1. 1 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Instituto Superior Técnico – Instituto de Sistemas e Robótica Av. Rovisco Pais, 1 – 1049-001 Lisboa - Portugal A Probabilistic Approach For The Localisation of Mobile Robots in Topological Maps Alberto Vale Maria Isabel Ribeiro vale@isr.ist.utl.pt mir@isr.ist.utl.pt

2. 2 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Objective Robot Navigation in Outdoors Environment Highly non-structured environments Large amount of available information Physical area with large dimensions

3. 3 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Problem Relevance Safety concerns are leading to an increase in the use of robots. Mainly in outdoors environments where a communication channel might not be available and the robot may have to operate autonomously rather than being remotely operated by a central station Outdoors environments mean large and unstructured physical area, which can change in time and where scarce a priori information is usually available

4. 4 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Navigation Uncertainty Uncertainty Impossible to work with T T+1 T+3 T+2 Uncertainty Mobile platform navigation along time …

5. 5 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Navigation Uncertainty Bounding Uncertainty Environment Model + Sensor Model Probabilistic Approach... TT+1T+2 Uncertainty Probabilistic Approach...

6. 6 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Navigation Block Diagram Environment Model Defines a set of states as an environment model using Markov Models Localização Localization Probabilistic approach to evaluate the localization on the environment model Navigation Defines an optimized trajectory to the goal based on the environment model Path Execution Guides the mobile robot through the trajectory with obstacle avoidance

7. 7 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION q t {s 1,s 2,s 3,s 4,s 5,s 6,s 7 } robot state in time instant t set of states of the topological map A set of properties defines each state s i (ex: color, pattern, geometry, reflectance, temperature, height, etc) s2s2 s3s3 s6s6 s5s5 s7s7 s1s1 s4s4 Topological Map, q 2 = s 4 t =2, q 3 = s 5 t =3 q 4 = s 3 t =4, q 5 = s 6 t =5 q 1 = s 1 t =1 Environment Model sum of Gaussians

8. 8 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Markov Models (to support robot navigation) q1q1 q2q2 q3q3 qtqt o1o1 o2o2 o3o3 otot... q t is the robot state in time instant t, q t {s 1,s 2,...,s i,...,s N } o t is the observation in time instant t Q T ={q 1,q 2,...,q T } is a sequence of states from t=1 to t=T O T ={o 1,o 2,...,o T } is a sequence of observations from t=1 to t=T states of the topological map

9. 9 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Initial State Distribution State Transition Probability Distribution Observation Probability Distribution Set of parameters of the model a priori information dependent of distances between states

10. 10 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Localization How to identify the state q t (or sequence of states) based on observations obtained until time instant T ? Information from the past of instant t Information from the future of instant t

11. 11 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 0 1 2 … t-1 t t+1 … T time t t Information from the past of instant t Information from the future of instant t Forward-Backward (FB) algorithm 0 t T

12. 12 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION FB algorithm revisited 0 1 2 … t... T 1 +1 time t T1T1 t T1T1 t T2T2 T2T2 T1T1 … T 2 time More observations = t T2T2

13. 13 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION FB algorithm revisited … (k-1)T kT t (k+1)T … time observations T kT t kT+1 t (i) kT+T t (i) kT+T

14. 14 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Simulation Results Experimental results of Robot Localization with 6 states ( s 1, s 2, s 3, s 4, s 5, s 6 ) Each state is identified with 3 different attributes (example) Attribute 1 (colors - RGB) Attribute 2 (geometry) Attribute 3 (temperature)...

15. 15 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Simulation Results Localization probability as result of a path execution P j - via points

16. 16 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Log of Prob. Localization (new paths) Observation variance 1 2 Observation variance 2 2 = 4 1 2 Observation variance 1 2 = 25 1 2

17. 17 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Future Development Development of new techniques to adjust the model parameters a ij (state transition probability distribution) Adjust the parameters k il, u il and R il of the environment model according to attributes Identify new attributes (if necessary) which adds more information to each state Identify and remove useless attributes

18. 18 Instituto de Sistemas e Robótica 10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION Future Development As a challenging application, this will be applied in the Rescue Project. The outdoor navigation will be applied on the wheeled robot using all the sensors information from the team. This project will endow a team of two outdoors robots with cooperative navigation capabilities in search and rescue-like operation under large-scale catastrophe scenarios.