EXAMENSARBETE INOM TECHNOLOGY, GRUNDNIVÅ, 15 HP STOCKHOLM, SVERIGE 2018

Improving robotic vacuum cleaners Minimising the time needed for complete dust removal

ANDREAS GYLLING

EMIL ELMARSSON

KTH SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Improving robotic vacuum cleaners

Minimising the time needed for complete dust removal

Andreas Gylling Emil Elmarsson

Handledare: Jana Tumova Examinator: Orjan¨ Ekeberg

KTH School of Electrical Engineering and Computer Science June 1, 2018

ii Abstract

The purpose of this study was to examine the cleaning efficiency of an au- tonomous vacuum cleaner robot; namely, reducing the cleaning time needed in an empty room. To do this we explored how the path planning could be improved upon given access to a dust map that would allow for more sophis- ticated algorithms depending on the state of the room. The approach we employed in order to compare different preprogrammed path patterns and our own greedy heuristic was to create a simulation environment in Unity3d. In this environment we could create a two dimensional plane to represent the length and width of a room with the size of our choosing. This plane was then subdivided into squared cells that would discretise the environment, which represented the dust map of the room. The tests were conducted in rooms with different dimensions in order to examine how different strategies’ efficiency developed in relation to each other. Employing an algorithm like our greedy heuristic after an initial zigzag sweep resulted in a significant im- provement in comparison to a robot that is restricted to template patterns only. Future work could involve finding the optimised solution for our heuris- tic in order to make full use of the dust map and thereby achieve minimal cleaning time for the robot.

iii F¨orb¨attrarobotdammsugare

Minimering av tiden som beh¨ovs f¨orfullst¨andigrenhet

Sammanfattning

Syftet med denna studie var att unders¨oka en sj¨alvstyrande robotdammsug- ares st¨adningseffektivitet och att minimera tiden som kr¨avsf¨oratt st¨ada ett tomt rum. Vi unders¨oktehur roboten kunde planera sina v¨agval b¨attre genom att f˚atillg˚angtill en dammkarta, det vill s¨agaett rutn¨at som h˚aller reda p˚adammf¨ordelningeni ett rum. Denna dammkarta m¨ojligg¨orf¨ormer sofistikerade algoritmer som beror p˚astatusen i rummet. Vi j¨amf¨ordeolika r¨orelsem¨onstersom sicksack, spiralen och v¨aggkramarenmed en egendefinierad heuristik. Ett enkelt ¨oppet rum simulerades i Unity3d, d¨arvi testade de olika algoritmerna. Rummet bestod av ett tv˚adimensionelltplan som representer- ade l¨angdenoch bredden av rummet som gick att justera till v˚arttycke. Detta plan delades sedan upp i ett rutn¨atsom representerar v˚ardiskretiser- ade dammkarta f¨orrummet. Testerna utf¨ordesi rum av olika dimensioner f¨oratt se hur de olika st¨adstrategiernaseffektivitet utvecklades i relation till varandra. Att anv¨andasig av en algoritm s˚asom v˚arheuristik efter ett f¨orsta svep med ett sicksackm¨onster resulterade i en signifikant f¨orb¨attringj¨amf¨ort med en robot som ¨arbunden till f¨ordefinierader¨orelsem¨onster. Framtida studier skulle kunna f¨ors¨oka hitta den optimala l¨osningentill v˚arheuris- tik, s˚aatt dammkartan kan utnyttjas till fullo, och d¨armeduppn˚aminimal st¨adningstidf¨orroboten.

iv Keywords autonomous robotic vacuum cleaner, dust map, path planing, coverage

v Contents

1 Introduction 1 1.1 Purpose ...... 2 1.2 Problem statement ...... 2 1.3 Assumptions ...... 3 1.4 Terms and definitions ...... 5

2 Background 6 2.1 Cell decomposition ...... 6 2.2 Path planning ...... 7 2.3 Template patterns ...... 8 2.4 PPCR algorithms ...... 8 2.5 Related work ...... 9 2.5.1 Algorithm 1: The pattern method ...... 10 2.5.2 Algorithm 3: The genetic method ...... 11 2.5.3 TSP-based: Hess’ algorithm ...... 12 2.5.4 Algorithm 2: The greedy method ...... 13

3 Methods 15 3.1 Implemented path planning algorithms ...... 15 3.1.1 Zigzag ...... 15 3.1.2 Spiral ...... 16 3.1.3 Wall-to-wall ...... 17 3.1.4 Greedy PPCR algorithm ...... 18 3.1.5 Greedy heuristic ...... 18 3.2 Cleaning strategies ...... 19 3.2.1 Strategy 1: pattern-based strategy ...... 19 3.2.2 Strategy 2: Proposed greedy heuristic after an initial sweep ...... 20

vi 3.2.3 Strategy 3: Greedy strategy ...... 20 3.2.4 Zigzag’s direction ...... 21 3.3 Building the test system ...... 21 3.4 Benchmarks ...... 22

4 Results 25 4.1 Obstacle free room with more dust along the walls ...... 26 4.1.1 Time ...... 26 4.1.2 Turns ...... 28 4.1.3 Distance ...... 29 4.1.4 Discussion ...... 31 4.2 Obstacle free room with more dust at the centre of the room . 31 4.2.1 Time ...... 32 4.2.2 Turns ...... 33 4.2.3 Distance ...... 35 4.2.4 Discussion ...... 36 4.3 Obstacle free room with uniform dust distribution ...... 37 4.3.1 Time ...... 37 4.3.2 Turns ...... 39 4.3.3 Distance ...... 40 4.3.4 Discussion ...... 42 4.4 Consequence of zigzag choosing different ways ...... 42 4.4.1 Turns ...... 42 4.4.2 Time ...... 43 4.4.3 Discussion ...... 44 4.5 Room with obstacles ...... 45

5 Discussion 48 5.1 The obstacle free room ...... 48 5.2 The room with obstacles ...... 49 5.3 Limitations and possible further improvements of the heuristic 50

vii 5.4 Reflection on the hypotheses ...... 51 5.5 General matters ...... 53

6 Conclusion 54

viii 1 Introduction

Path planning of autonomous robots has been a subject of interest since the beginning of robotics. The goal is to create an algorithm for the robot in order to manoeuvre within an environment and perform some tasks without human assistance. The task could range from navigating through a maze and finding the exit, steering a car on a highway, mowing the lawn, to vacuum cleaning a living room. We will focus on the latter; namely autonomous vacuum cleaner robots. More specifically, we will aim for the robot to try to attain a completely clean room in reasonable time.

Modern robotic vacuum cleaners use multiple types of optical sensors, ul- trasound, proximity sensors, lasers, magnets and/or cameras to navigate in their environment. These sensors are then used in combination with different predetermined path planning algorithms such as wall-to-wall, zigzag, random walk and spiral patterns. These could be executed separately or combined in order to ensure that maximum dust removal is achieved (Hasan et al. 2014). To monitor and assess the cleanliness of the environment the robots could use a so-called dust map which tracks the dust level in the entire room (Lee & Banerjee 2015).

Lee & Banerjee state that there are three different strategies that the robotic vacuum cleaner could employ for its path planning. These are the follow- ing:

1. Using a dust map which divides the room into cells and measures the amount of dust in each one. Algorithms that use this map can then generate efficient paths depending on which cell is still dirty.

2. A template based strategy which uses predefined path patterns (wall- to-wall, zigzag, etc.)

3. AI based methods. These methods have several learning techniques for

1 generating adaptive paths. In order to do this continuously information needs to be gathered from the environment.

The focus of our study will be on combining strategy 1 and 2 since we have chosen to adopt a static environment, i.e. an environment in which there are no moving people or furniture. In such environments there are no need for adaptive paths.

1.1 Purpose

The purpose of this case study is to examine the cleaning efficiency of an autonomous vacuum cleaner robot. Given access to a dust map, how would the robot determine an effective cleaning path? Could the robot reduce the cleaning time and consequently decrease the power consumption by combin- ing several preset patterns? Are there certain environments where such a combination would be particularly advantageous? How could we improve upon modern robotic vacuum cleaners in order to reduce the time needed to clean a room?

1.2 Problem statement

Our main focus will be on determining which path planning algorithms pro- duce the most efficient result in an open room without obstacles. However, we will also analyse how the efficiency is affected when obstacles are present in the room. We wish to find which advantages and disadvantages there are between different preprogrammed algorithms, assuming the environment is given and set. For simplicity, we assume that the dust map is given. It can be obtained by performing a first full-coverage sweep while simultaneously using sensors to detect the amount of dust remaining under the robot. From now

2 on, our attention will be restricted to planning after the first sweep in order to minimise the cleaning time. We aim to investigate the following:

• Given that the environment is known and static and with the help of a dust map; how should the robot move in the room’s current state in order to minimise the time needed for complete dust removal?

• How does the efficiency of the robot differ between different environ- ments; namely, an empty room and one filled with obstacles?

In particular, we are interested in the following hypotheses which are based on intuition:

• H1: As more dust is generally accumulated along the walls and corners of a room, following the walls of the room after a first sweep will reduce the cleaning time as the robot only has to clean dirty cells.

• H2: Moving towards the nearest uncleaned cell after the initial full sweep will reduce the required cleaning time compared to predefined patterns.

• H3: Employing a dust map algorithm will outperform template pat- terns no matter the state of the room.

1.3 Assumptions

We intend to simulate a vacuum cleaner robot and its environment with Unity3d (Unity Technologies 2018), which is an engine for making visual ap- plications, mostly focused on games. These are the assumptions we make:

• Omniscience - It is assumed that the robot knows everything about its environment, in the sense that it has access to a map of its surround- ings as well as of the dust distribution and concentration. Mapping is beyond the scope of this thesis. Hence, any potential inaccurate sensors

3 which might appear in real robotic vacuum cleaners are disregarded; we assume that the robot can measure its position accurately. One way for robots to map an environment previously unknown to them is SLAM (Simultaneous Localisation And Mapping). SLAM maps while navi- gating through the environment and determining the absolute position of the robot. For example, a robot could accomplish this by using ul- trasonic sensors or laser scanners. These would scan the environment to know where the obstacles and other terrain are. These obstacles are usually called landmarks and are used to tell where the robot is in relation to the room. As more observations are made, the uncertainty of the landmarks’ position and the measured distances between them decreases. This means that the position of the robot can be assessed more accurately. A difficulty that arises is merging the different scans into one three-dimensional model, as they are taken from different posi- tions and as the environment might be changing dynamically while the robot is moving. Another issue is that the sensors might be defective, so the estimations of the robot might not align with reality very well, which could result in the robot thinking it is somewhere it actually is not (Durrant-Whyte & Bailey 2006) (Gˆansari& Buiu 2014).

• 2D-plane - For the sake of simplicity the environment is assumed to be constituted by one single floor and represented by a two-dimensional plane. There is no third dimension involved. We would therefore not be able to go under furniture like a real robot would, there is either ”infinite” height or none at all. Some robots have cliff sensors for detecting ledges so as to not fall, like down a flight of stairs for example, but that is beyond the scope of this thesis.

• Cell decomposition - We assume that the environment is composed of square cells, like a chessboard, where each cell contains a dust level. (See section 2.1 for detailed description.)

4 • Static environment - We also assume that the environment is static, meaning the environment will not change, through moving obstacles for example.

1.4 Terms and definitions

Table 1: Terms and their definition. Data structure that keeps track of the amount of dust Dust map in each cell of a subdivided environment plane. PPCR Path Planning Coverage Region. The robot has performed a sweep once it has traversed and cleaned all cells of the environment once. Note that Sweep a successful sweep does not necessarily mean that the room has been cleaned, several sweeps may be needed to completely clean the room.

5 2 Background

2.1 Cell decomposition

Lee & Banerjee, Yakoubi & Laskri, Gajjar et al. describe cell decomposition as a method for managing the environment of the vacuum cleaner as a grid. The grid is generated by subdividing the two-dimensional plane, in other words the current room, into smaller squared cells which have the same side length as the robot’s diameter. The benefit of this strategy is that it facilitates the robot’s computational work because the direction of the robot can be decided by analysing the neighbouring cells. This is an advantage as the robot knows where it is and which areas have been covered, instead of relying on letting the robot go on in random predefined patterns and hoping for a complete coverage. Each cell consists of an integer which represents how much dust it contains and another for if it is an obstacle or not (see Table 2). The predefined pattern algorithms will only ever go in these directions; up, right, down, and left and do not analyse its neighbouring cells. This sets them apart from the dust map algorithms, which can move directly to any of its eight neighbouring cells.

Table 2: This table is an example of cell decomposition. It represents a dust map that is randomly generated for a 10 x 10 obstacle free room. A cell with value “obstacle” would have represented an obstacle if there were any.

6 10 10 5 4 10 9 17 13 9 7 15 4 2 2 6 8 4 9 7 9 9 2 2 3 7 9 3 9 8 10 7 2 4 1 3 1 2 6 6 8 12 2 3 8 8 3 9 6 2 14 12 2 6 2 8 2 3 5 1 5 12 8 7 7 5 5 5 6 9 8 5 5 7 3 5 4 3 5 1 11 8 6 1 9 6 8 9 1 4 14 12 11 7 10 12 13 7 11 17 15

2.2 Path planning

One of the key problems for autonomous robots is finding a path that sat- isfies a goal specification. The most basic constraint is simply moving from one starting point to a finishing point without hitting any obstacles. Path planning becomes more difficult as the goal specification and the constraints grow in complexity, meaning more is expected from the robot. In the example of the vacuum cleaner, it needs a Path Planning Coverage Region algorithm (see section 2.4) to keep track of the cleanliness as it goes along. It is not only about finding a path between two points anymore as the goal specification is not satisfied until all of the dust has been vacuumed; hence, finding a general algorithm proves more difficult. Parameters such as path length, travel time and amount of turns are evaluated when optimising the path planner (Moll et al. 2015, Gajjar et al. 2017).

7 2.3 Template patterns

Several template patterns have been suggested for path planning in section 1: (Gajjar et al. 2017, Hasan et al. 2014).

• Random walk - The robot will move in a straight direction until an obstacle is hit. It then rotates a random degree and moves forward again. This algorithm can be repeated endlessly until the room is cleaned or be exchanged by another algorithm.

• Wall-To-Wall - Moves along the walls of the room.

• Zig-Zag - Moves in a straight line, then one cell to the side and lastly it goes back in parallel with the previous direction. This is said to be the fastest motion for one full sweep of an empty room (Hasan et al. 2014).

• Spiral - Moves outwards and inwards in a spiral motion. It will continue in its spiral motion until an obstacle is met, after which it will stop. As we are working with a rectangular environment, we will implement squared spirals and not circular. Squared spirals, in the sense that the robot moves in straight lines and turns 90 degrees. The reason for this is we cannot guarantee a full sweep of a cell otherwise.

2.4 PPCR algorithms

A path plan where the entire accessible part of the environment is sweeped by the vacuum cleaner robot is known as the ”Path Planning Coverage Re- gion” algorithm (Yakoubi & Laskri 2016). When the environment has been mapped, the robot can combine its knowledge with a particular algorithm in order to ensure a PPCR. Naturally, problems arise if the area were to be changed dynamically, as the robot never could be sure of whether its

8 current mapping is up-to-date or not. This however, is not an issue in our implementation as we assume a static environment.

A wide variety of the available robots today only use predefined patterns (Hasan et al. 2014). One problem with this is that it only guarantees full coverage in an obstacle free room. Another problem with this strategy is that the robot will likely move over already cleaned cells as it does not employ the dust map or analyse the neighbouring cells. This will overtime causes an abundance of redundant paths (Lee & Banerjee 2015). An efficient trajectory of a PPCR has minimum amount of turns and revisited clean cells (Yakoubi & Laskri 2016).

Previous research tends to optimise the robot’s cleaning time by reducing redundant paths (Yakoubi & Laskri 2016, Gajjar et al. 2017). However, pre- vious research assumes that once a cell has been swept it is considered clean. Therefore the optimisation is only about finding the fastest PPCR that has the least amount of distance travelled. While this has its benefits for speeding up the full sweep, it assumes that the dust is evenly distributed on the floor and that one sweep is enough for the robot to collect the dust. In the real world, dust would likely be amassed in the corners and around obstacles. The suction would also gradually degrade as more dust is collected. The robot’s dust container would also eventually have to be emptied. A consequence of this could be that the robot does not clean the room completely after one sweep. This is the benefit of the dust map; the robot would know specifi- cally where the remaining dust is and it can adapt its movement pattern in accordance with that information (Lee & Banerjee 2015).

2.5 Related work

Once the environment has been divided into cells it is time to find an efficient path for traversing and cleaning them. In other words the algorithm of choice

9 has to build the PPCR.

2.5.1 Algorithm 1: The pattern method

An example of obtaining a PPCR is presented by Kang et al.. They use predefined template patterns such as zigzag and/or spiral paths. These pat- terns are favourable because they are not very complex and creating a path out of them does not put such a heavy computational burden on the robot. The environment consists of areas composed of numerous cells/squares. The environment gets divided into areas through a scan line which scans the area column by column from left to right. If the scan line detects any changes from the last scan line, new areas are created (see Figure 1). The areas are kept in three lists, OPEN, CLOSED and PRIORITY. The OPEN list stores cells yet to be covered, the PRIORITY list likewise, but its elements are prioritised unlike those of the OPEN list. That priority is assigned to areas which are isolated, i.e. have no uncleaned neighbours left. The CLOSED list contains the areas for which a path has already been calculated, which is where all areas eventually will have been put once the whole grid has been cleaned. In each step of the algorithm the area that is the closest to the robot and has the highest priority is chosen, for which the optimal path then will be calculated by combining pieces of the predefined template paths.

Cells are treated as areas and not individual cells which is not the case of the dust map, where each cell is treated separately. The areas are decided depending on the obstacles present in the room and the algorithm cleans the areas one by one. We disregarded this algorithm because it deviates from our implementations of a dust map algorithm too much.

10 Figure 1: Decomposing the room into rectangular areas when encountering obstacles. Source: (Kang et al. 2007)

2.5.2 Algorithm 3: The genetic method

A more complex approach is proposed by Yakoubi & Laskri. They apply a genetic algorithm to generate the PPCR. They treat the cells of the grid as genes and form chromosomes by combining a number of genes. These chromosomes will then represent the path that the robot could possibly take. Starting from each of the eight possible directions from the robot’s current position, different chromosomes will be generated by randomly choosing the next neighbouring gene. This initial calculation will have generated eight different paths, that are either straight lines or zigzagging motions. Each and every one of these paths will be evaluated by the amount of coverage; how many genes have already been cleaned and how many obstacles are in the way? The ideal choice is the path in which no cell has been cleaned and which has no obstacle in the way. Their idea of improving this genetic algorithm in order to obtain more efficient paths is either through a crossover point between 2 paths or mutating the chromosome by randomising a completely

11 new neighbour. The crossover method looks for a crossover point which differs by most one in the two compared chromosomes and then swaps that gene along with its tail with each other. Which one of the techniques that is chosen is determined by probability. If one of these methods is employed, the new child paths are reevaluated and if an improvement is made, the best child path will determine the path that the robot shall take.

The problem with this implementation is that full coverage can be obtained very late as probability will control the path of the robot, meaning it can leave cells uncleaned for a long time if their paths are not chosen. It does not use a map in a way that is suitable for this study.

2.5.3 TSP-based: Hess’ algorithm

Hess et al. uses a tessellated environment, which essentially is an environment decomposed into grid cells, similar to ours. Their focus is two-fold; firstly they introduce a model which estimates the dust distribution over time and secondly they discuss how this estimation of a dust distribution map can be used to generate efficient cleaning policies. For the generation of paths, they propose two policies. The first one is meant to guarantee that the dirtiest cell in the whole room will be cleaner than a threshold defined by the user. The second policy is likewise supposed to minimise the dirt level of the dirtiest cell, but within a cleaning cycle, whose maximum duration is defined by the user. They apply weights to their cells, which increase or decrease the urgency of cleaning them. These weights are also user-defined, for example after having cooked dinner a user might want the robot to focus on cleaning the kitchen. To generate the paths they model each cell as a node in a graph with according edges to adjacent nodes (cells). The problem is modelled as a travelling salesman problem (TSP). For the first policy, they apply a state-of- the-art TSP-solver to generate the shortest collision-free path that traverses all cells which exceed the user-defined dust threshold. For the second policy,

12 they apply the TSP-solver iteratively. Each iteration represents a cleaning cycle and the cleaning is continued until the robot has reached below the user-defined maximum dirt level.

The efficiency of the implementation varies. When applying the TSP-solver iteratively, great efficiency is achieved. However, with greater efficiency comes the drawback of longer computation times. The computation times with their different policies could range from one second to several minutes. We did not think their algorithm could guarantee complete cleanliness in real time.

2.5.4 Algorithm 2: The greedy method

Another way of generating a PPCR is by working with the 8 cells surround- ing the robot (Gajjar et al. 2017). At the beginning, each cell will have another integer value, apart from the dust value. This value represents how many obstacles surround the cell. The walls are also considered an obstacle. After this the path can be decided by path cost evaluation with the formula CoverageCost = S − U where S is the number of surrounding cells and U the number of uncovered cells. The cell with the highest coverage cost lower than 8 is chosen and the neighbouring cells are incremented by 1, since they now have one less uncovered neighbour. In Gajjar et al.’s version the priori- tisation is not put on cells that are already in the direction the robot is facing if two or more cells have the same coverage cost. If an already visited cell is chosen again the robot will backtrack until a next unvisited cell is found. If it keeps backtracking and does not find a new empty cell, no complete path is available. Otherwise the steps are simply repeated until every cell is visited.

This algorithm guarantees full coverage and makes use of the dust map with its coverage cost in the same way the robot uses it to track the dust level in

13 its neighbouring cells. This is the algorithm that we will implement in our test system.

14 3 Methods

The problem we have decided to focus on is how to reduce the cleaning time. The key to this is to focus on the state after the first sweep. Consider the initial zig-zag sweep as the first sweep in our tests. The reason for which is that the first sweep will clean most of the debris in the room leaving remaining dirty cells scattered. In a real world scenario, while the robot conducts the first sweep it will be able to scan every cell and thereby generate a remaining dust map that could be used in order to create efficient algorithms to proceed with.

The purpose of the testing suite we have implemented was to compare differ- ent strategies with different dimensions of the room and dust maps. Three different cleaning strategies were compared to each other. More details re- garding the testing is discussed in section 3.4.

3.1 Implemented path planning algorithms

In this section we discuss the path planning algorithms that we have imple- mented.

3.1.1 Zigzag

Firstly we made sure that the zigzag moved in the direction of the farthest side of the room. This approach will not require as many turns as performing them along the shorter side. Meandering movement based on turns is more costly than just moving straight, the aim should therefore be to take this into account in order to minimise the number of turns. We conducted tests where each 90 degree turn took one time unit. This way we could see that minimising the amount of turns is to be preferred in order to reduce time.

15 The robot kept doing the zigzag pattern until full coverage was achieved. In Figure 2 you can see a demonstration of this pattern.

Figure 2: An example of how a zigzag pattern could look like.

3.1.2 Spiral

Two variants of this pattern were implemented. The spiral could either be coiled inward or outward. These patterns are essentially similar, although the inward one would preferably start in a corner of the room, while the outward one would start in the middle of the room to achieve maximum coverage before the robot has to stop. We constructed the algorithm so that it stops completely when encountering an obstacle or a wall. The spiral will take an integer as a parameter which specifies the length of the last and longest arm of the spiral, i.e. it will continue until that spiral arm length has been achieved. In Figure 3 you can see a demonstration of this pattern.

16 Figure 3: An example of how a spiral pattern could look like.

3.1.3 Wall-to-wall

Dust tends to accumulate along the walls and in the corners, which other patterns might find hard to reach in short time. Therefore this pattern is efficient in combination with other template patterns to achieve a fully cleaned room. It achieves that without having to revisit too many clean cells that the zigzag and spiral would have to (Hasan et al. 2014). In Figure 4 you can see a demonstration of this pattern.

Figure 4: An example of how a wall-to-wall pattern could look like.

17 3.1.4 Greedy PPCR algorithm

Algorithm 2 is the the last algorithm described in section 2.5. After each visited cell had been visited and cleaned, the adjacent cells would be updated. This update consists of increasing the cell’s surrounding obstacles count by 1. The robot would then choose the cell with the highest surrounding obstacle count below 8 to be visited next. This process was repeated until all the cells had been visited. If two cells would have the same value, the one that would require the least turning angle was chosen. This was the improvement we applied from the Gajjar et al. (2017) version. If no adjacent cells had a value below 8, the robot would backtrack until it finds an empty cell.

3.1.5 Greedy heuristic

In order to answer hypothesis H2 we developed a greedy heuristic that moved to the nearest uncleaned cell as a minor goal specification. It scans one square area with radius + 1 cells away from the robot’s current position in order to find the nearest uncleaned cell; the radius initially being set to 0. If no cell is found within that perimeter, the radius is incremented by 1 until a cell is found or there is not a single dusty cell remaining. If several dusty cells are found within the square and one of them is either in front or behind of the robot, then they are prioritised. This is due to the fact that the robot will not have to turn, but instead simply move forward or backward, which makes them an optimal choice. This saves energy and time because the robot will not have to turn.

18 radius = 0; while radius within room do Find closest dirty cell radius cells from the robot; if No dirty cells found then radius++; end else Move to cell; Clean cell; radius = 0; end end Algorithm 1: The greedy heuristic’s pseudo code

3.2 Cleaning strategies

The strategies listed below are the different cleaning strategies used by the robot. They were compared to each other and that comparison constitutes the results of the simulations.

3.2.1 Strategy 1: pattern-based strategy

Strategy 1 consisted of performing a zigzag pattern followed by a wall-to-wall and finished off with an inward spiral pattern. This process was repeated until the room had been cleaned entirely (see Algorithm 2).

We opted to perform a spiral after the wall-to-wall instead of simply utilising the zigzag pattern in order to reach different cells of the room at different speeds. The reason for which is if only a few dirty cells remain at a place where they perhaps could be reached faster by using the spiral instead.

19 while room is dirty do if room is dirty then do zigzag; end if room is dirty then do wall-to-wall; end if room is dirty then do inward spiral; end end Algorithm 2: Strategy1’s pseudo code

3.2.2 Strategy 2: Proposed greedy heuristic after an initial sweep

Strategy 2 only performed an initial zigzag pattern as a first sweep followed by the greedy heuristic until no more dirty cells were found (see Algorithm 3).

if room is dirty then do zigzag; while room is dirty do greedy heuristic; end end Algorithm 3: Strategy2’s pseudo code

3.2.3 Strategy 3: Greedy strategy

The third and last strategy consisted of the heuristic only. The strategy re- lies on the dust map being known even before the first sweep which will be

20 discussed later (see Algorithm 4).

while room is dirty do greedy heuristic; end Algorithm 4: Strategy3’s pseudo code

3.2.4 Zigzag’s direction

The zigzag pattern was also evaluated for how the efficiency differed depend- ing on which wall it decided to perform its S-patterns along and how making the wrong decision could increase the overall time needed to perform the pattern. In this test the following rooms were used; 10 x 20, 10 x 50, 10 x 80 and 10 x 100.

3.3 Building the test system

Our testing suite was built in Unity3d with C# (Unity Technologies 2018). Unity3d is a platform which makes it easy to quickly focus on what it impor- tant, which in our case is the implementation of the different path algorithms. Having to handle the programming of an intricate visual rendering and co- ordinate system from scratch is not within the scope of this study.

The room itself was generated by two integer values, width and length. The cell objects, are represented by a 1x1 square (same length as the robot’s diameter). The cell contains numerous data fields such as dust value and the amount of adjacent obstacles (used by the PPCR algorithm described in section 2.5.4). There is also a field for whether the cell is an obstacle or not, which is generated at run time to fill out the grid.

21 As mentioned in section 2.4, the dust will most likely not form a uniform layer. Therefore the main dust map generation is performed by randomising an integer between 1 and 10 for every cell that is not near an obstacle. An additional random number is added to the initial dust values of the cells that are immediately adjacent to an obstacle or a wall. This means that the robot most likely will have to focus more time on these areas (see Table 2 for an example). The robot cleans at a rate of five dust per cell visit. The cells light up green once they have been completely cleaned.

In the second room scenario obstacles were placed inside the room. An obsta- cle is simply one squared cell in the grid but unavailable for the robot. The aim for this test was just to analyse how the robot’s efficiency of the initial sweep was affected compared to an empty room of the same dimension.

3.4 Benchmarks

The testing for the obstacle free rooms were conducted in the dimensions (width x length): 10x10, 10x20, 10x50, 10x80 and 10x100 with different dust map generations. Each strategy (see section 3.2) would iterate 100 times in each room with a newly generated dust map for each iteration. The starting position of the robot was determined by the last cell it cleaned during the previous test iteration. In other words, the randomly generated dust map would be the deciding factor on where the robot would stop depending on which strategy was used. For the obstacle room obstacle with the dimension 1x1 were placed on random positions throughout the room. They were placed successively so that we could see what effect it would have on the time, distance and amount of turns needed to clean the room. If the program read a cell of the dust map as “Obstacle” instead of an integer, an obstacle was placed at those coordinates.

The different strategies were compared by their respective times to complete,

22 lengths travelled and amount of turns.

There were three different type of dust map generations in which all the cleaning strategies were compared to each other. The reason for this was to see if one strategy outperformed the others no matter the dust distribution. The different dust maps were the following:

1. More dust gathered at the walls of the room.  random(1,10)+random(1,10), if x is adjacent to a wall cell(x) = random(1,10), otherwise

2. More dust gathered at the centre of the room (the inverse of the map above).  random(1,10)+random(1,10), if x is not adjacent to a wall cell(x) = random(1,10), otherwise

3. Uniform distribution across all cells with dust value 1. (Even though this scenario is unlikely, the purpose is theoretical.)

cell(x) = 1

The tests conducted in the closed room only involve the first sweep. The reason for that is discussed in the discussions chapter (see Section 5).

23 Figure 5: Visual representation of a 10x10 obstacle free room. A green cell is free of dust. Grey ones still have dust remaining. The black number represents the dust level in the cell. The blue circle represents the robot. (See 3.3 for more information.)

24 4 Results

For the following graphs presented in this chapter we compare the time needed to clean the room, amount of turns and distance travelled by the robot. The metrics are the following:

• Time: Each operation took a certain number of time units to execute in the test system. For example we decided that one 90 degree turn takes 1 time unit, which would be the same time as going forward one cell in a straight line. This was decided and not a property that is nec- essarily true for some robotic vacuum cleaners on the market. Instead of clocking the real simulated time for the computer to fully clean the room we measured the amount of time units depending on operations. The outcome of this gave a more accurate comparison. Nevertheless a lower value on the Time variable equals a faster algorithm for cleaning the entire room.

• Turns: One turn is registered when the robot has performed a 90 de- gree rotation from its current position. A reversing operation is not equal to making two turning operations and then going forward. In- stead the robot will simply reverse in a straight line; hence, no turning operation is registered. For turning operations such as 45 degrees or similar, the following formula was used for adding data to the Turns variable: angle/90

• Distance: The distance logged as the robot moves along different cells was obtained through Unity3d’s Vector3.Distance method. It calcu- lated the distance between the robot’s last position and its new one. Because the cell coordinates are calculated within its parent object (the floor object in Unity3d) it does not imply that a distance of 1 corre- sponds to moving across one cell. This is due to the way Unity3d han-

25 dles its objects in the project. Distance works in similar way as Time, we are talking about distance units not meters or cells, although, a lower value on the Distance variable means less travelled distance by the robot. It is a relative measurement.

4.1 Obstacle free room with more dust along the walls

This section presents the results of having a dust map generator which allows for a higher dust level in every cell adjacent to a wall. We let the simulation run 100 times for each dimension of the room and each strategy, with a new randomly generated dust map for every iteration. The data results are presented as an average value with a standard deviation in the graphs and tables below.

4.1.1 Time

Figure 6 represents the time it took for the robot to clean the room for the different strategies with the data from Table 3.

26 Figure 6: This graph shows how the three different strategies’ time variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 3: Time results by using different strategies (see section 3.2) in different dimensions of the room. x 10 20 50 80 100 Strategy 1 Avg 3.66 9.02 31.35 64.00 102.79 S.D 0.22 1.59 7.39 16.55 29.14 Strategy 2 Avg 2.72 5.02 12.12 19.20 26.87 S.D 0.12 0.18 0.39 0.51 0.63 Strategy 3 Avg 2.65 5.0 12.21 19.41 24.10 S.D 0.13 0.21 0.34 0.56 0.45

27 4.1.2 Turns

Figure 7 represents amount of turns it took for the robot to clean the room for the different strategies with the data from Table 4.

Figure 7: This graph shows how the three different strategies’ turn variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 4: Turn results by using different strategies (see section 3.2) in different dimensions of the room.

28 x 10 20 50 80 100 Strategy 1 Avg 56.81 83.74 156.86 228.17 311.2 S.D 2.80 13.86 38.35 62.62 92.68 Strategy 2 Avg 52.09 76.10 158.32 240.57 296.06 S.D 2.80 13.86 38.35 62.62 92.68 Strategy 3 Avg 48.53 85.48 181.60 277.66 329.5 S.D 4.55 8.35 18.38 22.73 22.60

4.1.3 Distance

Figure 8 represents distance travelled needed for the robot to clean the room for the different strategies with the data from Table 5.

29 Figure 8: This graph shows how the three different strategies’ distance vari- able develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 5: Distance results by using different strategies (see section 3.2) in different dimensions of the room. x 10 20 50 80 100 Strategy 1 Avg 4.63 10.00 32.33 64.98 103.76 S.D 0.23 1.59 7.40 16.55 29.14 Strategy 2 Avg 3.43 5.66 12.79 19.81 24.51 S.D 0.36 0.41 0.52 0.58 0.72 Strategy 3 Avg 3.25 5.66 12.93 20.02 24.75 S.D 0.37 0.43 0.46 0.59 0.55

30 4.1.4 Discussion

Drastic improvements can be seen with our simple adjustment to the cleaning strategy by using the heuristic after the initial zigzag sweep (Strategy 1 compared to Strategy 2). This also verifies our second hypothesis, which stated that “moving towards the nearest uncleaned cell after the initial full sweep will reduce the required cleaning time”. Strategy 2 managed to reduce the time needed for cleaning the entire room by roughly 26% in the smallest room and 74% in the 10x100 room (see Figure 6) compared to Strategy 1. Almost the same numbers apply to the distance variable between these two strategies. Both Strategy 2 and Strategy 3 resulted in close to identical improvements when compared against strategy1. However, the reason for why we suggest using Strategy 2 will be discussed in section 5. Note as well that the improvements are not conditioned by any lesser amount of turns conducted as they remained almost the same no matter the strategy. The only significant difference was the standard deviation of the first strategy, which is highly dependent on the starting position of the robot. A good starting position would give better results and vice versa.

4.2 Obstacle free room with more dust at the centre of the room

This section presents the results of having a dust map generator which allows for a higher dust level in every cell not adjacent to a wall. We let the simulation run 100 times for each dimension of the room and each strategy, with a new randomly generated dust map for every iteration. The data results are presented as an average value with a standard deviation in the graphs and tables below.

31 4.2.1 Time

Figure 9 represents the time it took for the robot to clean the room for the different strategies with the data from Table 6.

Figure 9: This graph shows how the three different strategies’ time variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 6: Time results by using different strategies (see section 3.2) in different dimensions of the room.

32 x 10 20 50 80 100 Strategy 1 Avg 5.58 19.10 77.52 165.03 243.23 S.D 0.48 2.41 9.25 21.30 31.06 Strategy 2 Avg 3.44 6.70 16.80 26.98 33.57 S.D 0.13 0.20 0.39 0.50 0.55 Strategy 3 Avg 3.32 6.70 16.77 26.94 33.72 S.D 0.13 0.19 0.39 0.50 0.69

4.2.2 Turns

Figure 10 represents amount of turns it took for the robot to clean the room for the different strategies with the data from Table 7.

33 Figure 10: This graph shows how the three different strategies’ turn variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 7: Turn results by using different strategies (see section 3.2) in different dimensions of the room. x 10 20 50 80 100 Strategy 1 Avg 86.36 179.70 398.35 601.2 744.48 S.D 6.28 23.14 47.93 78.02 95.12 Strategy 2 Avg 68.09 114.77 258.67 405.44 499.56 S.D 4.49 7.55 12.26 17.13 16.55 Strategy 3 Avg 58.59 113.36 264.31 412.62 511.48 S.D 5.97 8.27 13.06 17.11 24.54

34 4.2.3 Distance

Figure 11 represents distance travelled needed for the robot to clean the room for the different strategies with the data from Table 8.

Figure 11: This graph shows how the three different strategies’ distance variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 8: Distance results by using different strategies (see section 3.2) in different dimensions of the room.

35 x 10 20 50 80 100 Strategy 1 Avg 6.55 20.07 78.50 166.01 244.21 S.D 0.48 2.41 9.25 21.30 31.06 Strategy 2 Avg 3.99 7.23 17.31 27.42 34.05 S.D 0.38 0.45 0.49 0.58 0.63 Strategy 3 Avg 3.84 7.30 17.22 27.42 34.20 S.D 0.36 0.44 0.53 0.64 0.78

4.2.4 Discussion

The amount of time needed, turns conducted and distance covered was gen- erally higher for this room with the dust in the centre, compared to the other tests where the dirtiest cells were along the walls. This is to be expected, since there are more dirty cells to be cleaned repeatedly in the middle of the room than along the walls. As for the cleaning time, Strategy 2 managed to reduce the time compared to Strategy 1 by 38% in the smallest room and 87% in the largest room. Compared to the first dust map (see section 4.1) Strategy 2 performed even 12 percentage points better in this environment than Strategy 1. As for the amount of turns, a 21% improvement was found in the smallest room and 33% in the largest room. The total distance trav- elled was reduced by 39% in the smallest room and 86% in the largest one. Roughly the same improvement as with Strategy 2 was found when using Strategy 3 compared to Strategy 1 in every category except for the amount of turns in the smaller rooms. The reason for why both Strategy 2 and Strat- egy 3, which employ the implemented heuristic, perform even better in this scenario is that choosing the non-optimal cell will not be as costly. It will not have to traverse the entire room back and forth as the outer cells are completely cleaned before the cells in the middle (see 5.3).

36 4.3 Obstacle free room with uniform dust distribu- tion

This section presents the results of having a dust map generator where every cell contained a dust value of one. This meant the robot only had to pass each cell once in order to clean them. We let the simulation run 100 times for each dimension of the room and each strategy, with a newly generated dust map for every iteration. The data results are presented as an average value with a standard deviation in the graphs and tables below.

4.3.1 Time

Figure 12 represents the time it took for the robot to clean the room for the different strategies with the data from Table 9.

37 Figure 12: This graph shows how the three different strategies’ time variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 9: Time results by using different strategies (see section 3.2) in different dimensions of the room. x 10 20 50 80 100 Strategy 1 Avg 1.28 2.28 5.28 8.28 10.28 S.D 0 0 0 0 0 Strategy 2 Avg 1.28 2.28 5.3 8.3 10.3 S.D 0 0 0 0 0 Strategy 3 Avg 1.22 2.68 5.72 8.78 10.78 S.D 0.03 0.08 0.08 0.09 0.10

38 4.3.2 Turns

Figure 13 represents amount of turns it took for the robot to clean the room for the different strategies with the data from Table 10.

Figure 13: This graph shows how the three different strategies’ turn variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 10: Turn results by using different strategies (see section 3.2) in dif- ferent dimensions of the room.

39 x 10 20 50 80 100 Strategy 1 Avg 20 20 20 20 20 S.D 0 0 0 0 0 Strategy 2 Avg 20 20 20 20 20 S.D 0 0 0 0 0 Strategy 3 Avg 18.77 44.27 44.12 44.27 44.27 S.D 1.03 3.80 4.07 3.8 3.8

4.3.3 Distance

Figure 14 represents distance travelled needed for the robot to clean the room for the different strategies with the data from Table 11.

40 Figure 14: This graph shows how the three different strategies’ distance variable develops depending on the length of the room (x-axis), with a room width of 10. The blue dots represent Strategy 1, the orange ones Strategy 2 and the purple crosses Strategy 3 (see 3.2).

Table 11: Distance results by using different strategies (see section 3.2) in different dimensions of the room. x 10 20 50 80 100 Strategy 1 Avg 2.26 3.26 6.26 9.26 11.26 S.D 0 0 0 0 0 Strategy 2 Avg 2.29 3.27 6.29 9.29 11.29 S.D 0 0 0 0 0 Strategy 3 Avg 1.82 3.67 6.71 9.77 11.77 S.D 0.07 0.08 0.08 0.09 0.1

41 4.3.4 Discussion

Strategy 1 and 2 fared equally well in all three metrics (see section 4), which is reasonable since they both employ an initial zigzag pattern. In this case it was sufficient to clean everything because there was only a dust value of one in every cell and the robot will clean all of it in one sweep. Therefore Strategy 2 will not ever have to continue with the greedy algorithm (see section 3.1.5). However, Strategy 3 differed in the amount of turns conducted, namely a 6% reduction of the turns with Strategy 1 in the smallest room and a 121% increase for all of the other room sizes. For the distance metric it also differed a bit, a 19% reduction of the distance with Strategy 1 in the smallest room and an increase of 5% in the largest room. These differences could be attributed to the fact that the heuristic just takes the closest tile. If there are several which are as close, it will leave them behind and have to revisit them later, which might mean a lot of going back and forth, resulting in redundant turning and traversing.

4.4 Consequence of zigzag choosing different ways

As the zigzag is essential for the second cleaning strategy, (see 3.2), it’s important that it remains as efficient as it can possibly be in an empty room. The correct way is to follow the longest side of the room and not vice versa.

4.4.1 Turns

Figure 15 shows the amount of turns needed for the zigzag to perform a full sweep depending on which direction it initially follows. The data is shown in Table 12.

42 Figure 15: This graph shows how the zigzag’s turn variable develops depend- ing on the length of the room (x-axis) and which direction it conducts the movement.

Table 12: The table below is the turn data visualised in Figure 15 x 20 50 80 100 Correct Way 18 18 18 18 Wrong Way 40 100 160 200 We can see that the amount of turns is always two times larger than the length of the room if the robot chooses the wrong direction to perform the zigzag, while the correct way is unaffected.

4.4.2 Time

Figure 16 shows the time needed for the zigzag to perform a full sweep depending on which direction it initially follows. The data is shown in Table 13.

43 Figure 16: This graph shows how the zigzag’s time variable develops depend- ing on the length of the room (x-axis) and in which direction it conducts the movement.

Table 13: The table below is the time data visualised in Figure 16. x 20 50 80 100 Correct Way 1.98 4.68 7.38 9.18 Wrong Way 2.4 6 9.6 12 The consequence in time was that the wrong way was 21% slower in the smallest room and 31% slower in the largest room.

4.4.3 Discussion

The difference in time needed and amount of turns conducted if the zigzag chooses the wrong initial direction was significant. This was however ex- pected as following the shorter wall will result in having to conduct more turns if a full sweep is to be completed. Observe that, even though it will always be more time costly choosing the wrong way, the two lines would not

44 diverge the way they do if a turning operation took less time. We decided that it should take one time unit for a 90 degree turn, therefore the gap be- tween lines would have be smaller if we would have chosen differently.

4.5 Room with obstacles

As we mentioned in the section 1.2, the main focus of this study was on obstacle free rooms. However out of curiosity we wanted to analyse how an efficient PPCR algorithm’s results, such as Algorithm 2 in section 2.5.4, would compare against the optimal results of an obstacle free room. The comparison just involved the first sweep as the remaining dust cells would be optimally cleaned up by the heuristic as evaluated in the obstacle free room.

In the room with obstacle (see Figure 17), a black cell represents an obstacle that is unavailable for the robot and Table 14 are the base values compared to the data in Table 15. The obstacles were randomly placed upon generating the dust map and and they remained static through out the sweep.

Table 14: This table shows the base case for the zigzag pattern to perform a full sweep of a 10x10 obstacle free room Turns 20 Time 1.2 Distance 2.16

Table 15: This table shows the difference in efficiency for the first sweep be- tween a 10x10 room and a room with a varying amount of obstacles scattered around.

45 #Obstacles 0 1 2 3 4 5 6 7 8 9 10 Turns 40 43 43 52.5 51.5 50 51.5 52 50 57 55 Time 1.37 1.4 1.39 1.51 1.49 1.46 1.44 1.43 1.41 1.47 1.44 Distance 2.35 2.36 2.35 2.49 2.47 2.83 2.83 2.41 2.8 2.44 2.41 Of the tests conducted there is not a good correlation between the variable values and number of obstacles more than that they stay fairly consistent. Note that algorithm 2 never had to perform any backtracking which would increase the variable values.

46 Figure 17: Visual representation of an obstacle room. A green cell is free of dust. Grey ones still have dust remaining. A black cell represents an obstacle. The blue circle represents the robot. The black numbers represent the remaining dust in each cell. The red number is the surrounding obstacle value used by algorithm 2 (see 3.1.4).

47 5 Discussion

5.1 The obstacle free room

The results of the different cleaning strategies were collected in three different types of dust maps. The overall results proved that employing the heuris- tic will reduce the cleaning time. Both Strategy 2 and Strategy 3 (see 3.2) had very similar results when compared to Strategy 1. However, in the tests where only the heuristic (Strategy 3) was employed, a known dust map is required. This strategy would not be applicable in a real life scenario due to the fact that the robot has not made an initial sweep of the dust level. An as- sumed map could be generated, given that data has been collected over time. However, the zigzag pattern scans the cells while covering the entire room, without needing the dust map itself. When the zigzag has completed, a dust map is then complete and up-to-date for the heuristics disposal. Therefore we would opt for using Strategy 2 as the efficiency between them are almost identical, but Strategy 2 has the advantage of giving us the correct dust map. The results of the heuristic proves our second hypothesis H2.

Depending on the battery capacity, meaning how long the robot can clean without having to stop and recharge, the heuristic approach would theoret- ically reduce the total time needed by a significant margin. This could of course vary because both the amount of turns and distance travelled put strain on the motor which consumes power. However considering the major improvement on the distance travelled as well as time needed, the assump- tions seem reasonable.

48 5.2 The room with obstacles

The purpose of the room with obstacles was to illustrate the additional time needed for the first sweep when the complexity rises, which in turn affects the energy consumption (see Table 15). Energy consumption will affect the total cleaning time if the robot has to recharge. We had different amount of obstacles scattered around the room. This means that there are a number of cells the PPCR algorithm did not have to cross. In theory this should lower the distance travelled compared to the zigzag in the obstacle free room. However, this was not the case for PPCR Algorithm 2. The reason for that is that it moves in a diagonal snakelike pattern and a lot of turns had to be conducted. A consequence is that the time increases as well. The PPCR Algorithm 2 is efficient in its environment, we are just highlighting that all variables increase when the complexity of the room increases. Template patters are extremely effective in an obstacle free room, but the room has to remain that way for these patterns’ efficiency to remain. Otherwise more sophisticated algorithms are needed, like the PPCR Algorithm 2 that we implemented.

The only difference with our own heuristic implementation in the room with obstacles is that the logic of the code has to be improved to move around obstacles. In example the robot should not be able to move diagonally around an obstacle. However in the obstacle free room, we have already proven the benefits of the heuristic with the use of a dust map when cleaning up the remaining uncleaned cells. Therefore, we opted not to implement this logic due to the short planning horizon of this study. It would arguably only give the same results as the obstacle free room, meaning the heuristic would outperform the template patterns when cleaning up the remaining dirty cells.

49 5.3 Limitations and possible further improvements of the heuristic

The greedy heuristic could be optimised further. Its current approach is greedy due to the fact that it does not know if selecting another cell would have been a better decision later on. For example, imagine there is one dusty cell to the right of the robot and one to the left of the robot as well as two more further to the left. The robot will choose the left side as this is the cell checked before the right one, meaning it will continue to the left and then lastly have to go all the way back to the right cell. The heuristic cannot predict which of the two would be the better choice for minimising the total distance travelled. This could possibly be mitigated on average by selecting the direction on random from multiple equally desirable choices. Finding an optimised dust map algorithm would improve the efficiency of using a dust map even further. We have proven the efficiency of the dust map technology, which will help achieving minimal cleaning time needed.

Our heuristic always selected the closest dirty cell and cleaned it once it arrived. When the robot travelled diagonally in the grid it would partially overlap several squares on its way, which would raise questions of how the dust level would be affected in those squares if they were not clean already. One could probably just calculate how much the robot overlapped the square, remove a certain percentage of the dust based on how great of a overlap it was and instead represent the dust with floating-point numbers. This would possibly prove to be problematic though, because in the predefined patterns our robot moved one tile at a time and did not clean anything until it reached its goal, as opposed to a robot in a real environment which would continuously clean as it went along. The dust values of the cells in our simulation just represented how much dust each cell contained. There was no locality to the dust other than that it was within a specific cell. It could

50 be presumed that the dust was evenly distributed in the cells, but not having any explicit locality to the dust would in our case mean that a cell could be completely cleaned simply by scraping the corners of it enough times, even though in reality those corners would have already been cleaned and the dust would still remain in the middle. To combat this we could rework the dust map representation, for example by having each pixel represent a cell. Thus the cells would be smaller and not as large as the robot itself. The robot would then move continuously, not cell by cell, and clean every dust pixel it encounters. This would also be a more accurate representation of a real world vacuum cleaner environment.

5.4 Reflection on the hypotheses

As for the first hypothesis H1 we can conclude that following a wall after the initial sweep was not necessarily a flawless move. If only one cell had been completely cleaned along the wall during the initial sweep it would have been enough redundancy traversing this cell again using the wall-to-wall pattern instead of our greedy heuristic as it will do the same job without the redundant cell crossing, unless in the worst case scenario, where it would do the same job as wall-to-wall. To summarise, we can conclude that using a targeted dust map algorithm, such as our greedy heuristic, is a better choice than perform a wall-to-wall pattern after an initial sweep.

The second hypothesis H2 was discussed in section 5.1, where it was con- cluded that “moving towards the nearest uncleaned cell after the initial full sweep” did in fact “reduce the required cleaning time compared to predefined patterns”.

The third hypothesis H3 stated “Employing a targeted dust map algorithm will outperform template patterns no matter the state of the room.”. We can conclude that this is not the case. In the uniform dust map, (see 4.3), the

51 heuristic performed worse than the zigzag pattern. However in the other ob- stacle free room dust scenarios, which are more likely, the targeted algorithm (the heuristic) proved to be a major improvement compared to template patterns. The heuristic would have been just as good as the zigzag in the uniform case if the heuristic were optimal, as it would have mimicked the zigzag path. So a statement that applies is “Employing an optimal targeted dust map algorithm will in its worst case perform just as good as the template patterns no matter the state of the room.”

Template patterns such as the zigzag and the spiral are very effective in envi- ronments where they can move freely. More specifically, areas that are open. However when having access to a dust map, they quickly become inferior as seen by the results. The reason for this is simply that the implemented algorithms that make use of the dust map can mimic these patterns, possibly without cleaning redundant cells.

We were interested in the following questions:

“Given that the environment is known and static and with the help of a dust map; how should the robot move in the room’s current state in order to minimise the time needed for complete dust removal?” We have given one greedy solution to this problem. Find the closest cell and move straight towards it after the initial sweep. An optimised solution can of course be found as described in section 5.3.

“How does the efficiency of the robot differ between an empty room and one with obstacles present?” As seen in section 4.5, the amount of time clearly increases with obstacles in the room. Note however that it does not mean that the PPCR algorithms are inefficient. It is simply a reminder that once the robot works in a room with obstacles, which is a likely real life scenario, more sophisticated algorithms have to be used, as template patterns will struggle to perform as efficiently as the dust map algorithms.

52 5.5 General matters

Normally when one vacuums an area manually, a sweeping stroke is repeated on the same area until it has been cleaned. The reason for why this pattern is not mimicked by the robot is simply a matter of reducing redundancy. Going back and forth will most likely result in the robot having to go over an already cleaned cell when it is ready to move on to another area. As seen in the tests, going over already cleaned cells is costly and will thereby increase the time required to clean the room.

We previously mentioned that the first hypothesis ended up being falsified. However, if the robot never had access to a dust map, meaning a cheaper robot with less sensors, this approach would have been excellent to achieve maximum dust removal during a short period of time as higher concentration of dust is collected near the walls and only a proximity sensor would be needed at that point. Using our heuristic would require sensors for detecting the dust level as the robot moves along and the knowledge of knowing where its current position is in the room and where the next goal specification is located. This would require a larger memory for storing all of this data, which implies a more expensive robot. In the end this study focuses on improving the efficiency with a certain technology, specifically the dust map which makes the wall-to-wall and other predefined patterns method less desirable, but it is noteworthy to keep in mind for cheaper robots.

53 6 Conclusion

Creating path planning algorithms for an autonomous robotic vacuum cleaner can not be restricted to sweeping the entire room and potentially repeating the process for two reasons. The first one being that one sweep is not a guarantee for absolute cleanliness which was the basis for the dust map. The second one being that repeating that full sweep of the entire room would create significant redundancy and thus introduce inefficiency. There is no need to clean already cleaned cells as the results show.

The utilisation of the dust maps allows for targeted algorithms. Algorithms that set up minor goal specifications as the robot traverses the room. This will thereby minimise the cleaning time needed in order to fully clean the room. We have proposed a greedy heuristic in this study, which was, how- ever, not fully optimised as it accounted for a very short planning horizon. Yet it still proved to be a far more efficient approach to minimise the time compared to limiting the robot to predefined patterns in an obstacle free room scenario.

In general, obstacles will increase the power consumption drastically as the robot has to turn and move around them. This is why an efficient PPCR algorithm is needed for creating an optimised path for the initial sweep.

The downside to using the dust map technology is the need for accurate sensors that cheaper robot would not be equipped with. However, having more efficient robots will in turn save energy and compensate the high cost of the equipment.

The next step would be to further optimise the heuristic. This way the dust map is used at its full potential. We strongly believe that equipping the robot with a dust map is the key to make robotic vacuum cleaners efficient. With it they can focus on areas that need cleaning and thereby minimise the

54 cleaning time needed.

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