simple set-membership methods and control algorithms applied to robots for exploration fabrice le...
TRANSCRIPT
Simple set-membership methods and control algorithms applied to robots for exploration
Fabrice LE BARS
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 2
Outline
Introduction A simple localization example Interval analysis Other localization scenarios Line following Additional common problems and possible
methods Conclusion
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 3
Introduction
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 4
Robotics at ENSTA Bretagne
Main research areas :• Autonomous marine and submarine robotics using
interval methods
• Swarm of robots
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 5
Facts • Autonomous robotics rise new and difficult problems
• There are few demonstrations of cheap autonomous robots able to do survey, cartography, localization tasks, especially in marine and submarine environments
• Current methods : mainly probabilistics
Robotics at ENSTA Bretagne
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 6
Goals• Develop observation, control methods for submarine, marine,
ground and aerial robotics
• Demonstrate the use of interval methods through new applications in autonomous robotics
• Build real and convincing demonstrators
Copyright Ifremer
Robotics at ENSTA Bretagne
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 7
A simple localization example
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 8
A simple localization example
Context :• An underwater robot must follow a wall (not necessarily straight)
• The environment (walls to follow) is known
• The robot has a good compass and a sonar
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 9
A simple localization example
Assumptions :• The wall to follow is on the right of the robot
• We can approximate it as a line y=ax+b
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 10
A simple localization example
Assumptions :• The wall to follow is on the right of the robot
• We can approximate it as a line y=ax+b
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 11
A simple localization example
Assumptions :• The wall to follow is on the right of the robot
• We can approximate it as a line y=ax+b
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 12
A simple localization example
Assumptions :• The wall to follow is on the right of the robot
• We can approximate it as a line y=ax+b
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 13
A simple localization example
Assumptions :• The wall to follow is on the right of the robot
• We can approximate it as a line y=ax+b
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 14
A simple localization example
The robot needs to find :• Its distance to the line
• Its angle to the line (-> angle of the line)
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 15
A simple localization example
Available data :• The angle of the robot thanks to the compass
• Sonar data
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 16
A simple localization example
Methods :• Linear regression using least
squares
• What if we want to localize in a pool, a lake…?
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 17
Uncertainty representations : • Probabilistics
• Gaussians
• Particles
=> We try to get a probability density
• Sets• Zonotopes
• Ellipsoids
• Intervals
=> We try to enclose all possible solutions
A simple localization example
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 18
Interval analysis
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 19
, , are examples of intervals Operations
• smallest interval containing the set of possible values for
•
•
• Multiplication by a number, intersection, union
•
•
• Image by a function
•
1,4 , 2 ,
1,4 2,3 1,7 1,4 2,3 3,12 1,4/2,3 1/2,2
2 1,4 2,8 1,3 2,4 2,3
sin0, 0,1
1,2 3,4 1,4
, , , /x ,x y ,y
x y
Interval analysis
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 20
Interval analysis
Real intervals can be generalized• Vectors intervals (boxes)
• Sets intervals
• Functions intervals (tubes)
• Any set with a lattice structure
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 21
Contraction• If and , , , then
•
z2 expx y x 1,4 y 3.1,3.2 z 4,7x lnz2 y x x ln z2 y 2.5,3.9
x
y
z
Interval analysis
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 22
Contraction and propagation • We call contractor an operator that reduce the domain of
variables
• A propagation is a repeated call to contractors
• We can repeat contractions until a fix point
Interval analysis
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 23
Other techniques such as bisections can also be done
Interval analysis
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 24
Handling outliers : relaxed intersection (q-intersection)
Interval analysis
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 25
Other localization scenarios
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 26
xk xk ,yk , k ,vk . . . xk 1xk 2State
Measurements yk 2 yk 1 yk
For each k
xk 1 fkxk
yk gkxk.
gkxk ykgk 1 fk 1
1 xk yk 1. . .
gk n 1 fk n 1 1 . . . fk 1
1 xk yk nxk Rm,y i y i, i k n, . . ,k .
Other localization scenarios
Dynamic localization
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 27
EURATHLON 2013 • Task "Search and rescue in a smoke-filled
underground structure“
Other localization scenarios
Controller
Robot
w u
xy
Observer (implemented as an
interval simulator)
x fx,u
y gx,u
x midx
x fx,u
y gx,u
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 28
Localization of a swarm of robots with acoustic communication
Other localization scenarios
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 29
Line following
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 30
Purpose• Cover autonomously an area as accurately as possible
Line following
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 31
From waypoints following to line following• Primitive heading control loop
• Existing approaches : basic waypoint following • The robot follows a heading in direction of its waypoint • Waypoint reached when in a predefined radius• Problem : nothing prevent the drift between waypoints (because of
currents...)
• => Line following (use the distance to the line)
Line following
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 32
Line following
Primitive heading regulator
Robot
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 33
Init
GetSensorsData
NavigationManager
Supervisor
PrimitiveHeadingController
SetActuators
Line following
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 34
Line following• Primitive controller stage for heading control
• Rudder control
• Navigation manager sends lines to supervisor and validates lines• Validation condition
Line following
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 35
Line following• Desired heading is the line made by the 2 current waypoints with
an attractiveness angle to the line depending on the distance to the line
Line following
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 36
Additional common problems and possible methods
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 37
Additional common problems and possible methods
Evaluate the guaranteed covered area depending on localization accuracy
Obstacle avoidance using vector fields
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 38
Conclusion
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 39
Conclusion
• Interval methods can be efficient for parameters and state estimation problems
• Advantages : can give an estimation of the error together with the state, parameters
• Can also be used when there are outliers
• Line following can improve easily the accuracy of a trajectory following especially in marine environment
• Vector fields are interesting for obstacle avoidance or other higher level trajectory planning
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 40
Questions?
Contact• [email protected]
Simple set-membership methods and control algorithms applied to robots for exploration
19/04/23- 41