Robot Development and Path Planning for Indoor Ultraviolet Light Disinfection

The new coronavirus has changed our world forever. Among the many lasting changes prompted by the rapid spread of SARS-CoV-2 is the need for regular systematic disinfection of indoor spaces, which has gone beyond hospitals and care facilities where room disinfection has always been a critical task that was performed on a regular basis (e.g., when patients were discharged) to public and private spaces such as schools, colleges, hospitality settings, airlines, train companies, and mass transportation authorities. In these spaces, regular disinfection will become a critical component of any strategy to reopen societies after a pandemic like the current one. However, this increases danger and time strain to the human workforce that is already stretched thin. Automating these processes is therefore an attractive approach. In the words of UVD Robots CEO Per Juul Nielsen, whose company builds robots with ultraviolet C (UVC) lights: “Hospitals around the world are waking up to autonomous disinfection. We can’t build these robots fast enough.”¹¹1www.forbes.com/sites/richblake1/2020/04/17/in-covid-19-fight-robots-report-for-disinfection-duty/

While solutions of this nature exist (see 2), there are three main shortcomings of the current solutions that severely limit their utility and applicability: (1) cost (the existing robots are very expensive, in some cases upwards of $100,000), (2) formal guarantees that every surface is disinfected, and (3) efficiency. It is unclear how well existing systems operate in part because of the lack of formal guarantees of the disinfection process.

In this paper, we address all three aspects with the design of an autonomous inexpensive custom robotic platform for UVC disinfection tasks. The robot can carry a significant payload, allowing it to operate for extended periods of time on battery power. More importantly, by finding close-to-optimal paths through the indoor space, the robot minimizes power use while guaranteeing that all surfaces receive sufficient light to guarantee disinfection.

Ultraviolet light irradiation has been used in health care settings for quite some time to deactivate contaminants. Initial studies suggested COVID-19 would be similar to other corona viruses [15], and studies have since confirmed the exact irradiation dose necessary to deactivate the virus (e.g., [13]).

Existing approaches are split between systems which are stationary in operation (e.g., Tru-D™ or [2]) and mobile platforms that have become a more frequent research focus: consider UVD Robots®, [12], [14], and other ongoing projects which have seen media coverage.²²2See Violet (time.com/5825860/coronavirus-robot/), work by Rovenso (spectrum.ieee.org/automaton/robotics/industrial-robots/rovenso-uv-disinfection-robot), or the ”ADAMMS-UV” from the USC Viterbi Center for Advanced Manufacturing, footnote 1. However, these platforms have either focused on the ability to bring a UVC lamp to a region rather than validating disinfection or have focused on proving disinfection experimentally rather than formally. See [16], [18], and [20] as examples of stationary options, and [17] as an example of a non-stationary option using a UVC wand.

Keeping devices stationary in a single location is suboptimal because light energy falls off with the square of the distance (see Section 4.2.1 for details) and the farthest surface point from the device is thus the determinant of the overall irradiation duration based on the minimum light exposure needed to deactivate the coronavirus.

To see this, consider a UVC lamp placement in location $H$, the halfway point, in the simplified 1D irradiation problem in Fig. 1. We assume the irradiation at all points long the line need to be at least 1. Consider sequential lamp placed in $M$ and $N$ such that the light intensity at the farthest points from the lamp $I$ at $S$, $E$, and $H$ is the same. Since $I(S)=I(E)=1/d^{2}+1/(d+2\cdot d^{\prime})^{2}$ and $I(H)=2\cdot 1/d^{\prime 2}$, we want to find $d$ and $d^{\prime}$ such that $1/d^{2}+1/(d+2\cdot d)^{2}-2\cdot 1/d^{\prime 2}=0$. The solutions are $d=(E-S)\cdot(3-\sqrt{3})/6$ and $d^{\prime}=(E-S)\cdot\sqrt{3}/6$ and the overall irradiation time is $d^{\prime 2}$, $d^{\prime 2}/2$ each in $M$ and in $N$ (since we have to irradiate sequentially, it would be $d^{\prime 2}/2$ if it were to be done in parallel with two lamps), a significant savings compared to $(d+d^{\prime})^{2}$.

In real-world settings there are additional difficulties: (1) 2D floor plans are more complex than the 1D approximation of a hallway provided and will therefore require more complex point placement (see Section 4), (2) robot navigation constraints will create point placement constraints, and (3) some obstacles may cause zones not reachable with direct light. Additionally, the example does not address movement time as a disinfection opportunity (the lamp can remain turned on while traveling through its environment), and additional challenges arise from operating in 3D with a platform only capable of moving in 2D. In this paper, we attempt to address (1), (2), and (3), while leaving the remainder for future work.

We developed a low-cost robotic platform equipped with an NVidia Jetson Nano embedded computing board for onboard computing (as outlined in Section 3.1) and a UVC germicidal lamp (which produces 17 Watts of UV-C radiation per 100 hours) for UVC disinfection. The robot is made of aluminium extrusion, with a square base of 24 by 28 inches. This is wide enough to provide stability for the pillar (which holds the lamp 34 inches above the ground) and space for the uninterruptible power supply (UPS) used for rechargeable power, while being thin enough to fit through a standard sized door.

Also mounted on the pillar are the robot’s sensors. Two LIDAR units (the Hokuyo URG 04LX) provide a 360-degree view of the environment, which was found to be necessary to address points which were close to obstacles by allowing the robot to safely reverse out of such spots. The Intel Realesense D435i provides a depth point cloud of the environment in front of the robot, allowing for obstacle avoidance of objects that may fall above or below the linear cloud collected by the LIDAR. Although the on-board IMU was initially used for odometery, this was found to be unnecessary due to the accuracy of the Canonical Scan Matcher (CSM) [3] which instead uses laser scan matching for odometery calculation.³³3We have used the CCNY ROS wrapping of CSM, available in the ROS scan_tools package.

The platform is differentially wheeled for the purposes of cost reduction. Additional stability is provided through passive omni-directional wheels in each corner. Both 4-inch polyurethane wheels interface with 24-volt brushless DC motors via drivers controlled over a USB-to-serial connection, and are on a spring-loaded mechanism to maintain contact with uneven surfaces. Brushless DC motors were chosen for their ability to produce high torque even at low speeds (necessary for the stop-and-go behavior of the heavy platform). Hall effect sensors attached to each commutator provide wheel rotation data, which is fed into the odometry calculations.

Our path planning algorithm receives the point cloud from the robot’s sensors. For tractability and modularity, we divide our algorithm into three independent pieces: (1) mapping (given point cloud data gathered by the robot, we obtain a floor plan of the building represented by a simple polygon); (2) waypoint and time determination (find locations and amount of time that the robot should stop and turn on the UVC light to so fully disinfect the floor); and (3) route planning (choose the order in which the waypoints are visited so as to minimize travel time).

Splitting the algorithm into independent subproblems may introduce additional error. In particular, the static placement of waypoints does not take into account the additional disinfection that may happen while the robot moves between waypoints. This error is proportional to the ratio between the amount of time spent moving and the time spent at the waypoints. For our application, this ratio is quite small (we spend hours at waypoints and a few minutes in motion). Thus, we believe that the overall error produced is negligible.

We evaluate a solution by looking at (i) the percentage of the room that is disinfected⁵⁵5Some corners could not be disinfected in our instances while at the same time (ii) minimizing the time required to complete the disinfection. To establish a baseline for comparison, we propose a naive algorithm simulating a stationary disinfection routine: choose a single point near the center of $\mathcal{G}$⁶⁶6Specifically, the midpoint of the largest segment of the horizontal bisector of the polygon. This is implemented in the representative_point function of the Shapely library and wait as long as necessary to completely disinfect the farthest point of the room that it can see. Since rooms are rarely starshaped, it will be unlikely that a single point will be able to guard the room. We expect this naive algorithm to perform terribly (in both of our optimization criteria); we mainly use it as a baseline for comparison purposes.

Note that our disinfection coefficient is fairly high compared to similar experiments. Note that in our experiments, a point must be irradiated with $120600\mu Ws/cm^{2}$, which is a fairly high threshold (say, when compared to the $12000-22000\mu Ws/cm^{2}$ threshold required in a similar experiment [16].). We do this because SARS-CoV-2 has been shown to be fairly resilient to irradiation [5]. In any case, we note that the value of the parameter itself has little impact on the results: coverage is unaffected, and a change in the coefficient would have a linear impact in time needed by both our baseline (stationary) and our algorithm.

We can also find an upper bound on the disinfection percent and a lower bound on the time required to achieve that percent for any path the robot can take. We use a similar idea to the “pessimistic irradiance” algorithm, applied in reverse: we consider the best possible irradiance possible between a point in the grid cell around the robot location and a point in the room. Define the “optimistic irradiance” between a point $u\in G^{\mathcal{G}}$ and a point $v\in G^{\mathcal{R}}$ to be the maximum irradiance between any point in the grid cell containing $u$ and the point $v$. As the grid cells cover $\mathcal{G}$ (ie. all possible locations the robot can be), running the linear program with “optimistic irradiance” constraints will produce an upper bound on the disinfection percentage and a lower bound on the disinfection time. As the discretization parameter $\varepsilon$ approaches $0$, these bounds tighten.

Six rooms were mapped and served as test data. We closely examine one room, the “HRI lab”, as a case study for the various parameters of the proposed algorithm. ⁸⁸8Code & data available at github.com/pjrule/covid-path-planning.

To establish a baseline we compute the amount of time that a stationary light would need when placed in the position that would maximize the coverage (i.e., disinfect the largest possible portion of the room). Just to give an example, a naive stationary solution (described in 5) yields a baseline disinfection time of $99,937$ seconds to disinfect $41.65\%$ of the room. A low disinfection percent is caused by the nonconvexity of the lab (i.e., walls and doors create many visibility constraints). Table 1 and Fig. 4 give a comparison between the two algorithms described in 4.2 and the lower bound described in 5, run with various values of the $\varepsilon$ discretization parameter. Notice that as $\varepsilon$ decreases, the solution times and disinfection percents achieved by the algorithms appear to quickly converge to the lower bound, as expected. The best solution time achieved is 2.5 times faster than the naive solution and disinfects twice as large an area. The branch-and-bound algorithm is competitive for some values of $\varepsilon$, though it is highly sensitive to parameterization and therefore does not always produce tight bounds. The data suggest the “pessimistic irradiance” algorithm often converges quickly to optimal; branch-and-bound appears to converge more slowly or not at all.

The effect of the robot’s shadow was also investigated. Due to the physical interference of the robot, the UVC light cannot disinfect the area directly below it. As this is the point where distance is minimized, one might worry that this negatively affects solution times. Table 1 shows the results of the simulations run for variations that consider or ignore the visibility. At $\varepsilon=0.2$, the solution accounting for robot shadow only takes $4\%$ longer than the solution that ignores shadow while disinfecting the same area: the effect is negligible.

Table 2 summarizes the performance of the various algorithms across all rooms at the discretization parameter $\varepsilon=0.2$. Similar to the case study, the “pessimistic irradiance” algorithm performs well relative to the lower bound and is a significant improvement over the naive approach.

We have developed a low-cost autonomous robot platform together with a planning algorithm for UVC irradiation tasks and demonstrate effectiveness in simulation and hardware. While the current approach focused on using a floor plan for disinfection, future work will address the more difficult problem of computing the minimum necessary exposure time from 3D data, perhaps as a continuous path, which would allow the disinfection platform to use its travel time as disinfection time Additionally, improvements can be made to the platform, as the safety restrictions imposed as a result of COVID-19 impeded manufacturing and in turn forced design choices which could otherwise be avoided.

This project was funded in part by a Tufts COVID-19 Rapid Response Award. The authors would like to thank Diane Souvaine and the other members of the Computational Geometry laboratory at Tufts University for their suggestions and their helpful discussions.