Examples of using probabilistic ideas in robotics Reverend Bayes and review of probabilistic ideas

1. Used in Spring 2013 • Examples of using probabilistic ideas in robotics • Reverend Bayes and review of probabilistic ideas • Introduction to Bayesian AI • Simple example of state estimation – robot and door to pass • Simple example of modeling actions • Bayes Filters. • Probabilistic Robotics

2. Probabilistic Robotics:Sensing and Planning in Robotics

3. Examples of probabilistic ideas in robotics

4. Robotics Yesterday

5. Robotics Today

6. Robotics Tomorrow? More like a human • Boolean Logic and Differential equations are based of classical robotics • Probabilistic Bayes methods are fundaments of all math in humanities and future robotics.

7. What is robotics today? • Definition (Brady): Robotics is the intelligent connection of perception and action • Trend to human-like reasoning emotionalservice robots. • Perception, action, reasoning, emotions – all need probability.

8. Reactive Paradigm (mid-80’s) • no models • relies heavily on good sensing Trends in Robotics Research Classical Robotics (mid-70’s) • exact models • no sensing necessary Hybrids (since 90’s) • model-based at higher levels • reactive at lower levels Probabilistic Robotics (since mid-90’s) • seamless integration of models and sensing • inaccurate models, inaccurate sensors Robots are moving away from factory floors to Entertainment, Toys, Personal service. Medicine, Surgery, Industrial automation (mining, harvesting), Hazardous environments (space, underwater)

9. Examples of robots that need stochastic reasoning and stochastic learning

10. Entertainment Robots: Toys

11. Entertainment Robots: RoboCup

12. Autonomous Flying Machines

13. Humanoids

14. Mobile Robots as Museum Tour-Guides Life is full of uncertainties

15. Tasks to be Solved by Robots • Planning • Perception • Modeling • Localization • Interaction • Acting • Manipulation • Cooperation • Recognition of environment that changes • Recognition of human behavior • Recognition of human gestures • ...

16. Uncertainty is Inherent/Fundamental • Uncertainty arises from four major factors: • Environment is stochastic, unpredictable • Robots actions are stochastic • Sensors are limited and noisy • Models are inaccurate, incomplete

17. Range Data Nature of Sensor Data Odometry Data

18. Main probabilistic ideas in robotics

19. Probabilistic Robotics Key idea: Explicit representation of uncertainty using the calculus of probability theory • Perception = state estimation • Action = utility optimization

20. Advantages and Pitfalls of probabilistic robotics • Can accommodate inaccurate models • Can accommodate imperfect sensors • Robust in real-world applications • Best known approach to many hard robotics problems • Computationally demanding • False assumptions • Approximate

21. Introduction to “Bayesian Artificial Intelligence” • Reasoning under uncertainty • Probabilities • Bayesian approach • Bayes’ Theorem – conditionalization • Bayesian decision theory

22. Reasoning under Uncertainty • Uncertainty – the quality or state of being not clearly known • distinguishes deductive knowledge from inductive belief • Sources of uncertainty • Ignorance • Complexity • Physical randomness • Vagueness

23. Reminder of Bayes Formula likelihood

24. Normalization likelihood Algorithm: prior

25. Conditional knowledge has many applications • Total probability: • Bayes rule and background knowledge: See law of total probability earlier examples

26. I will present many examples of using Bayes probability in mobile robot

27. Simple Example of State Estimation The door opening problem

28. Simple Example of State Estimation • Suppose a robot obtains measurement z • What is P(open|z)?

29. Simple Example of StateEstimation • Suppose a robot obtains measurement z • What is P(open|z)? What is the probability that door is open if the measurement is z

30. count frequencies! Causal vs. Diagnostic Reasoning • P(open|z) is diagnostic. • P(z|open) is causal. • Often causal knowledge is easier to obtain. • Bayes rule allows us to use causal knowledge: We open the door and repeatedly measure z. We count frequencies

31. Examples of calculating probabilities for door opening problem Probability that measurement z=open was for door open Probability that measurement z=open was for door not open • P(z|open) = 0.6 P(z|open) = 0.3 • P(open) = P(open) = 0.5 • z raises the probability that the door is open.

32. Combining Evidence What we do when more information will come? • Suppose our robot obtains anotherobservationz2. • How can we integrate this new information? • More generally, how can we estimateP(x| z1...zn )?

33. Recursive Bayesian Updating Markov assumption: znis independent ofz1,...,zn-1if we know x.

34. Example: Second Measurement added in our “robot and door” problem What we do if we have a new measurement result? • P(z2|open) = 0.5 P(z2|open) = 0.6 • P(open|z1)=2/3 • z2lowers the probability that the door is open. If z2 says that door is open, now our probability that it is open is lower

35. A Typical Pitfall • Two possible locations x1and x2 • P(x1)=0.99 • P(z|x2)=0.09 P(z|x1)=0.07 x2 x1 probabilities Number of integrations

36. The behavior/recognition model for the robot should take into account robot actions

37. Actions Change the world? How to use this knowledge? • Often the world is dynamic since • actions carried out by the robot change the world, • actions carried out by other agents change the world, • or just the time passing by change the world. • How can we incorporate such actions?

38. Typical Actions of a Robot • The robot turns its wheels to move • The robot uses its manipulator to grasp an object • Plants grow over time… • Actions are never carried out with absolute certainty. • In contrast to measurements, actions generally increase the uncertainty.

39. Modeling Actions Probabilistically • To incorporate the outcome of an actionu into the current “belief”, we use the conditional pdf P(x|u,x’) • This term specifies the pdf that executing u changes the state from x’ to x. pdf = probability distribution function

40. Simple example of modeling Actions

41. Example: Closing the door

42. State Transitions State Transitions for closing door example P(x|u,x’) for u = “close door”: If the door is open, the action “close door” succeeds in 90% of all cases. Closing the door succeeded

43. Integrating the Outcome of Actions Continuous case: Discrete case:

44. Example: The Resulting Belief for the door problem Probability that door open Continue open/closed door example Probability that the door is closed after action u Probability that the door is open after action u

45. Concepts of Probabilistic Robotics Probabilities are base concept Bayes rule used in most applications Bayes filters used for estimation Bayes networks Markov Chains Bayesian Decision Theory Bayes concepts in AI Bayes Filters: Kalman Filters Particle Filters Other filters

46. Key idea of Probabilistic Robotics repeated Key idea: Explicit representation of uncertainty using the calculus of probability theory • Perception = state estimation • Action = utility optimization

47. 1. Probability Calculus Markov assumption: znis independent ofz1,...,zn-1if we know x.

48. 2. Main ideas of using Bayes in robotics • Bayes rule allows us to compute probabilities that are hard to assess otherwise. • Under the Markov assumption, recursive Bayesian updating can be used to efficiently combine evidence. • Bayes filters are a probabilistic tool for estimating the state of dynamic systems.

49. Bayes Filters

50. 3. Bayes Filters: Framework • Given: • Stream of observations z and action data u: • Sensor modelP(z|x). • Action modelP(x|u,x’). • Prior probability of the system state P(x). • Wanted: • Estimate of the state X of a dynamical system. • The posterior of the state is also called Belief: Markov assumption: znis independent ofz1,...,zn-1if we know x.