IROS2019国际学术会议论文集 0435

Understanding Multi Robot Systems on the Concept of Legibility Beatrice Capelli Valeria Villani Cristian Secchi Lorenzo Sabattini Abstract Legibility can be defi ned as the ability of a robot to communicate its intent to the user Legibility is relatively little investigated in multi robot systems but in the literature studies exist where the trajectory of manipulators is analyzed as a factor to improve the collaboration between robots and users In this paper we focus on the legibility of a group of mobile robots To this end we consider a set of motion variables trajectory dispersion and stiffness They are typical parameters that determine the motion of a group of robots To analyze the effect of the motion variables over legibility Fisher s exact test and ANOVA analysis of variance were carried out The data for the statistical analysis cover a full factorial plan and they were collected in a virtual reality set up where the users shared the environment with a group of robots We investigate two aspects of legibility the correctness and the rapidity of communication namely if the communication happens correctly and how fast it happens Trajectory was found to be relevant to correctly communicate the intention of the robots while stiffness and dispersion were relevant for the rapidity of legibility I INTRODUCTION Multi robot systems are almost ready to share our every day life but is there the right background for this future In particular if we want to collaborate with this type of systems it is very important to have a method of communication Nowadays most of these systems work by their own or in the best case they share the environment with human users but they do not interact e g automatic warehouse In this case there is no type of communication and the coexistence is ensured by a safety protocol Along the lines of the survey about human swarm interaction 1 it is possible to split the communication with this kind of robotic systems in two cases remote interaction and proximal interaction Remote interaction describes the communication between a user and a system that do not share the same environment In this case the communication is carried out through a computer or another electronic device that is able to transmit the input signal from the user to the system and possibly to bring back a feedback In the literature this type of communication is widely investigated in terms of teleoperation systems 2 3 Teleoperation is suitable for some types of applications such as search and rescue where the user can not work side by side with the robots for safety issues But it is important to remember that teleoperation needs a physical means to communicate and in a collaborative task it would be easier to interact with the robotic system as if it were another user AuthorsarewiththeDepartmentofSciencesand MethodsforEngineering DISMI UniversityofMod enaandReggioEmilia Italy beatrice capelli valeria villani cristian secchi lorenzo sabattini unimore it Proximal interaction encapsulates all the forms of commu nication that allow the user to directly interact with a multi robot system As every type of communication also this one needs a bilateral understanding Specifi cally the user needs to have the opportunity to control the robot by providing input commands and vice versa the robot should be able to inform the user about its status intention etc The second case namely the ability of the robot to communicate to the user is the focus of legibility and hence of this paper Regarding the communication from the robot to the user it is possible to divide the methods in explicit cues and implicit cues 7 Explicit cues imply that the robot explicitly informs the user of its intentions This can be achieved through voice 8 moving the head of the robot 9 with visual light indicators 9 or through LED indicators 10 Implicit cues can be achieved through the understanding of the movement of the robot and in general they do not need additional devices to allow communication An example is reported in 11 where the animation principles the same used to animate cartoons are employed to communicate the intent of the robot In 12 legibility and predictability are defi ned as two different characteristics of the motion of a robot While their study is focused on a manipulator here we extend the defi nition of legibility adapting it to a multi robot system In this paper we explore the defi nition of legibility for a multi robot system namely the possibility of using implicit cues in a proximal interaction scenario These systems have inherently more parameters that affect their motion compared to a manipulator because they are not a rigid body and they are constituted by multiple agents that must be controlled at the same time Hence we want to investigate if it is possible to communicate some information to the user using implicit cues in the case of proximal interaction We address in particular the problem of inferring the goal of a single multi robot system inside an environment shared with the user We decline the implicit cues into the motion of the robotic system and we choose to evaluate three motion variables trajectory dispersion and stiffness The contribution of this paper consists then in answering the following question do these motion variables signifi cantly affect the legibility of a multi robot system II DEFINITION Legibility is the ability of a robot to communicate its intention to the user without explicit communication Along the lines of 12 a legible motion is a particular type of motion not necessarily the most functional that helps the user to infer the goal of a robot in a quick and confi dent way In this paper we want to extend this concept to a multi robot 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE7349 system and we want to discover if some motion variables are relevant to infer the goal of a group of robots We consider a group of N mobile robots To evaluate the legibility of the system we need to introduce a function called inference function that maps the state of the system into the variable we want to infer i e the goal of the robots IGOAL G 1 where G is the set of possible goals of the multi robot system We describe the state of the system through three motion variables T trajectory of the center of the group D dispersion of the group S stiffness of the group These are only some of the possible variables that can be chosen to describe a multi robot system We choose trajec tory because it is fundamental for a group of moving robots and in general for every type of robot Moreover trajectory is also a parameter already analyzed in other studies about legibility 12 14 15 On the other hand considering the common control architecture based on artifi cial potential fi elds 16 dispersion and stiffness are parameters used to defi ne the motion characteristics of a multi robot system In particular dispersion represents the desired distance between the robots and stiffness is the strength of the potential The inference function IGOALmaps the state of the sys tem into the most likely goal for the group of robots Hence if we defi ne the probability of reaching a particular goal G G given a set of motion variables as P G T D S we can specify the inference function as IGOAL T D S arg max G G P G T D S 2 III METHODS The experiments aimed at understanding whether these motion variables signifi cantly affect the legibility of a multi robot system A Aim of the experiment During the experiment a group of mobile robots traveled towards random goals with different types of movement based on the values of the motion variables To evaluate the legibility of the multi robot system the user was asked to indicate as soon as possible the goal that she he thought as the most likely The aim was then to answer in the correct way as soon as possible B Experimental scenario To collect the data we built a virtual reality set up where the user shared the space with a group of robots Fig 1 a We chose virtual reality because it is possible to build a wide environment and to use a large number of robots which are characteristics very diffi cult to obtain in a real set up In addition virtual reality ensures higher repeatability with respect to a real scenario because it does not introduce localization errors slippage problems or other disturbing factors that are not easy to model As a consequence in a Example of the user s view during the experiments b Disposition of the goals colored cubes and of the robots circled in red with respect to the user camera icon Fig 1 Virtual reality environment our opinion the use of virtual reality represents a signifi cant improvement over experiments presented in 11 and 17 where the movement of robots was shown to users only through an off line video or a sequence of photos On the contrary virtual reality provides an immersive real time interaction that reproduces real environments faithfully and allows to replicate the interaction experience as proved in our previous work 18 The environment was developed in Unity which is a cross platform game engine and the experiments were reproduced with the Oculus Rift headset The set up consisted in a big area approximately with the dimension of a tennis court 22 11 m populated with some objects that represented the possible goals for the multi robot system The objects were cubes that emitted light of different colors and they were purposely designed with a very simple shape because they did not have to confuse or distract the user during the experiment The same goes for the rest of the environment minimal background and no sound All the focus of the user was moved towards the object of the experiment The multi robot system was made up of twenty omnidirectional robots with a cylindrical shape and a radius equal to 0 1 m C Factorial experiment In general when a series of experiments are used to un derstand the infl uence of some variables called independent variables over the response which can be represented by multiple dependent variables a factorial plan is built 19 For these experiments we had three independent variables trajectory dispersion and stiffness and for every variable we chose to investigate two levels In order to study the effect of each variables and of the interactions between them the 7350 plan must be fully investigated 23combinations To avoid the infl uence of disturbing factors some precau tions must be taken during the experiments These disturbing factors must be controlled as much as possible or they will infl uence the response We identifi ed the factors that we thought could affect the experiments and we tried to reduce their effects 1 Point of view In a virtual reality set up the user is immersed in the environment and she he can look around in every direction and in some applications like in video games she he can also move inside the space In this particular case we chose to fi x the position in the middle of the goals and to allow the user only to look around In fact if the user had the possibility to move around this would have introduced too much variability The movement of the head is a good trade off between the full freedom and a completely fi xed point of view Furthermore the movement of the head is fundamental to avoid the motion sickness caused by the decoupling of the sense of sight and the sense of balance 20 The position of the user with respect to the robots was like she he was standing among them This position is neutral in such a way that the user did not feel neither inferior nor superior towards the robots 17 Furthermore it is the most likely position for a collaborative proximal interaction task 2 Position of the goals The goals were positioned equally spaced in front of the user This limited the area of interest for the user and in this way it limited the need of looking around also improving the previous issue point of view Fig 1 b The goal in every trial was randomized Differently from 14 we introduced more than two goals because in general in a collaborative task with a multi robot system it is more frequent to have multiple goals given the intrinsic multiplicity of the system In addition we believe that inferring a goal that is surrounded by others is more diffi cult and hence this would be a more generic study For this purpose the possible goals were reduced to the three central because they were equally distributed namely they all had two neighbors 3 Learning effect In order to limit the impact of this factor every user received a brief training about the input method In addition everyone had a trial at the beginning where she he tried to interact with some objects in the same way they were supposed to interact with the cubes repre senting the goals The order of the trials was randomized to reduce the infl uence of the learning effect 4 Movements of the robots The trajectories of the robots were saved offl ine and they were reproduced exactly in every experiment The repeatability of the motions of the robots is fundamental since the core of the study was about the ability of the robots to communicate through their motion D Independent variables The motion variables trajectory dispersion and stiffness are the independent variables of the study They are defi ned in two levels which have been chosen suffi ciently distant to recognize the difference between them as detailed below The multi robot system is composed by N mobile robots each one modeled as a dynamic system in a n dimensional space Mi xi wii 1 N 3 where Mi Rn n positive defi nite and xi Rnare the inertia matrix and the position of the i th robot respectively The control input and all the external forces that act on the robot are included in the term wi Rn For simplicity of notation we will hereafter consider Mi mI where I Rn nis the identity matrix The control architecture is based on a potential fi eld which allows to move a group of robots with a cohesive behavior and to avoid collisions At the same time it enables to drive the multi robot system through an environment following a virtual agent that moves along a desired trajectory 1 Trajectory We chose two of the infi nite possible trajectories that link two points in a n dimensional space The trajectory specifi es the position of the virtual agent in each instant of time The fi rst is a minimum jerk trajectory namely a trajectory that minimizes the square of the magnitude of the jerk rate of change of acceleration We chose to investigate this trajectory because it is the typical movement that a human does while grasping an object 21 Furthermore in 22 it has been discovered that for a user it is easier to interact with a manipulator that moves with a minimum jerk trajectory instead of a trapezoidal one However in standard industrial applications with robotic arms the trapezoidal velocity profi le is preferred 23 To the best of the authors knowledge no works can be found about the correlation between minimum jerk trajectory and legibility of a multi robot system If we consider a point that follows a one dimensional trajectory t from a start point t 0 to a fi nal point t f with f 0 its position is described in every instant of time t by t 0 f 0 10 t f 3 15 t f 4 6 t f 5 4 This can be easily adapted to a n dimensional trajectory applying 4 componentwise The second trajectory called arc trapezoidal follows the animation principles of Slow In and Out and Arcs from 24 These principles have already been investigated in 11 for assistive free fl yers but not yet for multi robot system The trajectory is drawn with an arc of circle and with a trapezoidal velocity profi le The direction counter clockwise or clockwise is random Both trajectories lead the virtual agent from the starting point to the desired goal in 60 seconds The time interval is chosen in such a way that the overall experiment can not last more than 10 minutes to avoid discomfort to the user for the use of the head mounted display 2 Dispersion and stiffness While the virtual agent fol lows the given trajectory the real robots are linked to the virtual agent and among each other with a potential fi eld and a damping element If we consider the i th robot we 7351 can rewrite 3 as Mi xi Bi xi Vi 5 where Bi Rn n positive defi nite is the damping factor which must be introduced for a smooth movement and xi Rnis the velocity of the i th robot We consider a homogeneous friction coeffi cient along all directions hence Bi bI The term Vi is the gradient of the potential fi eld Vi applied to the i th robot The potential fi eld Viis described by1 Vi N X j 1 j6 i Vai j xi xj N X j 1 j6 i Vrepi j xi xj Vvi xi xv 6 where Vai jis the cohesive part of the potential and is equal to Vai j 1 2Kai j dij d0 2if dij d1 0otherwise 7 and dij kxi xjk is the Euclidean distance between the i th and the j th robot Then Vrepi jis the repulsive component whose purpose is to avoid collisions between the robots Vrepi j 1 2Krepi j dij dmin 2if dij dmin 0otherwise 8 At the end Vviis the attractive potential between the i th robot and the virtual agent Vvi 1 2Kvi v div d0v 2if div d1v 0otherwise 9 All the potentials are defi ned with a positive constant re spectively Kai j Krepi jand Kvi v Their action is different from zero only in a limited area near the i th robot which is represented by the terms d1 dminand d1v The independent variables dispersion and stiffness are defi ned by the parameters of the potential fi eld Vi In particular dispersion is represented by the distance d0 that is the desired distance between the robots The level Small requires the group to maintain a distance ten times the dimension of the single robot 0 1 m of diameter while the level Large thirty times The stiffness parameter defi nes the dynamic behavior of the multi robot system namely the constants that state the strength of the potential fi eld Kai j Krepi j and the values of