1. Particle Filter & Search
Unit 3 & 4 Udacity

2. Particle Filter Show relation to Kalman. Implementation & examples.
MATLAB Demo

3. Particle Filter Estimates the state of a system.
Same as Histogram filters and Kalman filters
Used in localization and tracking.

4. Advantages of particle filters compared to KF and HF
Easiest to program
Most flexible
Can easily handle non-linear and non-gaussian systems.
Multimodal

5. Remember kalman? Motion/Prediction Measurement update
Estimate of position x(t2)
Corrected Optimal est x(t3)
Measurement z
Prediction x’(t3)
Prediction x’(t3)

6. Demo Show video Initiation of multiple guesses (x,y,Ѳ)
Survival of the fittest

7. Approach (1) – Initialization
Determine robot position
Initialization of multiple guesses

8. Approach(2) – Measurement/Weight
Laser sensor
Measurement noise
Sandsynligheden for at robotten er placeret i en position, givet målingen o.
- Weights of each particle are determined by the chance of being correct.

9. Approach(3) – Likelihood
Calculate weights
Normalize factor
Mini Quiz 1:
Sandsynligheden for at en position er korrect givet en måling.
Normalized weight
Mini Quiz 2:

10. Approach(4) – Resampling
Survival of the fittest
Resampling wheel
Resampling

11. Approach(5) – Resampling
Measurement update (Kalman)
Corrected Optimal est x(t3)
P(X) angiver vores priori state.
P(Z|X) angiver vægtningen af hver partikel.
Measurement update dannes ved at resample.
Measurement z
Prediction x’(t3)

12. Approach (5) – Motion

13. Approach (6) - Prediction/Motion
In the context of localization, the particles are propagated according to the motion model.
Motion update D1 (Kalman)
Motion Update D2
Posteriori/Estimate of position x(t2)
Prediction x’(t3)
Each particle is added noise -> gaussian distribution

14. Approach (7)
Sandsynligheden for at robotten er placeret i en position, givet målingen o er stadigvæk den samme.
Men fordi man benytter sine tidligere forudsigelser kan vi altså få et bedre estimat.

33. Demo – Finding wally
Matlab code is provide in ParticleFilterUdacity.zip

34. Motion Planning Find the ”shortest” path to a given goal.
Discrete planning (This lecture)
World divided in grid cells
Continuous planning

35. Motion Planning (Search)
Planning Problem
Given
Map
Starting location
Goal location
Cost
Goal
Find the minimum cost path

36. The Search Problem – Path Planning
Find the shortest path from Start to Goal.
Done with an expand approach.
Openlist: Possible expansions.
G-value: Number of expansions need to reach a given grid cell.
Algorithm continues until goal is reached or openlist is empty.

37. Demo – Search Algorithm
MATLAB: MotionPlanning2DSearchStar

38. Search - A-star Minimizes the number of expansions
Prioritized search by adding heuristic function.

39. Demo: Search - A start
MATLAB: MotionPlanning2DSearchStar

40. Demo: Search A-Star Quadrocopter

41. Dynamic programming Given Outputs: Best Path from ANYWHERE.
Map
Goal
Outputs: Best Path from ANYWHERE.
Creates a Policy.
Gives the optimal action for every grid cell.

42. Dynamic Programming Approach
Create a value grid

43. Cons and pros Pro: Gives the optimal path for any location.
Con: Is more computional.

44. Demo: Dynamic Programming
MATLAB: MotionPlanningDynamicProgramming.m

45. Stochastic motion
Avoid robots from getting to close to an obstacle.

46. Stochastic motion
Avoidance from the deterministic model.

47. Example: Forward(1)

48. Example: Falling of the grid (2)

49. Stochastic motion
By updating the value function with a stochastic model. The robot will move away from obstacles.