1. A Probabilistic Approach to Concurrent Mapping and Localization for Mobile Robots S. Thrun, W. Burgard, and D. Fox

2. Problem 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

3. Robot 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

4. Robot 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

5. Data, 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

6. 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,  )

7. Maximum likelihood estimation 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

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

9. Maximum likelihood estimation (2) M-step  implements a mapping step which operates under the assumption that the robot’s locations are known  Probability map of the environment is an assignment of probabilities,where is a location measured in global coordinates, and is a random variable that corresponds to the generalized landmark type at  The M-step computes the most likely map under the assumption that accurately reflects the likelihood that the robot was at at time t

10. counts how often the generalized landmark l was observed from location, divided by some generalized landmark was divided for that location

11. 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

12. Results

13. Thesis Robot simulation 센서 데이터에 불확실성 추가 임무  1. 지능적 센서 데이터 해석을 위한 센서 해석 루틴 의 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