Is Robotics Going Statistics The Field of Probabilistic Robotics Sebastian Thrun School of Computer Science Carne gie Mellon Uni ersity httpwww PDF document - DocSlides

Is Robotics Going Statistics The Field of Probabilistic Robotics Sebastian Thrun School of Computer Science Carne gie Mellon Uni ersity httpwww PDF document - DocSlides

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cscmuedu thrun draft please do not circulate Abstract In the 1970s most research in robotics presupposed the ailability of xact models of robots and their en vironments Little emphasis as placed on sensing and the intrinsic limitations of modeling co ID: 22285

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Presentations text content in Is Robotics Going Statistics The Field of Probabilistic Robotics Sebastian Thrun School of Computer Science Carne gie Mellon Uni ersity httpwww

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Is Robotics Going Statistics? The Field of Probabilistic Robotics Sebastian Thrun School of Computer Science Carne gie Mellon Uni ersity http://www thrun draft, please do not circulate Abstract In the 1970s, most research in robotics presupposed the ailability of xact models, of robots and their en vironments. Little emphasis as placed on sensing and the intrinsic limitations of modeling comple ph ysical phenomena. This changed in the mid-1980s, when the paradigm shifted to ards reacti techniques. Reacti controllers rely on capable sensors to generate robot control. Rejections of models were typical for researchers in this field. Since the mid-1990s, ne approach has be gun to emer ge: probabilistic robotics. This approach relies on statistical techniques to seamlessly inte grate imperfect models and imperfect sensing. The present article describes the basics of probabilistic robotics and highlights some of its recent successes. Intr oduction In recent years, the field of robotics has made substantial progress. In the past, robots were mostly confined to actory floors and assembly lines, bound to perform the same narro tasks er and er ag ain. recent series of successful robot systems, ho we er has demonstrated that robotics has adv anced to le el where it is ready to conquer man ne fields, such as space, medical domains, personal services, entertainment, and military applications. Man of these ne domains are highly dynamic and uncertain. Uncertainty arises for man dif ferent reasons: the inherent limitations to model the orld, noise and perceptual limitations in robot sensor measurements, and the approximate nature of man algorithmic solutions. In this uncertainly lies one of the primary challenges aced by robotics research today Three xamples of successful robot systems that operate in uncertain en vironments are sho wn in Fig- ure 1: commercially deplo yed autonomous straddle carrier [3], an interacti museum tour guide robot [7 11], and prototype robotic assistant for the elderly The straddle carrier is capable of transporting contain- ers aster than trained human operators. The tour guide robot—one in series of man y—can safely guide visitors through densely cro wded museums. The Nursebot robot is presently being de eloped to interact with elderly people and assist them in arious daily tasks. All of these robots ha to cope with uncertainty The straddle carrier aces intrinsic limitations when sensing its wn location and that of the containers. similar problem is aced by the museum tour guide robot, ut here the problem is aggra ated by the presence of people. The elderly companion robot aces the additional uncertainty of ha ving to understand spok en language by elderly people, and coping with their inability to xpress their xact wishes. In all these appli- cation domains, the en vironments are highly unpredictable, and sensors are comparati ely poor with re ard to the performance tasks at hand.
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(a) Straddle Carrier (b) Robotic museum tour guide (c) Personal Robotic Assistant for the Elderly Figure 1: Three robots controlled by probabilistic softw are: robotic straddle carrier museum tour guide robot, and the Nursebot, robotic assistant for nurses and the elderly As these xamples suggest, the ability to accommodate uncertainty is requirement for contempo- rary robotic systems. This raises the question as to appropriate mechanisms for coping with uncertainty What type of internal orld models should robots emplo y? And ho should sensor measurements be inte- grated into their internal states of information? Ho should robots mak decisions en if the are uncertain about en the most basic state ariables in the orld? The probabilistic approach to robotics addresses these questions through single idea: epr esenting information pr obabilistically In particular orld models in the probabilistic approach are conditional prob- ability distrib utions, which describe the dependence of certain ariables on others in probabilistic terms. robot state of kno wledge is also represented by probability distrib utions, which are deri ed by inte grating sensor measurements into the probabilistic orld models gi en to the robot. Probabilistic robot control an- ticipates arious contingencies that might arise in uncertain orlds, thereby seamlessly blending information athering (e xploration) with rob ust performance-oriented control (e xploitation). The mo to probabilistic techniques in robotics is paralleled in man other subfields of artificial intelli- gence, such as computer vision, language, and speech. Probabilistic robotics le erages decades of research in probability theory statistics, engineering and operations research. In recent years, probabilistic tech- niques ha solv ed man outstanding robotics problems, and the ha led to ne theoretical insights into the structure of robotics problems and their solutions. Models, Sensors, and The Ph ysical orld Classical robotics te xtbooks often describe at length the kinematics and dynamics of robotic de vices. These topics address the question of ho controls af fect the state of the robot and, more broadly the orld. Ho we er te xtbooks often suggest deterministic relationship: The ef fect of applying control action to the robot at state is go erned by the functional relationship u; for some (deterministic) function or xample, might be the configuration and elocity of robotic arm, and might be the motor currents asserted in fix ed time interv al. Such an approach characterizes idealized robots only—free of wear and tear inaccuracies, control noise, and the alik e. In reality the outcomes of control actions are uncertain. or xample, robot that ecutes control le eraging its position by one meter forw ard might xpect to be xactly one meter ay from where it started, ut in reality will lik ely find itself in an unpredictable location nearby The probabilistic approach accounts for this uncertainty by using conditional probability distrib utions to model robots. Such models, commonly denoted u; specify the posterior probability er states that might result when applying control to robot whose state is Put dif ferently instead of making deterministic prediction, probabilistic techniques model the act that the outcome of robot controls
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Algorithm particleFilters( u; let aux // forw ard projection step for to do retrie -th particle from particle set dra u; using the motion model u; add to aux end for // resampling step for to do dra random from aux with probability proportional to add to end for return end algorithm able 1: Basic particle filter algorithm, which implements Bayes filters using approximate particle repre- sentation. The posterior is represented by set of particles which is roughly distrib uted according to the posterior distrib ution of all states gi en the data that is commonly calculated by Bayes filters. is uncertain, by assigning probability distrib ution er the space of all possible outcomes. As such, the generalize classical kinematics and dynamics to real-w orld robotics. In the same ein, man traditional te xtbooks presuppose that the state of the robot be kno wn at all times. Usually the state comprises all necessary quantities rele ant to robot prediction and control, such as the robot configuration, its pose and elocity the location of surrounding items (obstacles, people, etc.). In idealized orlds, the robot might possess sensors that can measure, without error the state Such sensors may be characterized by deterministic function capable of reco ering the full state from sensor measurements that is, Real sensors are characterized by noise and, more importantly by range limitations. or xample, cameras cannot see through alls. The probabilistic approach generalizes this idealized vie by modeling robot sensors by conditional probability distrib utions. Sensors may be characterized by forw ard models which reason from state to sensor measurements, or their in erse —depending on algorithmic details be yond the scope of this article. As this discussion suggests, probabilistic models are indeed generalizations of their classical counter parts. The xplicit modeling of uncertainty ho we er raises fundamental questions as to what can be done with these orld models. Can we reco er the state of the orld? Can we still control robots so as to achie set goals? Pr obabilistic State Estimation first answer to these questions can be found in the rich literature on probabilistic state estimation. This literature addresses the problem of reco ering the state ariables from sensor data. Common state ariables include parameters re arding the robot configuration, such as its location relati to an xternal coordinate
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(a) Robot particles Person particles (b) Robot particles Person particles (c) Figure 2: Ev olution of the conditional particle filter from global uncertainty to successful localization and tracking. frame. The problem of estimating such parameters is often referred to as localization parameters specifying the location of items in the en vironment, such as the location of alls, doors, and objects of interest. This problem, kno wn as mapping is re arded one of the most dif ficult state estimation due to the high dimensionality of such parameter spaces [1], and parameters of objects whose position changes er time, such as people, doors, and other robots. This problem is similar to the mapping problem, with the added dif ficulty changing locations er time. The predominant approach for state estimation in probabilistic robotics is kno wn as Bayes filter Bayes filters of fer methodology for estimating probability distrib ution er the state conditioned on all ailable data (controls and sensor measurements). The do so ecur sively based on the most recent control and measurement the pre vious probabilistic estimate of the state, and the probabilistic models x; and discussed in the pre vious section. Thus, Bayes filter do not just “guess the state Rather the calculate the probability that any state is correct. Popular xamples of Bayes filters are hidden Mark models, Kalman filters, dynamic Bayes netw orks and partially observ able Mark decision processes [5 10]. or lo w-dimensional state spaces, research in robotics and applied statistics has produced wealth of literature on ef ficient probabilistic estimation. Remarkably popular is an algorithm kno wn as particle filter which in computer vision is kno wn as condensation algorithm and in robotics as Monte Carlo localiza- tion [2 ]. This algorithm approximates the desired posterior distrib ution through set of particles articles are samples of states which are distrib uted roughly according to the ery posterior probability distrib ution specified by Bayes filters. able states the basic particle filtering algorithm. In analogy to Bayes filters, the algorithm generates particle set recursi ely from the most recent control the most recent mea- surement and the particle set that represents the probabilistic estimate before incorporating and It does so in tw phases: First, it “guesses states based on particles dra wn from and the probabilistic motion model u; Subsequently these guesses are resampled in proportion to the perceptual lik e- lihood, The resulting sample set is approximately distrib uted according to the Bayesian posterior taking and into account. Figure illustrates particle filters via an xample. mobile robot, equipped with laser range finder simultaneously estimates its location relati to tw o-dimensional map of corridor en vironment and the number and locations of nearby people. In the be ginning (P anel 2(a)), the robot is globally uncertain as to
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(a) −20 −15 −10 −5 10 15 20 −10 10 20 30 40 X (m) Y (m) Estimated Path of the Vehicle Feature Returns Tentative Features Map Features Vehicle Path (b) Figure 3: (a) 3D olumetric map, acquired by mobile robot in real-time. The lo wer part of the map is belo the robot sensors, hence is not modeled. (b) Map of underw ater landmarks, acquired by the submersible ehicle Oberon at the Uni ersity of Sydne Courtesy of Stef an illiams and Hugh Durrant-Wh yte. where it is. Consequently the particles representing its location and that of the person are spread throughout the free space in the map. As the robot mo es (P anel 2(b)), the particles representing the robot location quickly con er ge to tw distinct locations in the corridor as do the particles representing the person lo- cation. fe time steps later the ambiguity is resolv ed and both sets of particles focus on the correct positions in the map, as sho wn in anel 2(c). Localization algorithms based on particle filters are ar guable the most po werful algorithms in xistence. As this xample illustrates, particle filters can represent wide range of multi-modal distrib utions. The are easily implemented as esour ce-adaptive algorithm capable of adapting the number of particles to the ailable computational resources. And finally the con er ge for lar ge range of distrib utions, from globally uncertain to near -deterministic cases. wards Millions of Dimensions In high-dimensional state spaces, computational considerations may pose serious obstacles when estimating state. Robot mapping to name popular xample of high-dimensional problem, often in olv es thousands of dimensions, if not millions! or xample, the olumetric map sho wn in Figure 3(a) is comprised of se eral millions of te xture alues, in addition to thousands of structural parameters. This raises the question as to whether probabilistic techniques are equipped to perform state estimation in such high-dimensional spaces. The answer is quite intriguing. date, virtually all state-of-the-art algorithms in areas such as localization, mapping, and people tracking are probabilistic. Man probabilistic approaches estimate the mode of the posterior which is simply the most lik ely state (there might be more than one). Some techniques, such as Kalman filters, also compute co ariance matrix, which measures the curv ature of the posterior at the mode. The specific techniques for estimating the mode and the co ariance ary widely depending on the nature of the state estimation problem. In the robotic mapping problem, tw of the most widely used algorithms are xtended Kalman filter (EKFs) [5] and the xpectation maximization (EM) algorithm [6]. Extended Kalman filters are applicable when the posterior can reasonably assumed to be Gaussian. This is usually the case when mapping the locations of landmarks that can be uniquely identified. Kalman filter techniques ha pro en to be capable of mapping
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lar ge-scale outdoor and underw ater en vironments while simultaneously estimating the location of the robot relati to the map [1]. Figure 3(b) sho ws an xample map of landmarks in an underw ater en vironment, obtained by researchers at the Uni ersity of Sydne [12]. In the general mapping problem, the desired posterior may ha xponentially man modes—not just one. Dif ferent modes commonly arise from uncertainty in calculating the correspondence between map items sensed at dif ferent points in time—a problem commonly kno wn as data association pr oblem Man of today best algorithms for state estimation with unkno wn data association are based on the EM algo- rithm [6 ]. This algorithm performs local hill-climbing search in the space of all states (e.g., maps), with the aim of calculating the mode. The “trick of the EM algorithm is to search iterati ely by alternating step that calculates xpectations er the data association and related latent ariables, follo wed by step that computes ne mode under these fix ed xpectations. This leads to sequence of state estimates (e.g., maps) of increasing lik elihood. In cases where both these steps can be calculated in closed form, EM can be highly ef fecti algorithm for estimating the mode of comple posteriors. or xample, the map sho wn in Figure 3(a) has been generated through an on-line ariant of the EM algorithm, accommodating errors in the robot odometry and xploiting Bayesian prior that biases the resulting maps to ards planar surf aces [4]. In all these applications, probabilistic model selection techniques are emplo yed for finding models of the “right comple xity Pr obabilistic Planning and Contr ol State estimation is only half the story Clearly the ultimate goal of an robotics softw are system is to control robotic de vices. It should come at no surprise that probabilistic techniques specifically tak uncertainty into consideration when de vising robot control. By doing so, the are rob ust to sensor noise and incomplete information. Probability theory pro vides sound frame ork for acti information athering, smoothly blending xploration and xploitation as most beneficial for the control goals at hand. Existing probabilistic control algorithms can mainly be grouped into tw cate gories: gr eedy and non- gr eedy Both amilies assume the ailability of payof function, which specifies the costs and benefits associated with the arious control choices. Whereas greedy algorithms maximize the payof for the imme- diate ne xt time step, non-greedy algorithm consider entire sequences of controls, thereby maximizing the (more appropriate) cumulati payof of the robot. Clearly non-greedy methods are more desirable from performance point of vie The computational comple xity of planning under uncertainty ho we er mak greedy algorithms welcome alternati es that ha found widespread applications in practice. The immediate ne xt payof is easily calculated by maximizing the conditional xpectation of the payof under the posterior probability er the state space. Thus, greedy techniques maximize conditional xpec- tation. In the museum tour guide project, such an approach as successfully emplo yed to pre ent the robot from alling do wn staircases. Similar techniques ha been successfully brought to bear for acti en viron- ment xploration with teams of robots [9 ], using payof functions that measure the residual uncertainty in the map. Non-greedily optimizing robot control—o er multiple time steps—remains challenging computational problem. This is because the robot has to consider multiple contingencies during planning, paying trib ute to the uncertainty in the orld. orse so, the number of contingencies may increase xponentially with the planning horizon, which mak es for most challenging planning problem [10]. Ne ertheless, recent research has led to flurry of approximate algorithms that are computationally ef ficient. The coastal navigation algorithm described in [8] condenses the posterior belief to tw quantities: the most lik ely state, and the entr opy of the posterior This state space representation is xponentially more compact than the space of all posterior distrib utions. It captures, ho we er still the de gree of uncertainty in
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the robot posterior Planning with this condensed state space has led to scalable robotic planning systems that can cope with uncertainty or xample, in mobile robot implementation reported in [8 ], this technique has been found to na vig ate robots closed to kno wn landmarks, in order to minimize the danger of getting lost—e en though this might increase the erall path length. Experimentally coastal na vig ation as sho wn to be superior to motion planners that do not re ard uncertainty in the planning process, in densely populated en vironments. This and man other xamples in the literature illustrate ho careful consideration of uncertainty often leads to superior control algorithms, which xplicitly consider uncertainty in planning and control. Conclusion This article pro vided brief introduction into the vibrant field of probabilistic robotics. The idea of probabilistic approaches is commitment to probability distrib ution as the basic representation of informa- tion. The pro vide sound solutions for the inte gration of inaccurate model information and noisy sensor data. date, probabilistic robotics is one of the most rapidly gro wing subfield of robotics. While man research challenges remain, the approach has already led to fundamentally more scalable solutions to man hard robotics problems, specifically in the area of mobile robotics. The ha led to deep mathematical insights into the structure of robotics problems and solutions, And finally probabilistic techniques ha pro en their alue in practice. The are at the core of dozens of successful robotic systems to date. This article as necessarily brief, and the interested reader is in vited to consult the rich literature on this topic. Additional introductory material can be found at the author eb site thrun Ackno wledgment The author ackno wledges the in aluable contrib utions by arious the members of CMU Robot learning lab Generous financial support by ARP (TMR, MARS, CoABS and MICA programs) and NSF (ITR, Robotics, and CAREER programs) is also gratefully ackno wledged. Refer ences [1] G. Dissanayak e, Ne wman, S. Clark, H.F Durrant-Wh yte, and M. Csorba. An xperimental and theoretical in estig ation into simultaneous localisation and map uilding (SLAM). In Cork and J. re elyan, editors, Lectur Notes in Contr ol and Information Sciences: Experimental Robotics VI pages 265–274, London, 2000. Springer erlag. [2] A. Doucet, J.F .G. de Freitas, and N.J. Gordon, editors. Sequential Monte Carlo Methods In Pr actice Springer erlag, Ne ork, 2001. [3] H.F Durrant-Wh yte. Autonomous guided ehicle for car go handling applications. International our nal of Robotics Resear 15(5), 1996. [4] Liu, R. Emery D. Chakrabarti, Bur ard, and S. Thrun. Using EM to learn 3D models with mobile robots. In Pr oceedings of the International Confer ence on Mac hine Learning (ICML) 2001. [5] Maybeck. Stoc hastic Models, Estimation, and Contr ol, olume Academic Press, Inc, 1979.
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[6] G.J. McLachlan and Krishnan. The EM Algorithm and Extensions ile Series in Probability and Statistics, Ne ork, 1997. [7] I. Nourbakhsh, J. Bobenage, S. Grange, R. Lutz, R. Me yer and A. Soto. An af fecti mobile robot with full-time job Artificial Intellig ence 114(1–2):95–124, 1999. [8] N. Ro and S. Thrun. Coastal na vig ation with mobile robot. In Pr oceedings of Confer ence on Neur al Information Pr ocessing Systems (NIPS) 1999. to appear [9] R. Simmons, D. Apfelbaum, Bur ard, M. ox, D. an Moors, S. Thrun, and H. ounes. Coordination for multi-robot xploration and mapping. In Pr oceedings of the AAAI National Confer ence on Artificial Intellig ence Austin, TX, 2000. AAAI. [10] E. Sondik. The Optimal Contr ol of artially Observable Mark Pr ocesses PhD thesis, Stanford Uni ersity 1971. [11] S. Thrun, M. Beetz, M. Benne witz, Bur ard, A.B. Cremers, Dellaert, D. ox, D. ahnel, C. Rosenber g, N. Ro J. Schulte, and D. Schulz. Probabilistic algorithms and the interacti mu- seum tour -guide robot minerv a. International ournal of Robotics Resear 19(11):972–999, 2000. [12] S. illiams, G. Dissanayak e, and H.F Durrant-Wh yte. ards terrain-aided na vig ation for underw a- ter robotics. Advanced Robotics 15(5), 2001.

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