A Mobile Robot that Understands Pedestrian Spatial Behaviors


 Phillip Jones
 3 months ago
 Views:
Transcription
1 The 00 IEEE/RSJ International Conference on Intellient Robots and Systems October , 00, Taipei, Taiwan A Mobile Robot that Understands Pedestrian Spatial Behaviors ShuYun Chun and HanPan Huan, Member, IEEE Abstract In human society, there are many invisible social rules or spatial effects existin in our environments. The robot that does not comprehend these spatial effects miht harm people or itself. This paper presents a spatial behavior conition model (SBCM to describe the spatial effects existin between people and people, people and environments. By understandin the spatial effects in humanlived environments, the robot not only predicts pedestrian intentions and traectories but also behaves socially acceptable motions. Moreover, the concept of pedestrian eoraph (PEG is proposed to efficiently query pedestrianlike paths for traectory prediction. Model evaluation and experiments are shown to verify the proposed idea in this paper. T I. INTRODUCTION ODAY robots are no loner only operated in laboratories or factories. Lots of novel robots were desined to work in the populated or outdoor environments. In the near future, more and more robots will appear in our human society. To make robots smoothly coexist and share the environments with humans, robots should try to understand human behaviors and execute socially acceptable motions. In this paper, behavior understandin mainly tarets at spatial interactions. A factor which can affect the pedestrian behaviors is represented as a spatial effect in this paper. There are many social rules or implicit spatial effects existin in human society. Pedestrians usually have hihlevel conition to reason, infer, and interact with the environments in appropriate ways (Fi.. In other words, the environments seem to enerate some spatial effects that force pedestrians to perform certain motions. Our purpose is to make robots understand these spatial effects and further predict pedestrian intentions or behave humanlike motions. However, these spatial effects are usually invisible and immeasurable by sensors. It leads spatial effect understandin into a difficult task. Fortunately, people sometimes interpret their feelins or intentions throuh nonverbal communications such as their paths, postures, facial expressions, and eye contact etc. We are able to infer the spatial effects by observin pedestrian behaviors. Previous researches also studied the spatial interactions between people and robots [, 0, ]. This work is partially supported by the Industrial Development Bureau, Ministry of Economic Affairs of R.O.C. under rants E00MY C0. Shu Yun Chun is currently a Ph.D. student in Department of Mechanical Enineerin, National Taiwan University, Taipei, Taiwan ( Han Pan Huan is a professor of Department of Mechanical Enineerin, National Taiwan University, Taipei, Taiwan (phone: ; fax: 0; Fi. Some social rules and spatial effects existin in human society, pedestrians usually stand to one side of the escalator to allow others to rapidly pass, people naturally keep the social distance between roups. However, most of these works were limited to certain situations or behaviors. They lacked a eneralized framework for describin the relationships between different spatial effects. This paper mainly contributes two points. At first, the concept of pedestrian eoraph (PEG is represented. PEG is created based on the statistical results from collected traectories of pedestrians and is utilized to rapidly enerate pedestrianlike path for traectory prediction. Second, the framework of spatial behavior conition model (SBCM is proposed to describe the spatial effects in most humanlived environments. The robot is further able to comprehend and incrementally detect new spatial effects throuh SBCM. This paper is oranized as follows. In section II, the structure of PEG is introduced. SBCM and spatial effects learnin are discussed from section III to V. In section VI, the probability model of prediction is derived. The model evaluation and the experiment are demonstrated in section VII. The conclusions are summarized in section VIII. II. PEDESTRIAN EGOGRAPH In eneral, it is not easy to rapidly predict the pedestrian traectory in hihly dynamic environments. Most developed methods [, ] only consider the reactive social forces which enerate the next action of the pedestrian based on current observations. It is usually suited for the trackin problem but not the prediction problem. Because of its reedy property, this kind of methods may fail in lon term prediction and et blocked in the areas with local minimum cost. Althouh some alorithms were proposed for lon term prediction [, ], they inored the spatial effect between pedestrians and cannot model the avoidance behaviors between pedestrians. This paper presents the concept of pedestrian eoraph (PEG to overcome this drawback. An eoraph [] is a local motion plannin approach used in the field of mobile robots, especially for the robots with motion constraints []. It is a raph that athers several possible robot states and enerates different traectories /0/$ IEEE
2 throuh these states by considerin kinematics and dynamics constraints. Since each traectory is only associated to certain states, it is able to efficiently score all the traectories online and choose one of traectories for the next motion stratey. In daily life, pedestrians usually adopt similar strateies to avoid obstacles. Thus we utilize the concept of eoraph to predict pedestrian traectories. On the other hand, eoraph also retains the characteristic of multiple hypotheses which is helpful to create the probability model of prediction. The procedure for buildin the PEG from collected traectories is discussed below. At first, 0 traectories are collected from different places includin indoor and outdoor environments. The movin direction of the initial state in each traectory is rotated to the upward direction (Fi.. Each traectory is divided into several traectory pieces with lenths of ~ m. In this case, traectory pieces are obtained. partitions distributed in layers are defined dependin on the radial distance and orientation to the center of PEG (Fi.. partitions from different layers become one partition set. Thus partition sets are enerated in the preliminary PEG. Accordin to the location in the PEG, each traectory piece fits into one of the partition sets. From the statistical results, partition sets with fewer traectory pieces are removed. Finally, only partitions and partition sets are reserved. Moreover, the statistical traectory clusterin method [] is utilized to estimate the reression model of traectories in each partition set (Fi.. y(m x(m y (m x (m Fi. 0 traectories are collected, preliminary partition distribution The reressive traectories in each partition are rearded as the policies of pedestrians. At the final, traectories are shown in pedestrian eoraph as shown in Fi.. III. SPATIAL BEHAVIOR COGNITION MODEL (SBCM We assume the pedestrian spatial behaviors are influenced by some spatial effects existin in the environments. Accordin to the frequency of occurrence, the spatial effects are classified into eneral spatial effects (GSEs and specific spatial effects (SSEs. GSEs usually exist in most environments and represent the basic spatial considerations of pedestrians. On the contrary, SSEs are only associated with certain environments or certain social rules of human society. Both kinds of spatial effects often coexist and affect pedestrian behaviors at the same time. We propose a framework, called SBCM, to describe the relationships between pedestrian behaviors and environments. It consists of two main parts, the pedestrian model and SSE database. The architecture of SBCM is shown in Fi.. The pedestrian model retains all the spatial effects associated with current environment. Thus GSEs always exist in pedestrian model and SSEs are only considered while associated features are detected in the environments. The pedestrian behaviors are represented by fusin the spatial effects in the pedestrian model. However, there are two difficulties for buildin SBCM. The first is correctly interatin different spatial effects. To solve this problem, we model pedestrian behaviors as Markov decision processes and estimate the cost weihtin of each spatial effect by inverse reinforcement learnin (IRL []. The second difficulty is to detect and learn the new SSEs in the environments. Our proposed idea is to learn a eneral behavior model which only enaes with GSEs at first. Then this eneral behavior model helps to detect the SSE. The SSE can be further identified and learned by subtractin GSEs from pedestrian behaviors. The learned SSE is stored in SSE database and can be used to model pedestrian behaviors or detect new SSEs while the associated feature of learned SSE appears in the environments. The section IV and V will further discuss the cost functions of GSEs and SSEs. The IRL for cost learnin is also introduced in each section. Fi. Traectory clusterin and reression the red curve shows the reressive traectory in one partition set, sometimes two reressive traectories appear in one partition set. Fi. pedestrian eo raph (PEG, PEG can rapidly enerate multiple hypotheses for traectory prediction. Fi. Spatial behavior conition model
3 IV. GENERAL SPATIAL EFFECT LEARNING We assume that pedestrian spatial behaviors influenced by four GSEs (traectory lenth, static obstacle, movin obstacle, constant steerin. Each GSE associates with a cost function C i for pedestrian state o k in time step k. The cost function under GSEs, C GSE, is written as a linear combination of C i with different weihts w i shown as Eq(. The followin sections describe the formulation of each cost function. CGSE ( ok = wdescdes ( ok + wobscobs ( ok + wmocmo ( ok + wstrcstr ( ok ( A. Traectory Lenth We hypothesize that all pedestrians have certain destinations and move toward destinations with pedestrian policy. The traectory lenth which indicates the distance from the current location of the pedestrian to the destination is rearded as a type of cost. Thus the cost function to the destination C des can be described by Euclidean distance ( dist( between two sequential states. ( Cdes ok = dist( ok ok ( B. Static Obstacles In eneral, pedestrians would like to avoid obstacles for safety. Thus obstacles can be viewed as a repulsive force that enerates hih cost while pedestrians are closed to it. Distance transform (Dist is used to obtain the closest distance to obstacles (Fi.. Moreover, we adopt the similar formulation in [] for the cost function C obs. σ is defined as 0. estimated from []. C ( o = exp( 0. Dist( o σ ( obs k k C. Movin Obstacles Hall [] demonstrated that personal space (PS plays an important role in spatial interactions between humans. PS can be considered as a selfown area surroundin each person. The violation of PS often causes emotional reactions dependin on the relation between two persons. PS usually forms as an elliptic shape shown in Fi.. In this paper, the concept of PS also helps to formulate the cost caused from other pedestrians. Accordin to [], PS around the pedestrian can be modeled as a combination of twodimensional Gaussian functions shown in Fi.. The cost function of pedestrian i suffered from other pedestrians, C mo, can be described as the summation of cost from pedestrian to pedestrian i, C i, shown in Eq.(. Fi. Distance transform (Dist. The obstacle is displayed as black color. The oriinal map is shown in Fi., the cost function of personal space. ( t i i i ( = = exp 0. ( Σ ( ( C o C o o o o mo k i k k k k if is in front of i σ 0 Σ= 0 σ also defined as 0. in this paper., others σ Σ= 0 0 σ. σ is D. Constant Steerin Since pedestrians usually avoid frequently chanin movin directions, the last cost function of GSE is to penalize the steerin variation as shown in Eq.(. C ( o = steerin ( o steerin ( o ( ( str k k k E. Model Learnin We assume the pedestrian spatial behaviors can be represented as a MDP. The pedestrian traectory consistin of sequential discrete states (o 0, o, o follows the pedestrian policy. The value function V for the policy π evaluated at pedestrian state o 0 is iven by Eq.(. ( ( γ ( γ ( π V o = C o + C o + C o + ( 0 0 Where γ [0, is the discount factor. C(o k is the total cost at state o k. In this section, since the pedestrian model only considers GSEs, C(o k is equal to C GSE (o k. Our purpose is to estimate the parameter w i under the pedestrian policy. This estimation can be viewed as an inverse reinforcement learnin (IRL problem. We adopt the method [] which formulates IRL as maximizin the difference of quality between the observed policy and other policies. The optimization can be efficiently solved by linear prorammin methods. Here the optimization problem becomes π max V ( o V ( o λ w ( o0 X0 ( 0 0 π s.. t λ, 0 < wi wmax, V ( o0 V ( o0 X 0 is the set of initial states of pedestrian traectories. λ is the penalty to prevent lare w i. Several policiesπ, which separately consider C des, C obs, or randomly combination of other cost functions, enerate different traectories for V ( o0 The model evaluation for GSEs is discussed in section VII. V. SPECIFIC SPATIAL EFFECT LEARNING i π. However, some spatial effects only appear in certain environments or from certain obects and cannot be described by GSEs. SSEs help to compensate this part. SSEs are rearded as the additional spatial effects to influence pedestrian behaviors. If the cost function C represents the cost of observed pedestrian behaviors, we are able to detect SSEs and even further estimate SSEs by subtractin GSEs from the cost function C. The complete cost function C can be written as C( ok = CGSE ( ok + CSSE ( ok ( C GSE (o k is available from Eq.(. The cost function C SSE is
4 represented as a rid map tabulatin the costs of the SSE in discrete locations (Fi.. Similar to the last section, the cost estimation can be transformed into an optimization problem shown in Eq.(. Hist(s, which records the frequency of pedestrian passin location s, is also provided as the penalty term. One thin we should notice is that only the parameters of the SSE are estimated in Eq.(, the parameters of GSEs are reserved. Moreover, we enerate several C SSE by slihtly translatin the coordinate of C SSE to different locations (Fi.. After fusin these C SSE, a hih resolution C SSE is available. π max V o V o λ Hist( s C ( s ( ( ( 0 ( 0 o0 X0 ( ( π max 0 0 st.. λ > 0, 0 C ( s C, V o V o SSE Where s indicates all the discrete states in the rid map. A simple experiment is desined to verify the idea. Five destinations and the rid map of the environment are shown in Fi.. An interactive exhibition locates in the center of the environments. The pedestrians are not allowed to o into the interactive area in this case. However, the robot equipped with a laser rane finder cannot detect the interactive area from the rid map and also cannot model the forbidden behavior from GSEs. It is required to detect and learn this SSE (the forbidden behavior from the observed pedestrian traectories. pedestrian traectories are collected while 0 traectories are detected as unusual by the pedestrian model only considerin GSEs (Fi.. Fi. demonstrates the historam Hist(s of pedestrian traectories. The cost function of SSE, C SSE, is further estimated by Eq.(. The estimated results are displayed in Fi. 0. The result of estimated C SSE without Hist(s is also shown for comparison. After addin C SSE to the pedestrian model, SBCM enerates the new pedestrian policy. The policy of the before and the after considerin SSE are illustrated in Fi.. The policy considerin the SSE is closer to the pedestrian policy. SSE o indicates the discrete states of the pedestrian at time k step k. G describes the destination of the pedestrian. The prediction of behaviors consists of short term and lon term prediction. In short term prediction, only the area within PEG is concerned while the lon term prediction considers the areas out of the PEG. In the followin pararaphs, three situations, short term prediction, lon term prediction and multiple destinations are discussed. A. Short term prediction The probability model of short term prediction is represented as p( o k+t o k,g. Here we assume the pedestrian takes T time steps to walk throuh the PEG area. The probability is obtained from the statistical results that compare the predicted traectory with real pedestrian traectories. Fi. The cost function is represented as the discrete states, fusin multiple learned cost functions to enerate one hih resolution cost function Fi. unusual traectories are shown in red color, Hist(s. VI. PROBABILITY FRAMEWORK In this section, the probability model of prediction is derived. To clarify the meanin of symbols, some symbols are defined as follows. O k is represented as the pedestrian traectory from time step to k. O o, o, o (0 k { } k Fi. 0 Cost function of SSE, without Hist(s, with Hist(s. Fi. History allery, the interactive exhibition is in the center of the map and destinations are denoted as reen circles, environment pictures. Fi. Pedestrian policies for destination E, without SSE, with SSE.
5 (c Fi. Simulation of lon term prediction in different time steps, t = s, t = s, (c t = s. B. Lon term prediction In the lon term prediction, the prediction result is represented in discrete state in rid map. The probability of the prediction from time step k to k+n is modeled as p( ok+ N ok, G. Accordin to the total probability, it is factorized as p o o, G = p o o, G p o o, G ( k+ N k ( k+ N k+ N ( k+ N k ok+ N k+ N ( = p ( oi+ oi, G p( ok+ T+ ok+ T, G p( ok+ T ok, G i= k+ T+ oi ok+ T Each rid state has directions toward its next states. Thus we can utilize similar estimation method as short term prediction to estimate ( p o, i+ oi G. The final term p o o, G of Eq.( can be derived to the summation of ( k+ T k the multiplication of state discretization and the short term prediction as shown in Eq. (. Fi. shows the simulation result. p( ok+ T ok, G = p( ok+ T ok+ T p( ok+ T ok, G ( ok+ T discretization short term prediction C. Multiple destinations In eneral, the destination of the pedestrian is usually unknown. However, we are able to derive the weihtins of different destinations from the pedestrian traectory. By Bayes rule, the posterior of oal weihtin p(g k O k in time step k can be described as the multiplication of one step prediction and oal weihtin in time step k. In other words, it is able to iteratively estimate the oal weihtin while the new information of the pedestrian is available. p( Gk Ok p( ok ok, Gk p( Gk Ok ( = p( ok ok, Gk p( Gk Ok Based on the pedestrian traectory O k, a eneralized lon term prediction model p ( ok+ N Ok in multiple destinations environments is represented by the combination of individual lon term pedestrian models with different weihts shown as m i i ( k+ N k = ( k+ N k, k ( k k i m ( i i = p( ok+ N ok, Gk p( Gk Ok p o O p o O G p G O i Prediction Goal Weihtin VII. MODEL EVALUATION AND ROBOT EXPERIMENT A. Model Evaluation In the trainin phase, traectories are collected from one outdoor (seq_eth [] and two indoor environments. In the testin phase, the traectories of PEG are scored and prioritized online by V π as shown in Eq.(. The traectory with the lowest value of V π is chosen as the predicted traectory of the pedestrian. However, the scores of the first several prioritized traectories usually have a sliht difference. In other words, they all have lare chances of bein chosen by pedestrians. To demonstrate the characteristic of multiple hypotheses, PEG is represented in three different types: PEG, PEG, and PEG0. The number indicates the amount of prioritized traectories in PEG compared to the round truth. The best one is chosen as the evaluated traectory. For example, PEG means that the evaluated traectory is the best matchin traectory chosen from the first five prioritized traectories. Moreover, PEG is also evaluated by comparin with other pedestrian models includin constant velocity (CV and linear traectory avoidance (LTA []. 0 testin traectories are randomly selected from the dataset (seq_hotel []. However, the traectories of short lenth or those belonin to a roup are removed. The prediction results are shown in Fi.. The averae error and its one standard deviation in different distances of prediction are listed in TABLE I and TABLE II. All the models perform well while predicted distance is lower than meters. However, performance difference is obvious in lon distance prediction. Because of the advantae of multiple hypotheses, PEG and PEG0 dramatically decrease the prediction error and shrink the uncertainty of prediction. B. Robot Experiment This section demonstrates a service robot performs pedestrianlike motions by considerin the spatial effects discussed in section IV and V. The robot platform is shown in Fi.. The laser raner finder equipped on the robot is used for localization and pedestrian trackin. By learnin the spatial effects, the robot is able to search a path similar to the pedestrian behavior that detours around the interactive exhibition (Fi.. While a pedestrian is movin toward the rihtbottom side of the map, the robot is able to utilize
6 the pedestrian model to predict the potential location of the pedestrian in the next few seconds. To prevent the potential collision, the robot queries a new path surroundin the other side of the interactive exhibition (Fi. (c(d. VIII. CONCLUSION In this paper, we present the concept of pedestrian eoraph (PEG and the framework of spatial behavior conition model (SBCM. PEG provides humanlike traectories for modelin pedestrian behaviors. By the advantaes of multiple hypotheses, PEG is helpful to build the probability model of prediction. Moreover, the proposed framework of SBCM not only provides a ood ability to discover new spatial effects but also estimates the correspondin cost functions. Furthermore, the probability models of prediction includin short term, lon term and multiple destinations are also derived. The pedestrian model combinin PEG and SBCM shows excellent results in the model evaluation. Finally, we have further demonstrated a practical application that a service robot behaves socially acceptable motions by detectin and learnin the spatial effects in the environment. REFERENCES [] T. Amaoka, H. Laa, S. Saito, and M. Nakaima, "Personal Space Modelin for HumanComputer Interaction," Proc. th Int. Conf. on Entertainment Computin, Paris, France, pp. 0, 00. [] M. Bennewitz, W. Burard, G. Cielniak, and S. Thrun, "Learnin Motion Patterns of People for Compliant Robot Motion," Int. J. Robotics Research, vol., pp. , 00. [] D. Ellis, E. Sommerlade, and I. Reid, "Modellin Pedestrian Traectories with Gaussian Processes," th Int. Workshop on Visual Surveillance, Kyoto, Japan, 00. [] S. Gaffney and P. Smyth, "Traectory Clusterin with Mixtures of Reression Models," Proc. of the th ACM SIGKDD int. conf. on Knowlede discovery and data minin, San Dieo, CA, USA, pp. ,. [] E. T. Hall, The Hidden Dimension. Anchor Books,. [] D. Helbin and P. Molnár, "Social Force Model for Pedestrian Dynamics," Physical Review E, vol., pp. ,. [] T. M. Howard and A. Kelly, "Optimal Rouh Terrain Traectory Generation for Wheeled Mobile Robots," Int. J. Robotics Research, vol., pp. , 00. [] T. Kanda, D. F. Glas, M. F. Shiomi, and N. F. Haita, "Abstractin People's Traectories for Social Robots to Proactively Approach Customers," IEEE Trans. on Robotics, vol., pp. , 00. [] A. Lacaze, Y. Moscovitz, N. DeClaris, and K. Murphy, "Path Plannin for Autonomous Vehicles Drivin over Rouh Terrain," Proc. IEEE Int. Sym. on Intellient Control, Gaithersbur, MD, USA, pp. 0,. [0] Y. Nakauchi and R. Simmons, "A Social Robot That Stands in Line," Autonomous Robots, vol., pp. , 00. [] A. Y. N and S. J. Russell, "Alorithms for Inverse Reinforcement Learnin," Proc. of the Seventeenth Int. Conf. on Machine Learnin, Stanford, CA, USA, pp. 0, 000. [] E. Pacchierotti, H. I. Christensen, and P. Jensfelt, "Evaluation of Passin Distance for Social Robots," Proc. The th IEEE Int. Sym. on Robot and Human Interactive Communication, Hatfield, UK, pp. 0, 00. [] S. Pellerini, A. Ess, K. Schindler, and L. v. Gool, "You'll Never Walk Alone: Modelin Social Behavior for MultiTaret Trackin," Proc. IEEE Int. Conf. on Computer Vision, Kyoto, Japan, pp. , 00. []B. Ziebart, N. Ratliff, G. Gallaher, C. Mertz, K. Peterson, J. A. Banell, M. Hebert, A. Dey, and S. Srinivasa, "PlanninBased Prediction for Pedestrians," Proc. IEEE Int. Conf. on Intellient Robots and Systems, St. Louis, MO, USA, pp. , 00. [] TABLE I STATISTICAL RESULTS AVERAGE ERROR (UNIT:METER m m m m m m m CV LTA PEG PEG PEG TABLE II STATISTICAL RESULTS STANDARD DEVIATION (UNIT:METER m m m m m m m CV LTA PEG PEG PEG Fi. Prediction results in different pedestrian models. The riht imae shows LTA fails in the area with local minimum cost. Black: round truth. Red: PEG. Blue: LTA. Green: CV (c (e Fi. the experiment of naviation. (d