Recovery Motion Analysis for False Ceiling Inspection Robot

Abstract

The false ceiling plenum is a common and essential part of building infrastructure. However, false ceiling infrastructure requires constant maintenance, which is cumbersome and dangerous for humans since they have to work at high heights and conduct repetitive actions for false ceiling panel replacement. As a solution, robots have been developed to inspect false ceilings. However, these robots can fall during navigation in false ceilings, such as in rugged areas. Therefore, this paper discusses the self-righting capabilities implemented on a false ceiling inspection robot known as FalconX. Mechanisms that aid in self-righting the robot back to a moving position after being toppled due to obstacles within the false ceiling environment were explored, along with their force analysis. Simulations were conducted in Gazebo environments and real hardware experiments were conducted to validate the robot’s self-righting capabilities. The experimental results confirm the self-righting capability of the robot.

1. Introduction

False ceilings are often used in buildings to store and hide disorderly but essential building infrastructure [1,2] such as heating, ventilation ducts and air-conditioning (HVAC), electrical wiring, and plumbing systems [3]. The false ceiling space, also known as the plenum, acts as an infrastructural measure to limit fire damage [4] and regulate the thermal conditions [5] and acoustical capabilities [6,7] of the main space below. Maintenance works on false ceilings have to be conducted on a regular basis. Otherwise, there would be potential health and safety compromises to building occupants because of pest infestations and other forms of degradation in false ceilings [8]. Infrastructural elements could be tampered with by pests inhabiting false ceilings if maintenance is neglected. Pollutants or airborne pathogens can enter damaged HVAC vents and circulate in the building, spreading diseases through the air if maintenance is not regularly carried out. Thus, sporadic checks of false ceilings can lead to the failure of amenities such as HVAC or lighting fixtures, causing problems for the occupants using the rooms below.

The need for frequent inspection and maintenance puts a heavy strain on the skilled workforce. These people have to work at height and continually with the risk of falls. Falls from high heights can cause severe contusions, bone fractures, and other injuries. These injuries can prevent human workers from working for extended periods of time while they recover. Maintenance companies can also face financial losses and manpower shortages when injured personnel are unable to work.

The existing false ceiling maintenance process is greatly dependent on human labour. With the myriad of obstructions that exist within false ceilings and the poorly lit conditions, there are many risks faced by human workers during the inspection phase of false ceiling maintenance. The components in the plenum are often laid for convenience during construction instead of ease of access and maintenance. Disorganised wiring, piping and the haphazard arrangement of other elements can cause higher occurrences of injuries to human workers. This does not exclude unexpected encounters with pest infestations [9] or the dislodging of heavy items while performing maintenance in the plenum. Each false ceiling site is different across every building and sometimes varies among individual floors due to differing requirements in fixtures and amenities. Design guidelines are often neglected for ease of installation and meeting tight deadlines. Wiring and the compacted arrangement of fixtures close together can pose as navigational and visual obstructions for inspection tasks, even for robotic aids.

There are studies that look into automated inspection solutions to alleviate the burden on skilled human labour for false ceiling inspection works. Many research interests in robotic solutions have been taken up in recent years to aid human workers in the field of maintenance for the built environment [10,11]. These mobile robotic solutions are often made small and lightweight to navigate tight and hard-to-reach spaces and are often installed with cameras to conduct visual inspection [12,13,14,15].

However, using robotic means for such tasks still carries the risk of having the robot encounter obstacles within the false ceiling plenum and being stopped prematurely before completing its visual sweep of the area. With the haphazard layout of amenities in the false ceiling plenum, robots can get stuck due to its form or locomotion methods, getting caught by stray cables and pipes or the crowded layout of infrastructure within false ceilings. This is counterproductive for inspection works as manpower would still then be required for the manual retrieval of the robot.

Self-righting robotic mechanisms have been explored in works such as [16] for toppled robots on inclined planes [17,18], regarding usage of added tail mechanisms for self-righting, and even self-righting mechanisms used for jumping robots [19,20]. However, little research regarding self-righting robots has been conducted for robots working within complex and haphazard environments such as a false ceiling plenum.

This study contributes to this field by conducting an analysis of the self-righting motion of a novel false ceiling inspection robot called FalconX. FalconX builds upon the existing class of Falcon false ceiling inspection robots for improved surveys of false ceilings. The research goal of this study was to determine and analyse a mathematical model for the self-righting mechanism of FalconX and validate the model using the robot in real life.

Section 2 of this paper discusses the typical fixtures found in false ceilings, the need for their regular maintenance and how robotic aid can alleviate issues faced by human workers during inspection. Section 3 details the Falcon class of inspection robots and their capabilities and limitations. Section 4 introduces the mechanisms added to the FalconX robot for re-balancing after being toppled by fixtures in the false ceiling setting. Section 5 discusses the force analysis for the re-balancing mechanism. Section 6 then concludes this paper with future directions to refine the FalconX robot for enhanced false ceiling inspections.

2. Background

The most common type of false ceiling is the concealed panel grid suspended ceiling used in many office buildings [21]. It is often accessed by means of specific access panels or hatches to reach the plenum. However, using the access panels carries work risks as it requires the human worker to be familiar with the scope of their tasks. Mishandling of the access panels prevents proper sealing of the false ceiling space when the maintenance work is completed and allows entry to pests that can reside in the dark conditions, which are ideal for them to hide from their predators in the urban environment. The lack of standardisation in the design aspect for false ceiling panel dimensions makes it difficult for regulated safety measures in using access panels and how to design them for repeated use and incident prevention.

2.1. Problems Encountered During Indoor False Ceiling Maintenance

Concealed false ceilings have the issue of being neglected as the components are hidden from view. Problems when false ceilings are left unattended over long periods of time include, but are not limited to, (a) the presence of pests and rodents that enter false ceilings through crevices or gaps, (b) ventilation and plumbing system leakage that leads to hazardous chemicals and vapours circulating through the building, (c) mould or stains on false ceiling panels, and (d) the eventual damage or breakdown of infrastructure due to neglect and deterioration. These problems can escalate in severity and incur large repair costs over time or even cause health ailments for occupants. To counter such issues, Facility Management (FM) inspection works and examinations of the structural integrity of buildings themselves are often conducted regularly for the inspection of support structures that reside above false ceilings.

Moreover, removing a single false ceiling panel is unlikely to enable a human worker to view the entire false ceiling plenum since, without the aid of additional equipment such as expensive and bulky endoscopic cameras, the worker’s field of view would likely be obstructed by the complex and non-systematic arrangement of infrastructure within the false ceiling plenum. Hence, the removal of multiple panels at different points of the false ceiling is necessary to comprehensively inspect a false ceiling interior. This process of removing and replacing panels requires the constant and cumbersome shifting of equipment to allow a human worker to reach a false ceiling at a height; this also adds to the wear and tear of false ceiling access panels. These issues could be mitigated if robot-inclusive principles were implemented for false ceiling plenums [22].

These robot-inclusive principles would be cumbersome to implement retroactively for existing buildings. Mobile robots could enable automated robotic inspections within false ceilings for buildings. The dimensions of the robot would need to account for a site’s layout in terms of robot-inclusive Accessibility and Observability principles. Thus, these robots need to be designed as small and lightweight to nimbly navigate within constrained spaces, while still accounting for the robotic components for inspection tasks. For other sites, spatial information of false ceilings would be needed to design a customised robot suited for the site that could move efficiently through the zone for comprehensive scans of the false ceiling.

2.2. Using Mobile Robotic Solutions for False Ceiling Inspection

Using mobile robots for false ceiling inspection is a promising solution for the multiple problems encountered regarding successful false ceiling maintenance [23,24]. Robots with various designs in terms of locomotion and form factors are capable of performing tasks in the plenum that are difficult or dangerous to reach for humans. Locomotion modes by such robots can be in the form of wheels, tracks or jointed legs. These mobile robots can perform regular inspections within false ceiling plenums when equipped with visual cameras and thus minimise human intervention in the maintenance process. This would directly reduce incidents of human occupational accidents when working at high heights and injuries involving false ceiling elements or human fatigue. Prior to implementation, case studies would be examined of robots made for navigating constrained spaces and in-pipe inspections [25].

Halder et al. [26] reviewed the various types of robots used in the inspection and monitoring of built infrastructure, mostly having unmanned aerial vehicles (UAVs) and drones to conduct the tasks. The drones usually required an open space to navigate and relay information, instead of working in constrained spaces, as in our case. Lattanzi and Miller [27] also noted in their review of inspection robots that there is a trade-off between sensor technologies and locomotion capabilities for this kind of inspection robot. Thus, little work has been conducted on this specific topic of robotic aid for false ceiling inspection. Research papers found on false ceiling inspection robots are mainly centred around other versions of Falcon robots. Other inspection robots gathered in the literature review were not designed for obstacle crossing [28,29] or had cumbersome equipment such as tethers and excessive points in the design that could cause the robot to become trapped or entangled [30,31].

Commercial designs for inspection robots in tight spaces such as SuperDroid [32] utilised tracks for robot locomotion. These designs would face the issue of being trapped by the low-height false ceiling support frame when the frame is between the locomotion system, preventing the main body from extracting itself. Moreover, crawler robots made by Uplink Robotics and Techmatics use large wheels to avoid this issue but face a problem where they are unable to access short crawlspaces. These robots were not designed for self-righting capabilities. The limitations of these robots and the operation environment, ability of equipment working within the isolated false ceiling, or inspection range would not match the requirements of the task. This shows that using robotic aid for false ceiling inspection is still a potential research area worth exploring.

Koh et al. [33] described a duct-cleaning mobile robot using cameras and tethered means to navigate in ducts and a laser system to track the cross-section within the duct. This design had the basic requirements an inspection robot would need for its tasks. However, its large size is not suitable for our use case of an entire false ceiling zone.

Filipek and Kaminski [34] detailed a robot built for inspection with a mounted arm end-effector, with a camera separately mounted on the robot’s vertical support wheel, built from aluminium profiles. It was controlled remotely with attached cables. This provided a basis on what components and items would be expected of an inspection robot. However, this robot had multiple protrusions and positions whereby it could be caught by the disordered environment within a false ceiling interior, which would be counterproductive for maintenance and inspection work.

Ab Rashia et al. [35] reviewed the various robots built for in-pipe inspection and other constrained spaces. The review paper investigated findings regarding various locomotion modes, providing insights into their kinematics and behaviour within constrained environments. For our case, we focus on wheeled mobile bases as the means of locomotion. A wheeled base provides the benefits of ease of operation and replacement if needed, along with a well-researched locomotion mode to work upon.

The Mantis robot is a wall-climbing robot that detects surface defects and can work at heights due to its use of vertical adherence as a means of travel and mounting [36]. Its three-module design enables it to circumvent vertical support mullions along walls and can implement visual capabilities to inspect ceilings. However, it is limited to inspecting areas near walls due to its need for vertical mounting points for locomotion.

Self-righting robots typically involve legged or bipedal robots, using the limbs as end-effectors to push themselves off a surface and flip themselves back to their neutral position to operate their intended movements and tasks again. This function is critical for robots working in complex environments [16,37] to allow them to recover without external help in constrained areas.

Some studies regarding self-righting involve multi-legged robots [38,39]. Other research works take inspiration from nature [37], utilising an additional tail effector [17,18] or wing effectors [16,40] to achieve similar results to let robots recover their operational state after falling [41].

These robots were mainly tested under ideal conditions or used in the domain of duct inspection rather than a full false ceiling plenum. These robots were not designed to adapt to dark and disordered conditions for inspecting false ceiling interiors. The navigation requirements within disorderly structural arrangements and MEP components were not thoroughly explored in the case studies. A common type of inspection robot possesses wheel or tracked mechanisms. These mechanisms allow for easy deployment and adaptation in diverse settings, as well as having fewer components compared to legged or crawling modes of locomotion. As such, to maximise the efficacy of false ceiling robots in their inspection tasks, they should operate with minimal assistance from human operators until retrieval. This would involve determining the form factors and mechanisms to enable the robot to extract itself from scenarios whereby it gets stuck in a complex false ceiling environment by self-righting after being toppled over.

The previous versions of Falcon robots were small inspection robots that utilised tracks for locomotion [42,43,44]. They were designed for false ceiling inspections within buildings that comply with the AS/NZS 2785 and BS EN 13964 false ceiling design standards [45]. They are installed with cameras for vision, enabling human workers to control the robot and view the plenum remotely for false ceiling inspection.

The previous tracked version of the Falcon robot had issues with getting stuck due to protrusions in the false ceiling that trapped the robot in the middle, with the tracks being unable to pivot the robot away from the obstacle, or getting trapped due to the layout and positioning of the robot, as seen in Figure 1. This study thus sought to mitigate cases where such false ceiling inspection robots would become stuck in disordered false ceiling infrastructure by adding recovery mechanisms and determining the motions required for recovery.

More research is needed to develop a refined mobile robot that is lightweight and that has visual capabilities to scope out false ceiling interiors and the ability to self-right.

3. Materials and Methods

FalconX is a new design of false ceiling inspection robot with a recovery mechanism. The robot design built in real life is shown in Figure 2. The FalconX robot was designed by the authors and is not commercially available. The robot has a forward-facing visual camera and illumination LEDs in front of the robot for lighting up dark, false ceiling spaces during operation. The main changes involve using a reconfigurable base for the robot to actively climb over false ceiling support runners and other low-height obstacles. The robot has a mounted storage shell on top to enable it to roll over and continue moving even when flipped and provision for a compact wireless WiFi visual camera for easier maintenance and replacement. Rounded wheel caps are used to mitigate scenarios where the robot would be stuck when flipped on its side. The mass of the robot is 576 g. The dimensions of the robot’s bounding box are 20 cm in length, 18 cm in width and 9 cm in height. The wheel diameter is 5 cm, while the length of the rotary arm is 8 cm, also seen in Figure 3.

Thus, the FalconX robot utilises a new wheeled base with rotary arms, with wheels on the ends to enable the robot to circumvent false ceiling support runner grid structures. This enables the robot to avoid scenarios where it becomes stuck due to the spatial constraints within the false ceiling. The robot has zero turning radius, beneficial for navigating within the constrained space in false ceilings.

The design of the FalconX wheel base rotary wheels allows the robot to climb low-height obstacles (less than or equal to the wheel diameter of 5 cm) by rotating the rotary wheels over the obstacle and using them as a pivot to bring the robot over the obstacle, as seen in Figure 4.

Upon encountering a low-height obstacle, the robot’s rotary arms are lifted over the obstacle (Figure 4(1–5)). The rotary arms are then used to pull the main body of the robot over the low-height obstacle (Figure 4(6–9)). Once the robot passes over the obstacle, the rotary arms are returned to the original position (Figure 4(10–12)) and the FalconX robot can continue its inspection tasks.

The new model is wider at its base to reduce the probability of toppling when travelling on a flat plane, as seen in Figure 2. Figure 5 shows the first contact points of the robot with the ground plane if toppled from front and back directions.

A front bumper wheel on the front edge of the robot enables the robot to roll when it is tilted forwards. The camera holder design also keeps the robot from resting along its front edge but also lets the offset robot’s centre of gravity to self-right the robot back to its neutral position.

The robot has two support wheels at its back edge, as seen in Figure 2. The top support wheel enables continued movement even after flipping over when the rotary wheels are in the correct position. The other bumper wheel at the back edge is the first contact point when the robot is tilted backwards.

However, the efficacy of robotised false ceiling inspection is also dependent on the robot’s ability to recover and continue moving. The robot currently uses a rechargeable LiPo battery for driving and a power bank of 10,000 mAh for the camera and light modules. Current tests indicate a battery life of about 6 h for the inspection equipment and about 1 day of continuous movement of the wheels from full battery levels. The robot can then explore more of the false ceiling plenum or return to its retrieval point. The following experiments and results indicate the means of recovery for FalconX after being toppled in various directions due to potential stopping conditions within the false ceiling plenum space during operation.

3.1. Mathematical Formulation: Jump-Start Motion

For FalconX, the main method of recovery is to position the rotary wheels perpendicular to the robot’s length and ground surface, thereby letting the robot move using a 3-point wheeled contact with the ground surface. When moving off from a stationary position, the robot experiences a jump-start that jerks the back edge of the robot with the support wheels upwards. The pose the FalconX robot has to take before self-righting is seen in Figure 6a. This is achieved by having the rotary wheels contact the ground after the robot has been flipped over.

The motion for jump-starting the robot is crucial in getting the FalconX robot into the proper position for self-righting using a vertical surface. This can be modelled using a force diagram of the flipped robot, as seen in Figure 7. The main forces to be modelled would be those acting on the support wheel and those from the rotary wheels. The torque from the rotary wheels has to overcome the robot’s inertia to provide the upwards jerk for the robot to assume the required position for self-righting.

$$\begin{array}{c}T+mgw\prime -f{h}_2=0\end{array}$$

(1)

$$\begin{array}{c}w\prime =w_2\cos P\end{array}$$

(2)

$$\begin{array}{c}h\prime =\sqrt{{w_2}^2+{h_2}^2}\sin (\arctan {\displaystyle \frac{h_2}{w_2}}+P)\end{array}$$

(3)

$$\begin{array}{c}{T}_{lim}=fr\end{array}$$

(4)

Assume that after the robot reaches its flipped position, it keeps moving without further self-rotation. The torque balance equation on the robot is shown in Equation (1). Equations (2) and (3) are to calculate the horizontal and vertical distances between the contact point on the ground and the centre of gravity. Equation (4) is to calculate the torque limit to make the robot flip. These equations are based on static equilibrium and constant friction assumptions.

Solving the equations for f (the friction from the ground surface) and T (torque required to jump-start the robot to encounter the vertical surface for self-righting) with values $m=0.576$ kg, $g=9.81$, $h_2=$ 4.5 cm, $w_2=$ 6.5 cm, and angle P $=25°$ (i.e., the angle required for the support wheel to rotate from its existing ground contact position to that required for contacting the wall for self-righting) results in the following.

From the calculations based on the mathematical model, the amount of torque needed by the rotary wheel was calculated to be 0.2435 Nm for this FalconX iteration as seen in

Table 1. Step-by-step explanation and computation of required torque for jump-start motion.

Explanation	Formula	Calculation with Values
1. Horizontal distance between contact point and CG	$w\prime =w_2\cos P$	$0.065\ast \cos \left(25\mathrm{deg}\right)=0.0589$ m
2. Vertical distance between contact point and CG	$h\prime =\sqrt{w_2^2+h_2^2}\ast \sin (\arctan ({\displaystyle \frac{h_2}{w_2}})+P)$	$\sqrt{0.{065}^2+0.{045}^2}\ast \sin (\arctan (0.045/0.065)+25\mathrm{deg})$ = 0.0592 m
3. Torque balance at contact point	T + mg w′ − f h′ = 0	–
4. Frictional torque relation	T = f r	–
5. Solve for friction force f	$f={\displaystyle \frac{mgw\prime }{h\prime -r}}$	${\displaystyle \frac{0.576\ast 9.81\ast 0.0589}{0.0592-0.025}}=9.74N$
6. Final required torque	T = f r	9.74 ∗ 0.025 = 0.2435 Nm

. The robot’s motors would have to provide this amount of torque to the rotary wheel for the robot of this design and mass to achieve the intended self-righting pose. The robot could then self-right after achieving the required position. This is described in the next section and subsequently validated in the Results section.

3.2. Mathematical Formulation: Self-Righting

The toppled robot (in its upside down position) contacts the wall first, with its back and top support wheels at an angle above the horizontal plane (about 10° from horizontal) to achieve the configuration for self-righting. The calculation for the torque for the self-righting process is modelled in Figure 8 with the subsequent equations.

The values for the minimum torque ($T_{limit}$) needed for flipping the robot upon contacting the vertical wall were derived using Equation (5), an analogue of the power formula. Equation (5) was derived by balancing the torque required for self-righting with the forces from the wall, ground and the robot’s own gravity; hence, the overall moment is considered to be 0 at the robot’s wheel contact point with the ground plane, labelled as A in Figure 8. The parameters are then adjusted in the context of the robot flipping over, shown in Equations (6)–(9). $f_{grd}$ is the frictional contact force the robot has with the ground surface. It is also the same force for $C_{wall}$ to overcome in order to let FalconX move itself up against the wall and self-right afterwards.

$$\begin{array}{c}\sum M_A=-C_{wall}H+f_{wall}w+mg{W}_3=0\end{array}$$

(5)

The equation of static equilibrium on the x-axis leads to $C_{wall}=f_{grd}$ and $F_{wall}=\mu C_{wall}$. Thus, contextualising the terms to our case study gives

$$\begin{array}{c}-C_{wall}H+\mu C_{wall}W=-mg{W}_3\end{array}$$

(6)

$$\begin{array}{c}{f}_{grd}H-\mu f_{grd}W=mg{W}_3\end{array}$$

(7)

Simplifying Equation (9) gives the formula in Equation (3) for the force required for $f_{grd}$.

$$f_{grd}={\displaystyle \frac{mg{W}_3}{H-\mu W}}=mg{\displaystyle \frac{W_3}{H-\mu W}}=mg{\displaystyle \frac{W_3}{H(1-\mu \frac{W}{H})}}=mg{\displaystyle \frac{W_3}{H(1-\mu \tan \theta )}}$$

(8)

It is assumed that the force $f_{grd}$ comes from the moment that will be on the wheel of radius r, thus giving the formula for $T_{limit}$ to be determined as

$$\begin{array}{c}\hfill T_{limit}\ge f_{grd}r=mg{\displaystyle \frac{W_{3}r}{H(1-\mu \tan \theta )}}\end{array}$$

(9)

where m is the robot’s mass, g is the gravitational constant, r is the robot’s wheel radius, h is the vertical height from the top support wheel contact point with the wall to the ground plane, $h_3$ is the current vertical height of the centre of mass from the ground plane, $\mu$ is the frictional coefficient between the wall and the support wheel, w is the horizontal distance between the centre of the rotary wheel and the vertical wall, and $W_3$ is the horizontal distance between the centre of the rotary wheel and the robot’s centre of gravity. Constants are m, g, r and $\mu$, while the other parameters change during the process of self-righting. $\theta$ is the angle made by the top support wheel contact point with the wall. The virtual hypotenuse is made by connecting the top support wheel contact point with the wall and the rotary wheel contact point with the ground plane, labelled A denoted in Figure 8. These parameters are diagrammed in Figure 8.

This implies that as $\theta$ decreases when the robot pushes up during the process of flipping, $\tan \theta$ decreases and the denominator value gets larger, which leads to lesser $T_{limit}$ required for flipping over as the robot leans closer to the wall when flipping back to its neutral position.

Solving Equation (8) with parameter values of m = 0.576 kg, g = 9.81, wheel radius of 2.5 cm, $W_3$ = 5 cm, H = 16 cm, frictional coefficient of 0.2 and $\theta$ of 70°, the $T_{limit}$ at the initial contact of the robot and wall was calculated to be about 9.80 Nm. Assumptions needed for the equation to work would be for $\mu \tan \theta$ to be less than 1 (implying that the frictional coefficient $\mu$ has to be less than 1 or that $\theta$ has to be $\ge 45°$ for $\tan \theta$ to be smaller or equal to 1).

4. Results

The robot was modelled using Rhinoceros3D, while simulations were carried out in Gazebo for determining the required forces needed for the robot to self-right when flipped over onto its side or upside down. Diagrams of the forces required for the robot to self-right itself from a toppled state were analysed for their respective scenarios. The neutral position of the robot is as seen in Figure 2, fit for operation. The four main scenarios of the robot’s toppled states are as follows:

1.

Flipped onto side

2.

Flipped onto back edge

3.

Flipped onto front edge

4.

Flipped upside down

The robot’s mass was modelled to be concentrated as a point represented by the red dots in Figure 9, where its centre of gravity (CG) is closer to its base and towards the front of the robot, where the bulk of the robot’s weight is found. The main strategy of recovery is to let the robot roll onto its back if able to continue moving by using the rotary wheels and the top support wheel to move along the ground plane.

4.1. Scenarios Where Robot Falls onto Its Side

Rounded wheel caps mitigated scenarios where the robot would be stuck on its side. These rounded wheel caps enabled the robot to roll on its side compared to the conditions where they were kept flat. This modification enabled the robot to recover even when toppled onto its side, as seen in Figure 9b, when the rotary wheels were used to prop the robot onto its back and continue moving with the rotary wheels and top support wheel. ${\theta }_3$ is 12°. The offsetting from the robot’s CG caused rotation along the rounded wheel cap as the pivot point, leading to the robot rolling over onto its back, where it could utilise the recovery process whereby the robot self-rights upon toppling onto its back.

Further toppling was addressed by getting the robot to roll onto its back using the customised shell design. The rotary wheels were then used to form a three-point contact with the top support wheel and move upside down with the two rotary wheels and the top support wheel. Afterwards, the rotary wheels were then able to move the robot towards a vertical plane (such as the walls or dividers within the false ceiling) for it to pivot and flip over back to its neutral position, as described in the previous subsection whereby the robot can flip onto its back.

4.2. Scenarios Where Robot Falls onto Its Back Edge

In cases where the robot is tilted backwards, the robot uses the back bumper wheels and falls back to its neutral position due to the offset centre of gravity, as seen in Figure 9c. Angle ${\theta }_4$ is 3°, with the offset CG causing the robot to fall back to its neutral position. The rotary wheels helped in pushing the robot up from other obstacles and enable the robot to move if needed.

4.3. Scenarios Where Robot Falls onto Its Front Edge

For cases where the robot is tilted forwards (such as driving into a gutter or depression) within a false ceiling plenum, the front bumper wheel arrests further movement and the robot can recover by reversing and using the rotary wheels as leverage, as seen in Figure 9d, where angle ${\theta }_5$ is 72°.

4.4. Scenarios Where Robot Is Flipped Upside Down

For self-righting scenarios, the modifications enable the robot to self-right after being flipped upside down, with the curvature of the top shell preventing the robot from being stuck on its back. The low height of the storage shell enables the robot’s rotary wheels to contact the ground when raised perpendicularly from the robot body. The robot is thus able to move upside down to a vertical surface to pivot and flip itself over.

The robot model was simulated in Gazebo to use a vertical surface as leverage to self-right from a flipped-over position, as seen in Figure 10. The environment setup in Gazebo is shown in

Table 2. Setup parameters in Gazebo simulation.

Component	Description
Robot model	FalconX robot (a URDF file)
Wall	A cube (1.0 × 1.0 × 1.0 m), mass = 10 kg
Static friction coefficient of the wall	1.0
Sliding friction coefficient of the wall	0.8
Physics engine	Open Dynamics Engine (ODE)

. The robot formed a three-point contact with the ground with the rotary wheels and top support wheel. The initial jump-start from a stationary position jerked the back edge of the robot upwards to contact the vertical surface with the support wheels. After contacting the vertical surface as seen in Figure 10a, the robot needed $T_{limit}$ to push itself up and leverage the vertical surface to flip it the right side up. The force values of simulated $C_{wall}$ and $f_{wall}$ are shown in Figure 11, showing the contact force changes as the robot first contacted the wall surface.

This process was validated by having the actual robot pivot itself over using a wall and flip back to its neutral position with the proposed method, as seen in Figure 12. This enabled the FalconX robot to flip itself back to its neutral position after being toppled for retrieval.

A further validation test was conducted at a false ceiling site above the SUTD lab. Figure 13 shows the self-righting process performed in actual site conditions.

Figure 13a,b show FalconX in position for self-righting, Figure 13c–e show the self-righting process, while Figure 13f–h show the robot returning to its neutral state for further inspection. This hence validates the self-righting method put forth in this paper.

The mechanical modifications and recovery methods thus help the robot in prolonging its ability to move and explore false ceiling areas. This is pertinent for cases where a robot has toppled in a false ceiling. The ability to self-right reduces the need for manual retrieval and re-deployment and lets the robot continue inspection tasks with minimal human intervention. Thus, FalconX can navigate and inspect false ceilings with the ability to self-right if toppled due to the new design compared to the previous Falcon model. The real-life results in Figure 12 validate the simulated results in Figure 10 and show that the findings, both simulated and actual, agree with each other.

4.5. Summary

A summary of the results is listed in

Table 3. Summary of robot fall scenarios and corresponding recovery mechanisms.

Scenario	Recovery Mechanism	Key Features
Falls onto its side	Rounded wheel caps allow rolling to back; rotary wheels and top support wheel form 3-point contact to let the robot flip upright using vertical surface.	${\theta }_3=12°$, offset CG enables roll
Falls onto its back edge	Offset CG causes natural fall to neutral position; rotary wheels help in further motion or overcoming obstacles.	${\theta }_4=3°$, offset CG helps recovery
Falls onto its front edge	Front bumper wheel stops forwards motion; the robot uses rotary wheels as leverage to reverse.	${\theta }_5=72°$, uses reverse + rotary wheels
Flipped completely upside down	Curved top shell and low storage height allow rotary wheels to touch ground; robot moves to vertical surface, pivots and flips upright.	rotary wheel to support, $T_{limit}\ge f_{grd}r=mg{\displaystyle \frac{W_{3}r}{H(1-\mu \tan \theta )}}$

.

5. Discussion

The recovery process would only fail in the fringe scenarios where the robot gets trapped in small niches or caught in spatial layouts that prevent the robot wheels from moving. This is also mitigated with the updated FalconX by preventing the robot from slipping through smaller gaps due to its size or going into spaces that it cannot reverse or move out of. In cases where the robot is unable to self-right after extensive motion of the rotary wheels, it will still require manual retrieval by a human operator. However, this form of robotic aid will still minimise the number of times a human operator is required to climb to access the false ceiling and be susceptible to fall risks and potential pathogen exposure.

As the experiments were conducted in the Gazebo program, a bottleneck was found in the model that was limited to rigid-body objects, which limited the modelling of the actual (albeit minute) flexibility of the different materials of the real-life robot. This issue could be solved if there are improvements to the modelling program in this aspect. The current mathematical model also adopted simplified assumptions, which may not fully represent the dynamic and complex interactions experienced during real-world recovery manoeuvrers. These assumptions were used to provide an analytical formulation for this problem. In real-world scenarios, the robot may benefit from momentum or inertial effects, making the required torque less than the theoretical amount. The static equilibrium can thus provide an upper-bound estimate for the required recovery torque.

Previous versions of Falcon robots were unable to perform self-righting, and that was the main reason for designing this robot: to mitigate cases where the previous robots would get trapped in a false ceiling when flipped over. Other robots with self-righting functions would be impractical to fit and operate within the typically tight and constrained false ceiling spaces.

6. Conclusions

This paper discussed and evaluated the key contributions of both creating and validating a virtual and actual self-righting mechanism implemented in the FalconX robot used in false ceiling inspection for deployment in actual false ceiling sites. These self-righting mechanisms and its force analysis diagram were presented, along with insights into its limitations due to simulation software constraints in terms of material flexibility for the virtual model and niche obstacle layouts in real-life false ceiling conditions. Upon toppling, the robot utilises its rotary-wheeled arms to land itself on its back. It then uses self-righting methods to flip itself over to be right side up using a vertical surface. The derived equations for determining the torque required for self-righting were expressed and analysed, along with the simulated and validated results in real life.

Future works would entail the addition of other sensors and end-effectors on the robot to detect other maintenance parameters such as humidity or polarised light. The detection add-ons would be needed for checking other parameters (such as using humidity sensors for plumbing leakage or polarised light for checking excessive stress or tension on support structures that cannot be viewed with just a visual camera) within the false ceiling plenum to further automate the inspection process. This information would help greatly in false ceiling rectification works. Considerations can be made in designing specialised sensor mounts for these sensors. The design would determine how FalconX could still self-right with the customised sensor mounts for expanded detection capabilities. A dynamic model can be further developed to make it more accurate for real-world deployments.