A Probabilistic Approach to A Probabilistic Approach to Concurrent Mapping and Localization Concurrent Mapping and Localization for Mobile Robotsfor Mobile Robots

S. Thrun, W. Burgard, and D. Fox

ProblemProblem

Map building: problem of determining the location of entities of interest To determine the location of entities-of –interest: the robot must

know where it is To determine where it is: the robot must know the locations of the

entities-of-interest

How can a robot construct a consistent map of an environment, if it occasionally observes a landmark?

Presents an algorithm that is based on rigorous statistical account on robot motion and perception

Robot motionRobot motion :

determines the probability that the robot is at

Motion model: The darker a value, the more likely it is that the robot is there

Robot perceptionRobot perception :

determines the likelihood of making observation 0 when the robot is at location , assuming that m is the correct model of the environment

implies that after observing o, the robot’s probability of being at is proportional to the product of P(|m) and the perceptual probability P(o| ,m)

Uncertainty of sensing landmarks

Data, maps, and the map likelihoodData, maps, and the map likelihood

Maps are built from data, by maximizing the likelihood of the map under the data

In statistical terms, the problem of mapping is the problem of finding the most likely map given the data

Difficulty Involving search in the space of all maps-space often dimensions Evaluation of a single map would require integrating over all possible

locations at all points in time (would require over more than variables)

Solution- EM algorithms E-step: the current map is held constant and the probabilistic for the

robot’s locations at the various points in times are estimated M-step: the most likely map is computed based on the estimation result of

the E-step

A function of the data d, the perceptual model P(o|m, ), and the motion model P(`|u, )

Maximum likelihood Maximum likelihood estimationestimation

E-Step A localization step with a fixed map The current-best map and the data are used to compute

probabilistic estimates for the robot’s position

Computation of the

Computation of the

The result of the E-step is an estimation of the robot’s location at the various points in time t

Maximum likelihood estimation Maximum likelihood estimation (2)(2)

M-step implements a mapping step which operates under the as

sumption that the robot’s locations are known Probability map of the environment is an assignment of

probabilities ,where <x,y> is a location measured in global coordinates, and is a random variable that corresponds to the generalized landmark type at <x,y>

The M-step computes the most likely map under the assumption that accurately reflects the likelihood that the robot was at at time t

counts how often the generalized landmark l was observed from location <x,y>, divided by some generalized landmark was divided for that location

Caching: The motion model is computed in advance for each control in d and cached in a look-up table

Exploiting symmetry: Symmetric probabilities are stored in a computer

Coarse-grained temporal resolution: Locations are only estimated if at least one landmark has been observed, of if the robot moved 20m

Selective computation: Computation focuses on location whose probability is larger than threshold

Selective memorization: Only a subset of all probabilities are stored for each , namely those are above the threshold described above

ResultsResults

ThesisThesis

Robot simulation 센서 데이터에 불확실성 추가 임무

1. 지능적 센서 데이터 해석을 위한 센서 해석 루틴의 진화

2. 처한 환경에 대한 반응 루틴 진화 3. 진화된 루틴들의 결합을 통한 제어

프로그램생성 4. 전체 GP 트리를 하나의 xc6200 에 구현하기

위한 알고리즘 개발