segment dimensions | 100 mm × 2577 mm × 70.5 mm | |

Unit segment weight | 9 kg | |

Number of segments | 64 units | |

Number of active segments | 27 units | |

Number of GOPS in 1 GOP shaft | 54 units per 1 GOP shaft | |

Chain and timing belt | X-axis drive chain | Y-axis segment belt |

Pitch | 18.875 mm | 10 mm |

Width | 9.4 mm | 96 mm |

Actuation part specification | Sprocket | GOP shaft |

Pitch diameter | 396.375 mm | 114.59 mm |

The number of teeth | 21 | 36 |

Axis | Required Pulley Torque | Required Pulley Angular Velocity | Power |
---|---|---|---|

X | 1768 Nm (max.) | 15.63 rad/s | 28 kW (peak) |

563 Nm (avg.) | 8.8 kW (nominal) | ||

Y | 148.5 Nm (max.) | 52.35 rad/s | 8 kW (peak) |

81 Nm (avg.) | 4.2 kW (nominal) |

Y-axis Drive Mechanism | Active Surface Area/Thickness | Actuator Specification | Max. vel. (km/h) | Max. acc. (m/s^{2}) | ||
---|---|---|---|---|---|---|

US army ODT ^{1} | Frame stationery motor with omni-wheel | 1.3 × 1.3 m^{2}/0.46 m | X-axis | 4 kW (1 EA) | 7.2 | Under 1 |

Y-axis | 4 kW (1 EA) | |||||

Cyber Walk | Segment attached motor | 6.5 × 6.5 m^{2}/1.5 m | X-axis | 40 kW (4 EA) | 7.2 | 0.5 |

Y-axis | 37.5 kW (25 EA) | 10.8 | 0.75 | |||

Torus treadmill | Segment attached motor | 1 × 1 m^{2}/0.5 m | X-axis | 200 W (1 EA) | 4.3 | 1 |

Y-axis | 960 W (12 EA) | 4.3 | 0.8 | |||

Proposed ODT | Frame stationery motor with GOPS ^{2} | 2.5 × 2.5 m^{2}/0.64 m | X-axis | 8.8 kW (2 EA) | 10.9 | 3 |

Y-axis | 5.8 kW (2 EA) | 10.9 | 3 |

^{1}: omnidirectional treadmill, GOPS

^{2}: geared omni-pulley set.

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**MDPI and ACS Style**

Pyo, S.; Lee, H.; Yoon, J.
Development of a Novel Omnidirectional Treadmill-Based Locomotion Interface Device with Running Capability. *Appl. Sci.* **2021**, *11*, 4223.
https://doi.org/10.3390/app11094223

**AMA Style**

Pyo S, Lee H, Yoon J.
Development of a Novel Omnidirectional Treadmill-Based Locomotion Interface Device with Running Capability. *Applied Sciences*. 2021; 11(9):4223.
https://doi.org/10.3390/app11094223

**Chicago/Turabian Style**

Pyo, Sanghun, Hosu Lee, and Jungwon Yoon.
2021. "Development of a Novel Omnidirectional Treadmill-Based Locomotion Interface Device with Running Capability" *Applied Sciences* 11, no. 9: 4223.
https://doi.org/10.3390/app11094223