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Particle Filters in Robotics In Proceedings of Uncertainty in AI (UAI) 2002 Particle Filters in Robotics Sebastian Thrun Computer Science Department Carnegie Mellon University Pittsburgh, PA 15213 http://www.cs.cmu.edu/ thrun perfect models and and imperfect sensors through proba- Abstract bilistic laws, such as Bayes rule. Many recently fielded state-of-the-art robotic systems employ probabilistic tech- niques for perception [12, 46, 52]; some go even as far as In recent years, particle filters have solved several hard using probabilistic techniques at all levels of perception and perceptual problems in robotics. Early successes of decision making [39]. particle filters were limited to low-dimensional esti- mation problems, such as the problem of robot lo- This article focuses on particle filters and their role in calization in environments with known maps. More robotics. Particle filters [9, 30, 40] comprise a broad fam- recently, researchers have begun exploiting structural ily of sequential Monte Carlo algorithms for approximate properties of robotic domains that have led to success- inference in partially observable Markov chains (see [9] ful particle filter applications in spaces with as many for an excellent overview on particle filters and applica- as 100,000 dimensions. The fact that every model—no tions). In robotics, early successes of particle filter imple- mater how detailed—fails to capture the full complex- mentations can be found in the area of robot localization, ity of even the most simple robotic environments has in which a robot’s pose has to be recovered from sensor lead to specific tricks and techniques essential for the data [51]. Particle filters were able to solve two important, success of particle filters in robotic domains. This arti- previously unsolved problems known as the global local- cle surveys some of these recent innovations, and pro- ization [2] and the kidnapped robot [14] problems, in which vides pointers to in-depth articles on the use of particle a robot has to recover its pose under global uncertainty. filters in robotics. These advances have led to a critical increase in the robust- ness of mobile robots, and the localization problem with a given map is now widely considered to be solved. More re- 1 INTRODUCTION cently, particle filters have been at the core of solutions to much higher dimensional robot problems. Prominent ex- One of the key developments in robotics has been the adop- amples include the simultaneous localization and mapping tion of probabilistic techniques. In the 1970s, the predomi- problem [8, 27, 36, 45], which phrased as a state estima- nant paradigm in robotics was model-based. Most research tion problem involves a variable number of dimensions. A at that time focused on planning and control problems un- recent particle-filter algorithm known as FastSLAM [34] der the assumption of fully modeled, deterministic robot has been demonstrated to solve problems with more than and robot environments. This changed radically in the mid- 100,000 dimensions in real-time. Similar techniques have 1980s, when the paradigm shifted towards reactive tech- been developed for robustly tracking other moving entities, niques. Approaches such as Brooks’s behavior-based ar- such as people in the proximity of a robot [35, 44]. chitecture generated control directly in response to sensor However, the application of particle filters to robotics prob- measurements [4]. Rejections of models quickly became lems is not without caveats. A range of problems arise typical for this approach. Reactive techniques were ar- from the fact that no matter how detailed the probabilistic guable as limited as model-based ones, in that they replaced model—it will still be wrong, and in particular make false the unrealistic assumption of perfect models by an equally independence assumptions. In robotics, all models lack im- unrealistic one of perfect perception. Since the mid-1990s, portant state variables that systematically affect sensor and robotics has shifted its focused towards techniques that uti- actuator noise. Probabilistic inference if further compli- lize imperfect models and that incorporate imperfect sensor cated by the fact that robot systems must make decisions data. An important paradigm since the mid-1990s—whose in real-time. This prohibits, for example, the use of vanilla origin can easily be traced back to the 1960s—is that of (exponential-time) particle filters in many perceptual prob- probabilistic robotics. Probabilistic robotics integrates im- (a) Robot position Figure 2: Particle filters have been used successfully for on-board localization of soccer-playing Aibo robots with as few as 50 par- ticles [26]. ¦ serted in the time interval . The state in the Markov chain is not observable. Instead, one can measure ¢ , which ¢ (b) is a stochastic projection of the true state ¡ generated via ¢ ¢ ¡ the probabilistic law © . Furthermore, the initial © ¡! state ¡ is distributed according to some distribution . ¢ "¤¢# ¢¦¥$§ ¡ In robotics, © ¡ is usually referred to as ac- ¢% ¢ ¡ tuation or motion model, and © as measurement model. They as usually highly geometric and generalize Robot position classical robotics notions such as kinematics and dynamics by adding non-deterministic noise. The classical problem in partially observable Markov chains is to recover a posterior distribution over the state ¢ ¡ at any time , from all available sensor measurements ¢'& ¢+& )()) ())(), ( *¢ ¢ and controls . A solution (c) to this problem is given by Bayes filters [20], which com- pute this posterior recursively: 7 ¢ ¢ ./012 Robot position & ¢- )43 ¢6 ¢ ¢ £¢ ¢¦¥¨§ © ¡ © 5 ¡ © ¡ ¡ ¢¦¥¨§ ¢¦¥$§ 8 :9 ¡¢¦¥$§ © ¡£¢¦¥¨§ (1) & ; 8 * © ¡ under the initial condition © ¡ . If states, controls, and measurements are all discrete, the Markov chain is equivalent to hidden Markov models (HMM) [41] and (1) can be implemented exactly. Representing the pos- terior takes space exponential in the number of state fea- tures, though more efficient approximations exist that can Figure 1: Monte Carlo localization, a particle filter algorithm exploit conditional independences that might exist in the for state-of-the-art mobile robot localization. (a) Global uncer- model of the Markov chain [3]. tainty, (b) approximately bimodal uncertainty after navigating in the (symmetric) corridor, and (c) unimodal uncertainty after en- In robotics, particle filters are usually applied in continu- tering a uniquely-looking office. ous state spaces. For continuous state spaces, closed form solutions for calculating (1) are only known for highly spe- < © ¡£¢ ¢ ¡£¢¦¥¨§ cialized cases. If © ¡£ is Gaussian and lems. ¢= ¢ ¡ and © are linear in its arguments with added in- This article surveys some of the recent developments, and dependent Gaussian noise, (1) is equivalent to the Kalman 9A@* 9 points out some of the opportunities and pitfalls specific to filter [23, 32]. Kalman filters require >? time for - robotic problem domains. dimensional state spaces, although in many robotics prob- 9CBD lems the locality of sensor data allows for >? imple- mentations. A common approximation in non-linear non- 2 PARTICLE FILTERS Gaussian systems is to linearize the actuation and measure- ments models. If the linearization is obtained via a first- Particle filters are approximate techniques for calculat- order Taylor series expansion, the result is known as ex- ing posteriors in partially observable controllable Markov tended Kalman filter, or EKF [32]. Unscented filters [21] chains with discrete time. Suppose the state of the Markov obtain often a better linear model through (non-random) ¡¤¢ chain at time is given by ¡£¢ . Furthermore, the state sampling. However, all these techniques are confined to ¢¦¥¨§ depends on the previous state ¡ according to the prob- cases where the Gaussian-linear assumption is a suitable ¢ £¢ ¢¦¥¨§ ¤¢ ¡ abilistic law © ¡ , where is the control as- approximation. Particle filters address the more general case of (nearly) un- 4500 Standard MCL constrained Markov chains. The basic idea is to approxi- 4000 Mixture MCL ¡¢¡ £¥¤ §¦ mate the posterior of a set of sample states ¢ , or par- 3500 ¡¨¡ £¥¤ © ticles. Here each ¢ is a concrete state sample of index , 3000 where is ranges from to , the size of the particle fil- 2500 ter. The most basic version of particle filters is given by the 2000 following algorithm. Distance [cm] 1500 1000 & Initialization: At time , draw particles accord- 500 ing to © ¡ . Call this set of particles . 0 0 500 1000 1500 2000 2500 3000 3500 4000 ¡ £¤ ¡ Recursion: At time , generate a particle ¢ for Time [sec] ¢¦¥¨§ ¡¨¡ £¤ each particle ¢¦¥¨§ by drawing from the actua- Figure 3: MCL with the standard proposal distribution (dashed © ¡£¢ ¢ ¡ ?¢ £¤ ¡ curve) compared to MCL with a hybrid mixture distribution (solid tion model ¢¦¥¨§ . Call the resulting set . line) [51]. Shown here is the error for a 4,000-second episode of ¢ Subsequently, draw particles from , so that each camera-based MCL of a museum tour-guide robot operating in ¡ £¥¤ ¡ ?¢ ¢ is drawn (with replacement) with a probabil- Smithsonian museum [50]. © 5*¢ ¡ ¡ £¥¤ ity proportional to ¢ . Call the resulting set of ¢ particles . all times [2]. More general is the the global localization problem, which is the problem of localizing a robot under In the limit as , this recursive procedure leads global uncertainty. The most difficult variant of the local- ¢ to particle sets that converge uniformly to the desired ¢ ¢ ization, however, is the kidnapped robot problem [14], in 8 posterior
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