Design of a Dual-Function Autonomous Disinfection Robot with Safety Filter-Based Motion Control

Abstract

In the post-COVID era, international business and tourism are quickly recovering from the global lockdown, with people and products traveling faster at higher frequency. This boosts the economy while facilitating the spread of pathogens, causing waves of COVID aftershock with new variants like Omicron XBB. Hence, continuous disinfection of our living environments becomes our first priority. Autonomous disinfection robots provide an efficient solution to this issue. Compared to human cleaners, disinfection robots are able to operate tirelessly in harsh environments without increasing the risk of cross-infection. In this paper, we propose the design of a new generation of the Smart Cleaner disinfection robot, which is equipped with both an Ultraviolet-C (UVC) light tower and a hydrogen peroxide (HP) aerosol dispenser. The safety of an autonomous disinfection robot has been a persistent problem, especially when they work in complex environments. To tackle this problem, Hamilton–Jacobi (HJ) reachability is adopted to construct a safety filter for motion control, which guarantees that the disinfection path taken by the robot is collision-free without severely compromising the optimality of control actions. The effectiveness of the developed robot has been demonstrated by conducting extensive experimental studies.

1. Introduction

As COVID-19 restrictions are removed, social distancing is no longer restricted, and the world is officially entering the post-COVID era. However, rolling waves of infections with new COVID variants emerging still require frequent disinfection of public environments like transport hubs. During the past three years, the pandemic has stimulated the rapid growth of disinfection robots, which substitute for human workers in curbing coronavirus transmission. According to the survey [1], the applications of robots in response to COVID-19 are divided into six categories: public safety, clinical care, continuity of work and education, quality of life, laboratory and supply chain automation, and non-hospital care. For example, in crowded places like sports stadiums, ground robots can be used to broadcast messages or detect whether a person is infected with COVID-19 or not by using infrared imaging [2]. In hospitals, robots can perform hazardous jobs, like delivering contagious samples taken from patients or disinfecting wards and operating rooms. These tasks are exclusively done by ground robots on which viruses are hard to attach or maintain activeness. The deployment of robots in the transportation of biological hazards and disinfection of COVID-stricken areas can considerably reduce the time that healthcare providers and workers are exposed to pathogens.

The disinfection robot we propose is equipped with two sterilization facilities: a UVC light tower and an HP aerosol dispenser. The former method intends to physically destroy the deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) chains contained by pathogens, while the latter aims to chemically breach the shell or cell membranes of pathogens with an oxidation–reduction reaction [3]. Compared to monofunctional disinfection robots [4,5,6], the bifunctional disinfection robot features high adaptivity to complex disinfection scenarios. An aerosol dispenser aims to deliver disinfectant aerosols into the areas where pathogens potentially exist, ensuring homogeneous diffusion and maximal contact with inaccessible surfaces [7]. The HP solution is a strong oxidizer with reactive singlet oxygen, superoxide radicals, and hydroxy-free radicals.

Table 1. Comparison of disinfection methods.

Disinfectant	Principle	Advantages	Disadvantages
222 nm	Shatter DNA	Low cost,	Easily
UVC Light	or RNA	no residual,	blocked
	chain	efficient, safe
254 nm	Shatter DNA	Low cost,	Cause skin
UVC Light	or RNA	no residual,	cancer, easily
	chain	efficient	blocked
H2O2	Oxidation	Harmless	Difficult
		residual	storage
NaCLO	Oxidation,	Low cost	Highly
	chlorination	effective	toxic
HCLO	Oxidation,	Harmless	Expensive,
	chlorination	residual	corrosive
CLO2	Oxidation,	Harmless	Explosive,
	chlorination	residual	corrosive

demonstrates that compared with sodium hypochlorite, hypochlorous acid, and  chlorine dioxide, the HP solution is less corrosive and non-explosive. Despite strong oxidative properties, the HP solution can eventually break down to oxygen and water. According to research [8], the majority of respiratory viruses are predominately transmitted by contaminated aerosols, which can induce infection once inhaled by people. Therefore, an atomizer similar to that of the last two generations of Smart Cleaner robot [9,10] was used to produce HP aerosols, which can ensure homogeneous diffusion and maximal contact with inaccessible surfaces in target space.

The UVC light method has the advantage of being time-saving, because radiation needs less time than chemical reactions to take effect [11]. In addition, when UVC disinfection is finished, there will be no residual left to dissipate, so disinfection areas are allowed to be reopened without further delay. Additionally, places sensitive to humidity are exclusively suitable for UVC disinfection. Traditionally, 254 nm UVC light has been utilized due to its outstanding germicidal properties. However, when the human body is accidentally exposed to it, acute adverse reactions of skin or eyes could be induced. Long-term unprotected exposure could even lead to skin cancer. Comparatively, 222 nm UVC light is a much safer alternative, since its penetration depth (although much larger than the size of viruses and bacteria) is too small to get through the human stratum corneum or the ocular tear layer [12]. According to the research [13,14], 99.7% of SARS-CoV-2 viruses are inactivated after exposure to 3 mJ/cm² of 222 nm UVC irradiation, which is more efficient than 254 nm UVC light.

Safety is crucial for a robot that works in crowded places [15,16]. However, in terms of optimality, most motion planning algorithms like sampling-based method Rapidly Exploring Random Tree (RRT) [17] and search-based algorithms like $A^{\ast }$ [18] only take the path length between the start and target point into consideration, and safety constraints are simply referred to as path clearance. Level set methods like Control Lyapunov Functions (CLFs) [19], Control Barrier Functions (CBFs) [20], and HJ reachability analysis are commonly used to tackle safety-critical motion control problems. These methods require the design of a value function that incorporates safety constraints. By solving a convex optimal control problem that satisfies safety constraint, the initial set of states from which the system can always stay inside a safe region of attraction (ROA) are solved. Unlike HJ reachability analysis, CLFs and CLBs methods lack a general and constructive way of devising value functions. It is very difficult to devise a valid CLF or CBF by hand, especially when input constraints are considered. Additionally, CLFs and CLBs methods generate the min-norm of the control inputs, which means their controllers are not optimal in terms of safety. In contrast, HJ reachability analysis does optimal control with respect to safety constraints, maximizing the decelerating or accelerating rate of the value function [21]. Therefore, HJ reachability analysis is able to provide a less conservative and optimal safety controller, and it is a better solution for safety-critical situations. It is practical in various real-world applications, such as vision-based navigation of ground mobile robots [22], collision prevention in unmanned aerial vehicle (UAV) swarms [23], and online air traffic management [24]. In order to guarantee the safety of our disinfection robot, HJ reachability analysis has been employed as a safety filter to optimize the trajectory generated by a front-end geometric planner.

The main contributions of this work include the following:

(a)

A disinfection robot is developed with both HP aerosol and UVC radiation disinfection methods. As demonstrated in

Table 2. Performance comparison of typical disinfection robots.

Robot’s Nmae	UVC Wavelength	Aerosol Disinfection	Self-Navigation	Safety Filter	Perception Sensors
Xenex LightStrike	254 nm	-	-	-	-
Sterilray ADV	222 nm	-	🗸	-	C, L
UVD RobotLAB	254 nm	-	🗸	-	C, L
UVD BlueOcean	254 nm	-	🗸	-	C, L
RoverUV	254 nm	-	🗸	-	C, U
Smart Cleaner 3.0	222 nm	🗸	🗸	🗸	C, L, U, T

C, L, U, T stand for camera, LIDAR, ultrasonic sensor, and thermal camera, respectively. 🗸: available; -: not applicable.

, the proposed method achieves significant advancements in versatile disinfection capabilities and seamless sensor integration.

(b)

A safety filter, designed through HJ reachability analysis specifically for disinfection tasks, is integrated with a real-time motion control loop. This integration significantly enhances the robot’s obstacle avoidance capabilities and improves the coverage rate of disinfection points by 90.0% and 53.4%, respectively, in large-scale environments.

The outline of the paper is given as follows. In Section 1, the overall design of the Smart Cleaner robot is introduced. Then, Section 2 explains the principle of Hamilton–Jacobi reachability analysis acting as a safety filter to guarantee safety. Experimental studies are presented in Section 3 to demonstrate the effectiveness of the Smart Cleaner robot system. Section 4 concludes the work.

2. Design of the Disinfection Robot

The modular structure of the new generation of disinfection robot (Smart Cleaner 3.0), including hardware setup and system structure, are introduced in this section.

2.1. Modular Design

As illustrated in Figure 1, Smart Cleaner 3.0 is composed of a bifunctional disinfection module, a human–robot interface module, and an autonomous navigation platform, as explained in the following paragraph. The robot’s modular design allows it to reconfigure conveniently to adapt quickly to various disinfection scenarios. For example, a UVC radiation tower or ultrasonic atomizer could be easily removed from the disinfection module without affecting the function of other modules.

2.1.1. Bifunctional Disinfection Module

This module integrates a dual disinfection system, combining the aerosolized disinfectant method with 222 nm UVC light technology. The ultrasonic atomizer, responsible for generating hydrogen peroxide (HP) aerosols, is mounted on the autonomous navigation platform. Aerosols are delivered through a vertically installed plastic pipe to a spray nozzle positioned atop the robot. To enhance aerosol diffusion, the spray nozzle is installed at a height of 166 cm, which is 36 cm higher than in the previous version. Additionally, various spray nozzles are provided to accommodate the diverse needs of potential users.

The UVC disinfection module is positioned above the ultrasonic atomizer and consists of four vertically installed 222 nm UVC tubes (model: GKTFUVC-A1, GKTech, Foshan, China) whose durability are 5000 h. Each tube is housed within a rotatable cover, protecting it from dust and physical impact when not in use. The UVC module is designed to be removable, allowing for quick assembly and dismantling within minutes. This modularity enables the robot to adapt to complex operational scenarios.

Both disinfection modes can be independently controlled via a PS4 wireless joystick connected to the robot’s central control system, providing flexibility and ease of operation.

2.1.2. Human–Robot Interface Module

The human–robot interface module is mounted on the autonomous navigation platform of Smart Cleaner 3.0, positioned in front of the disinfection module. Designed in the shape of a cartoon human holding a touchscreen, this module integrates several advanced features to enhance functionality and user interaction. Inside the “head” of the module, a speaker is installed to broadcast warning messages, ensuring that people are informed during disinfection operations. Upon activation, the robot’s “eyes” light up, providing a visual indication of its operational status. The touchscreen serves as the primary interface, displaying real-time operating information of the Smart Cleaner 3.0. Human operators can interact with the robot by inputting command lines on the touchscreen, such as building maps or setting pathway points, enabling seamless control and customization.

The module is equipped with a high-resolution thermal camera (model: Lepton 2.5, FLIR, Wilsonville, OR, USA) capable of accurately measuring the temperature of non-contact objects. As illustrated in Figure 2, the thermal camera detects the body temperature of surrounding individuals with a thermal sensitivity of 0.050 °C, enabling the identification of potential COVID-19 carriers exhibiting abnormal body temperatures. Below the touchscreen, an RGB-D camera (model: RealSense D435, Intel, Santa Clara, CA, USA) is embedded in the “waist” area of the cartoon human. This camera has a detection range of 0.3 m to 3 m and captures both the image and depth information of objects in front of the robot, as demonstrated in Figure 3. The integration of these sensors enhances the robot’s ability to navigate complex environments and perform advanced tasks such as obstacle detection and temperature monitoring.

2.1.3. Autonomous Navigation Platform

This module serves as the mounting base and carrier for the bifunctional disinfection module and human–robot interface module of the Smart Cleaner 3.0. It is essential for enabling the robot to safely navigate previously unknown indoor environments, which is a prerequisite for completing autonomous disinfection tasks. The module features two front wheels for directional control and two rear wheels for forward and backward motion. Each wheel is equipped with an in-wheel motor, allowing independent control of the left and right wheels for precise maneuverability. At the core of the module is a central industrial computer (model: GTX1650, ZhanMei, Shenzhen, China), which processes data from sensors such as LIDAR, an RGB-D camera, and a thermal camera. This information is used to compute feasible trajectories for the low-level controller to execute. Instructions from the central controller are transmitted to the in-wheel motor control board (model: 8015D, ZhongLing Technology, Shenzhen, China), enabling the robot to move to specified positions accurately.

A LIDAR sensor is installed in the gap between the upper and lower sections of the autonomous navigation module. This sensor serves as the primary perception unit, utilizing light radiation to map the surroundings with a sampling frequency of 16,000 times per second and a range radius of up to 25 m. The high-resolution maps generated by the LIDAR are processed using high-level mapping and navigation packages running on the Robot Operating System (ROS) platform. Additionally, the module can be manually controlled via a PS4 wireless joystick, which provides low-level linear and angular velocity commands for direct operation.

The robot is deployed to the experiment’s starting point using a joystick. To ensure safety and prevent accidental collisions with humans or other autonomous vehicles at extremely close distances, two ultrasonic sensors are installed at the front of the platform. These sensors trigger an emergency stop if an unavoidable collision is imminent. Additionally, an emergency stop switch is mounted on the rear end of the module, serving as a last resort to cut off power and immobilize the robot in dangerous situations.

The platform’s design has been optimized for improved maneuverability, with a 20 cm reduction in width compared to the previous version. This enhancement allows the robot to navigate more effectively around obstacles and operate seamlessly in crowded environments. Further specifications of the Smart Cleaner 3.0 are detailed in

Table 3. Specifics of Smart Cleaner robot.

Parameter	Value
Height (mm)	166.0
Length (mm)	38.5
Width (mm)	38.0
Weight (Fully loaded with disinfectant) (kg)	53.7
Endurance (h)	5.0
Charging time (h)	<3.0
Spraying speed (L/h)	2.3
Spray range (m)	>1.5
222 nm UVC intensity (mW/cm2)	0.2
Maximum linear velocity (m/s)	1.2
Obstacle surmounting ability (mm)	14.0

.

2.2. Software System Structure

The robot system relies on an ROS to connect each module, which is installed in the Ubuntu 18.04 environment running in the central industrial computer. Communications between sensors, controllers, and actuators are realized by publishing and subscribing ROS topics (Figure 4).

2.2.1. Perception

In this work, the perception of an unknown environment is conducted by a LIDAR used to scan the robot’s surroundings. It generates millions of electromagnetic waves, which are then reflected back once encountering objects. The LIDAR receives the reflected waves, and the time of flight (TOF) is used to establish a distance map of the objects in the scene. The previous version of the Smart Cleaner series combined LIDAR and camera tools for mapping. However, the efficiency was compromised, and the computational burden naturally increased. Therefore, we solely employed the LIDAR to map the environment, which proved quicker and more accurate for trajectory planning. In particular, RPlidar A3 was chosen due to its sampling speed and compact size advancement.

2.2.2. Mapping

The depth information collected by RPlidar from all directions is filtered and used to feed the cartographer SLAM (Simultaneous Localization And Mapping) algorithm. This algorithm was selected because it achieves a smaller resolution radius of 5 cm with lower cumulative error than other SLAM methods, like Gmapping or Hector. First, local SLAM in the front end incorporates data from LIDAR, an IMU, and an odometer to build locally consistent submaps. To mitigate the disturbance of moving obstacles, global SLAM in the back end finds loop closure constraints and threads submaps together coherently. It employs a scan-matching method to compare each scan with submaps.

2.2.3. Planning

The Dijkstra’s algorithm serves as a global planner to generate a feasible path within the established grid map, guiding the disinfection process. Utilizing a breadth-first search (BFS) approach, it constructs a tree of the shortest paths from the starting point to all nodes on the map [25]. The algorithm maintains and updates the shortest distances from visited nodes to the starting point, ensuring the optimal path is identified as it explores unvisited nodes between the start and target states. This process, as detailed in Algorithm 1, systematically traverses all nodes to guarantee the selection of the shortest path. Dijkstra’s algorithm is a dependable method for finding the shortest path in graphs with non-negative edge weights, offering deterministic and consistent results, which is particularly beneficial for tasks requiring fixed routes, such as disinfection. Unlike A*, Dijkstra does not depend on heuristics, making it versatile for complex graph structures where defining an effective heuristic may be difficult. However, its uniform exploration of all paths can lead to inefficiencies in large search spaces compared to heuristic-driven algorithms (like A*) or sampling-based methods (like RRT). Nonetheless, Dijkstra’s ability to provide comprehensive insights into the graph structure and its predictable behavior makes it a robust choice for deterministic environments where consistent and reliable outcomes are essential.

Algorithm 1 Update($node1,node2,edge$)

if  $d\left(node1\right)>d\left(node2\right)+edge(node1,node2)$then

$d\left(node1\right)=d\left(node2\right)+edge(node1,node2)$

$node1.pre=node2$

end if

After achieving a global path between the initial position and target point, the local planner should track the given path and cope with emerging obstacles. The dynamic window approach (DWA) takes the differential kinematic model of the robot into consideration by shrinking the search space according to the reachable velocity of the robot in the time horizon [26]. The robot can stop before encountering the nearest obstacle under the velocity constraint. It chooses the paths based on an objective function considering the distance to obstacles, forward velocity, and progress toward goal points. The sampling interval of the DWA algorithm is relatively short so that it can track a path in real time [27]. By setting multiple target points around the disinfection area, the robot system can generate a closed disinfection loop connecting each point, and the robot will track the loop repeatedly while emitting UVC radiation and spraying HP aerosols through the disinfection module.

3. Safety via Reachability

How to robustly ensure the safety of an operating autonomous ground robot against all kinds of objects sharing its working space has always been a demanding task, especially during the design of disinfection robots that are meant to guard us against pandemics in our daily life. HJ reachability analysis provides an effective solution to this problem by building a safety filter for the motion control system, which characterizes reaching goals and avoiding obstacles as optimal control and differential games [28]. The reachability analysis algorithm computes the set of initial states, from which a control input can drive the system into a target set within a designated time horizon despite possible disturbances. This set of initial states is called a Backward Reachable Set (BRS) because it is computed backward in time. In addition, HJ reachability analysis also gives safety control inputs that ensure that the robot remains in a safe initial set.

As the disinfection robot is navigating in a previously unknown environment, the computation of the BRS with respect to a target set (that the robot system intends to reach) and an obstacle set to avoid are undertaken by HJ reachability analysis by using optimal control toolbox helperOC [29], as depicted in Figure 5.

The kinematic model to represent the mobile disinfection robot is employed as the differential three-dimensional Dubins’ car model:

$$\begin{array}{cccc}& & \hfill \left\{\begin{array}{cc}& {\displaystyle \frac{\partial s_x}{\partial t}}=vcos\theta +d_x,\hfill \\ & {\displaystyle \frac{\partial s_y}{\partial t}}=vsin\theta +d_y,\hfill \\ & {\displaystyle \frac{\partial \theta }{\partial t}}=\omega +d_{\theta },\hfill \end{array}\right.& \end{array}$$

(1)

with

$$v\in \left[\underline{v},\overline{v}\right],\left|w\right|\le \overline{w},|d_x|,|d_y|\le {\overline{d}}_p,\left|d_{\theta }\right|\le {\overline{d}}_{\theta }.$$

where the system’s state $x={\left[s_x,s_y,\theta \right]}^T$ is determined by the horizontal position $s_x$, vertical position $s_y$, and heading angle $\theta$ in the Cartesian coordinate system. In addition, $d_x$, $d_y$, and $d_{\theta }$ represent the disturbances and model mismatch of the vehicle. $u=(v,\omega )$ defines the control input, where v is the linear speed, and $\omega$ stands for the angular velocity. The control input and disturbances are bounded. The trajectory or solution of the dynamic system starting from state $x_{\tau }$ at time $\tau$ can be written as

$$\begin{array}{cccc}& & \hfill \epsilon ({\tau }_s;x_{\tau },\tau ,u(\ast ),d(\ast )):{\tau }_s\in \left[\tau ,0\right]& \end{array}$$

(2)

Next, perceived obstacles are defined as unsafe set $B_0$, and the corresponding BRS can be written as

$$\begin{array}{c}\hfill \begin{array}{cc}& B\left(t\right)=\{x:\exists d\in D,\forall u\in U,\exists {\tau }_s\in \left[\tau ,0\right],\hfill \\ & s.t.\epsilon ({\tau }_s;x_{\tau },\tau ,u(\ast ),d(\ast ))\in B_0\},\hfill \end{array}\end{array}$$

(3)

where D and U stand for the set of disturbances and controls, respectively.

The next step is to define an implicit surface function $l\left(x\right)$, which is the signed distance from the vehicle’s position to the surface of the unsafe region in the grid map. Therefore, the function is negative inside the unsafe region, i.e.,

$$B_0=\{x:l\left(x\right)\le 0\}$$

and positive outside of it. To obtain the lowest value of $l\left(x\right)$ during the time horizon $\left[\tau ,0\right]$, a differential game between control and disturbance is introduced:

$$\begin{array}{cccc}& & \hfill \Omega (t,x\left(t\right))=\underset{d(\ast )}{min}\underset{u(\ast )}{max}\underset{t\in \left[\tau ,0\right]}{min}l\left(x\left(t\right)\right)& \end{array}$$

(4)

in which the control input aims to steer the system as far away as possible from $B_0$, while the disturbance is doing precisely the opposite. Through dynamic programming [30], the abovementioned value function $\Omega ({\tau }_s,x\left({\tau }_s\right))$ can be solved. Subsequently, the BRS can be computed as the subzero level set of the value function.

Employing dynamic programming and Taylor expansion, a Hamilton–Jacobi–Issacs partial differential equation (HJIPDE) with the final value of constraint is deduced from Equation (4):

$$\begin{array}{c}\hfill \begin{array}{cc}& {\displaystyle \frac{\partial \Omega (t,x(t\left)\right)}{\partial t}}+\underset{u\in U}{max}\underset{d\in D}{min}{\displaystyle \frac{\partial \Omega (t,x(t\left)\right)}{\partial x}}{\displaystyle \frac{\partial x}{\partial t}}=0,\hfill \\ & \Omega (0,x(0\left)\right)=l\left(x\right(0\left)\right),t\le 0\hfill \end{array}\end{array}$$

(5)

where

$$H(x,t,V)=\underset{u\in U}{max}\underset{d\in D}{min}{\displaystyle \frac{\partial \Omega (t,x(t\left)\right)}{\partial x}}{\displaystyle \frac{\partial x}{\partial t}}$$

is called Hamiltonian. It considers the system’s state, the control input that aims to increase the value function, and the disturbance with contrary intention.

After solving the final value of the HJIPDE, we can obtain the value function $\Omega (t,x(t\left)\right)$. Consequently, the BRS can be solved as the subzero level set of value function $\Omega (t,x(t\left)\right)$:

$$B\left(t\right)=\{x:\Omega (t,x)\le 0\}.$$

The complement of the BRS is called a safe set $B{\left(t\right)}^c$, from which there will always be a feasible control input that can drive the robot away from obstacles. The safety controller employed to prevent the robot from entering BRS is constructed accordingly as follows:

$$\begin{array}{cccc}& & \hfill \widehat{u}(t,x)=\arg \underset{u\in U}{max}\underset{d\in D}{min}{\displaystyle \frac{\partial \Omega (t,x(t\left)\right)}{\partial x}}{\displaystyle \frac{\partial x}{\partial t}}.& \end{array}$$

(6)

It stays inactivated while the system’s state remains inside the boundary of $B{\left(t\right)}^c$ and is permitted to engage only when the system is about to breach the boundary. Therefore, the HJ reachability acts as a safety filter for the robot’s original motion controller. The optimal control toolbox used in the computation of the BRS is helperOC, which employs a level set method to solve Equation (5).

To guarantee the safety of our Smart Cleaner robot without compromising its disinfection ability, a reach-avoid problem was proposed. A target set T is the over-approximation of disinfection location that the robot must reach. Meanwhile, a safety constraint set S is the complement of the BRS with respect to the over-approximation of obstacles. They can be represented by the zero-level set of two signed distance functions of higher dimension, respectively, i.e.,

$$\begin{array}{cccc}& & \hfill (x,t)\in T⟷l_t\left(x\left(t\right)\right)\le 0,(x,t)\in S⟷l_s\left(x\left(t\right)\right)\le 0& \end{array}$$

(7)

The target set and safety constraint set are variable and can be updated at intervals. A trajectory is feasible over a time horizon $(t,t+\gamma ),\gamma >0$, if for all states of the dynamic system (1), there is the following:

$$\begin{array}{cccc}& & \hfill \epsilon ({\tau }_s;x_{\tau },\tau ,u(\ast ),d(\ast ))\in S,{\tau }_s\in \left[t,t+\gamma \right]& \end{array}$$

(8)

To make such a judgment, the attained maximum value of $l_s\left(x\left(t\right)\right)$ within the period is obtained. The safety constraint is broken if its maximum value is greater than zero. The next step is determining whether a feasible trajectory can reach the target set. To achieve this, we keep track of the minimum value of function $l_t\left(x\left(t\right)\right)$; if it is smaller than zero, then the target set is reachable over the time horizon.

The reach-avoid problem is characterized as a differential game between the control signal and disturbances. The former tries to drive the system into the target set and remain in the safety constraint set, while the latter tries to drive the system out of the target set or the safety constraint set. We refer to control input as player I and disturbance as player II. The binary decision of which player wins the differential game is defined by

$$\begin{array}{cccc}& & \hfill \begin{array}{c}\hfill \Pi (t,x\left(t\right))=\underset{u(\ast )}{min}\underset{d(\ast )}{max}\underset{{\tau }_s\in \left[t,t+\gamma \right]}{min}max\left\{l_t\left({\epsilon }_{x_{\tau },\tau }^{u,d}\left({\tau }_s\right)\right),\underset{{\tau }_d\in \left[t,t+\gamma \right]}{max}{l}_s\left({\epsilon }_{x_{\tau },\tau }^{u,d}\left({\tau }_d\right)\right)\right\}\end{array}& \end{array}$$

(9)

which is updated at each time instance ${\tau }_s$ in the time horizon $\left[t,t+\gamma \right]$. If at any ${\tau }_s$ the value function is smaller than or equal to zero, then player I wins the differential game, and the robot can reach the target set while avoiding the unsafe region. Therefore, the current value of the target function $l_t\left(x\left(t\right)\right)$ and the peak value of the safety constraint function $l_s\left(x\left(t\right)\right)$ during the period are expected to be non-positive. The value function $\Pi (t,x(t\left)\right)$ is then solved by calculating the unique viscosity solution of Equation (9), i.e.,

$$\begin{array}{cccc}& & \hfill \begin{array}{c}\hfill max\left\{min\{{\displaystyle \frac{\partial \Pi (t,x(t\left)\right)}{\partial t}}+R(x\left(t\right),\nabla \Pi (t,x\left(t\right))),\right.\left.l_t\left(x\left(t\right)\right)-\Pi (t,x\left(t\right))\},l_s\left(x\left(t\right)\right)-\Pi (t,x\left(t\right))\right\}\end{array}& \end{array}$$

(10)

where $\nabla \Pi (t,x(t\left)\right)$ stands for the spatial derivative of value function $\Pi$, and its Hamiltonian is given by

$$\begin{array}{cccc}& & \hfill R(x\left(t\right),\nabla \Pi (t,x\left(t\right)))={\displaystyle \frac{\partial \Pi (t,x(t\left)\right)}{\partial x}}{\displaystyle \frac{\partial x}{\partial t}}& \end{array}$$

(11)

Consequently, the reach-avoid control is generated as follows:

$$\begin{array}{cccc}& & \hfill \overline{u}(t,x)=\arg \underset{u\in U}{max}\underset{d\in D}{min}{\displaystyle \frac{\partial \Pi (t,x(t\left)\right)}{\partial x}}{\displaystyle \frac{\partial x}{\partial t}}.& \end{array}$$

(12)

Algorithm 2 illustrates that the safety filter is added in the motion control section to verify the safety of the Smart Cleaner robot. It does not change the decision of the original controller unless the robot has stepped out of the safe region. Therefore, the robot tracking a planned trajectory does not need to take a considerable detour, affecting the reaching of disinfection locations.

The kinematic parameters of the three-dimensional Dubins’ car model employed to represent the disinfection robot in simulation is illustrated as follows. The bounds of inputs are $\underline{v}=$ 0 m/s, $\overline{v}=$ 1.5 m/s, and $\overline{w}=$ 1 rad/s. The bounds of disturbances are ${\overline{d}}_p=$ 0.25 m/s and ${\overline{d}}_{\theta }=$ 0.1 rad. The target set that the system will eventually be pushed into by disturbances despite the best control efforts in 3 s is represented by a circle with a radius of r = 0.75 m. The obstacle that the system has to avoid during the reachability propagation in the grid map is also represented by a circle with the same radius. HJ reachability is employed to transform the computation of the BRS to optimal control and differential game problems, with control inputs minimizing the function value and disturbance maximizing it.

Algorithm 2 Safety verification for motion planning

Require: $\dot{x}=f(x,u,d)$ System’s model, E Sensed environment information, $x_c$ the current state and G the goal set

while  $x_c\notin G$  do

obtain E at this moment, and compute the safe set S by solving HJIPDE in (10)

while $x_c\notin S$ do

$u\left(t\right)=\overline{u}(t,x_c)$ which is the optimal avoidance velocity command in (12)

end while

$u\left(t\right)=u^{\ast }(t,x_c)$, which is the nominal velocity command

end while

In Figure 6, the value function $\Pi (t,x(t\left)\right)$ of the reach-avoid optimal control problem has been computed within a 3 s time horizon. In Figure 7, the BRS (blue) of the disinfection robot concerning a target set (green) and an obstacle set (red) has been computed by solving an optimal control problem using the dynamic programming technique. If the system’s state stays inside the BRS, there will always be a control input that can drive the system into the target set despite every possible disturbance. According to the level set method [31], the subzero level set of the computed value function is precisely the BRS that helps to define feasible states.

4. Experimental Results

The effectiveness and advancement of Smart Cleaner 3.0 was demonstrated in a disinfection assignment for our laboratory. The free space for navigation was limited, and experimental instruments were littered randomly. Table 3 illustrates that the robot is designed to be relatively small in length and width, facilitating navigation in cluttered environments. The disinfection setting was the laboratory with rows of desks, multiple chairs, and several mobile robots lying on the ground. The Smart Cleaner robot must navigate autonomously between previously unseen obstacles to complete the disinfection assignment. Moreover, the space between two rows of desks is very limited. Therefore, it is challenging to avoid collision on both sides. When the free space for navigation is limited or new obstacles emerge, the safety filter comes into full play.

In Figure 8, the Smart Cleaner robot conducted a disinfection task for a laboratory environment. To maximize the disinfection quality, we used the touchscreen in the human–robot interface module to set several goal points on the map for the disinfection robot to reach. These goal points were chosen in hard-to-reach places among chairs and experimental instruments to test the effectiveness of the proposed safety filter. Afterwards, the motion planner was activated to find a path connecting all these goal points in the detected free space. The disinfection robot then repeatedly traveled the path, back and forth, until its battery drains out. It took about five hours as tested. Any newly emerged obstacle could threaten the robot’s operation during this period. As illustrated in Figure 8, the Smart Cleaner robot reached all the goal points, tracking the feasible blue trajectory. Integrated as a safety filter in the control system, HJ reachability analysis can guarantee the smooth avoidance of all obstacles by computing the BRS at a frequency of 10 Hz. Once the robot’s state reaches the boundary of the computed BRS, the safety controller adjusts its trajectory by giving off-turning instructions. Thus, the chance of potential collision is eliminated beforehand. It is demonstrated that the Smart Cleaner robot successfully avoided all the edges of desks and chairs and made a smooth turn despite limited space. Without the safety filter, Smart Cleaner failed to keep a safe distance from the edges of desks and collided with them at two turns. In order to compare our proposed planner with popular algorithms like Rapidly Exploring Random Tree (RRT) and A-star, navigation experiments were conducted in two obstacle layouts, as illustrated in Figure 9. With the Rviz platform in Smart Cleaner’s ROS system, we were able to asses the safety of each trajectory by measuring distances to barriers. The result is presented in

Table 4. Average distances between trajectories generated by three different planners and three barriers in two experimental scenarios in Figure 9 for ten consecutive times.

Distance with Obstacle (cm)	RRT		A-Star		Our Method
Barrier 1	9.2	8.0	13.1	8.9	14.3	20.6
Barrier 2	7.5	12.5	9.7	8.5	22.5	15.5
Barrier 3	19.0	6.4	8.5	16.5	20.2	27.8

with average values of distances in ten consecutive experiments. Compared to the RRT and A-star algorithms, the average distance between the trajectory and obstacles in the aforementioned two scenarios increased up to 200% and 334.4% respectively, which demonstrates the advantage of our method in terms of keeping a safety margin with obstacles as large as possible. The navigation experiments in Figure 9c,f were finished within 19 s and 30 s, respectively, which demonstrates the time efficiency of our method.

A more thorough disinfection test was conducted and is illustrated in Figure 10. The Smart Cleaner robot traveled through seven narrow corridors and avoided multiple chairs that blocked its original path. Figure 11 comprises four working photos of the robot traveling in extremely limited spaces. The widths of the aisle in those subphotos are 83 cm, 90 cm, 63 cm, and 71 cm, respectively. The experiment compares the safety of disinfection robot before and after the HJ reachability-based safety filter was added into its control system, in which the robot has to navigate in an obstacle-cluttered room and reach all six disinfection points. The result in

Table 5. Operational statistics of 10 repeated experiments shown in Figure 10.

Specification	Without Safety Filter	With Safety Filter
Collision rate	100%	10%
Disinfection points coverage rate	43.3%	96.7%
Average navigation time	15.1 min	12.7 min

demonstrates that the safety filter enhanced the obstacle avoidance ability of the Smart Cleaner robot substantially, with its collision rate following 10 repeated experiments decreasing by 90%. Apart from the decrease in collision rate, the average navigation time was reduced by 15.9%. Additionally, the coverage of disinfection points was increased by 53.4%.

5. Conclusions

This paper presents the third generation of the Smart Cleaner robot, a novel bifunctional disinfection system that integrates hydrogen peroxide (HP) aerosols and 222 nm UVC light for enhanced disinfection capabilities. Notably, it is the first disinfection robot equipped with a formal safety filter, which ensures safe and efficient operation in complex environments. By incorporating Hamilton–Jacobi (HJ) reachability analysis as a safety filter in its control loop, our method achieved a larger safety margin compared to traditional planners such as RRT and A-star in densely cluttered environments. Experiments conducted in our laboratory demonstrate the robot’s ability to navigate safely while maintaining high disinfection quality, underscoring its operational efficiency and safety performance. The combination of physical (UVC) and chemical (HP aerosol) disinfection methods enables the Smart Cleaner 3.0 to safely and effectively disinfect complex environments, making it a promising solution for curbing the spread of potential pandemics.