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Enchaînement de tâches robotiques
Tasks sequencing for sensor-based control
Nicolas Mansard
Supervised by Francois Chaumette
Équipe Lagadic
IRISA / INRIA Rennes
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ContextSensor-based
controlMotion planning Control
architecture
initial
desired
Execution controller
Path deform.
Traj. planning
?
?
Path deformation
Dynamic planning
Motors Sensors
Motion planning
Execution level
Symbolic high-level controller
Data extraction
Motion prediction
Complete solutionGlobal convergence
Required knowledgeLack of reactivity
AccuracyReactivityRobustness
Local convergence
Realistic solution
Complex softwareInherent problems due to
the path planning
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Improve the expressivity of the sensor-based control methods
Less planning – More freedom
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Task sequencing for sensor-based control
GLOBAL TASK
CONSTRAINTS Centering
Zoom
Perspective
Z-rotation
Stack of Tasks
TASK-LEVEL CONTROLLER
add
removeswap
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Task sequencing for sensor-based control
Example
Centering
Zoom
Perspective
Z-rotation
Stack of Tasks
CONSTRAINTS
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Task sequencing for sensor-based control
CONSTRAINTS
Centering
Zoom
Perspective
Z-rotation
Stack of Tasks
TASK-LEVEL CONTROLLER
add
removeswap
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Outline
Credo
Low Level Stack of tasks Improvements
High Level Task-level controller Applications
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Sensor
4
12
3
4
1 2
3
What is a task?
Robot position: Robot control input:
An error between current and desired sensor values
A reference behavior of the error
The associated Jacobian matrix
Classical control law
[Samson91],[Espiau91]
Sensor
- +
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Stack of task
Principles Compute the control law from several (sub-) tasks
Ensure a hierarchy For avoiding any conflicts is perfectly realized is realized under the condition is realized is realized under the condition , … and are realized
Take into account additional constraints As a lowest-priority task Using the potential field formalism
Ensure the continuity at task changes
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z can be used to vary the trajectory (obstacle avoidance)
Stack of task
Redundancy formalism
P
We will use z to realize at best the second elementary task
[Rosen60],[Liegeois77]
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Two recursive equations to stack several tasks
Continuity at stack change
e1
ei-1
ei
STACK
en
Stack of task
Priority and continuity
[Chiaverini97]
[Robea-Egocentre04]
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Gradient Projection Method Potential function : 0 far from the obstacle
Maximal when the robot reaches the obstacle Gradient as a repulsive force Projection onto the remaining DOFs
Application to joint limits avoidance
Stack of task
Considering the constraints[Liegeois77],[Marchand98]
[Khatib87]
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Outline
Credo
Low Level Stack of tasks Improvements
Directional redundancy Varying-feature-set tasks
High Level Task-level controller Applications
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Directional redundancy
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Directional redundancy
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Directional redundancy
Comparison
Classical redundancy Directional redundancy
Additional DOF
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Varying-feature-set task
Final goal: Introduce the constraint IN the stack
Joint limits
JLmaxJLmin
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Varying-feature-set task
+
=
Positioning
Joint limits
Control law
CONTINU
Positioning
Joint limits
STACK
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Varying-feature-set task
+
=
Joint limits
Positioning
Control law
DISCONTINUOUSPositioning
Joint limits
STACK
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Varying-feature-set task
+
=
Joint limits
Positioning
Control law
Positioning
Joint limits
STACK
OSCILLATIONS
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Varying-feature-set task
Definition of a task: Error vector Activation matrix
Definition of a new inverse operator
Inverse of J activated by H: Associated projector:
Secondary task alone
Joint limits + secondary task
Joint limits alone
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Low level
Stack of tasks Control from several tasks + constraints Continuity at stack change Define some functionality for high-level control
Directional redundancy Enlargement of the main-task free space
Varying-feature-set task Enlargement of the expressivity
LOCAL CONVERGENCE
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Task sequencing for sensor-based control
CONSTRAINTS
Centering
Zoom
Perspective
Z-rotation
Stack of Tasks
TASK-LEVEL CONTROLLER
add
removeswap
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Outline
Credo
Low Level Stack of tasks Improvements
High Level Task-level controller Applications
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Higher Level Controllers
Stack controller
Joint-limit controller
Obstacle controller
Occlusion controller
…
CO
LLIS
ION
PR
ED
ICT
ED
?
Remove a task
e1
ei-1
ei
STACK
en
constraints
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Higher Level Controllers
Examples
REMOVE
JOINT-LIMIT COLLISION?
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Higher Level Controllers
Push-back controller
Joint-limit controller
Obstacle controller
Occlusion controller
…
CO
LLIS
ION
PR
ED
ICT
ED
?
Push-back controller
OB
ST
AC
LE
AV
OID
ED
?
Add a removed taskRemove a task
e1
ei-1
ei
STACK
en
constraints
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Higher Level Controllers
Examples
PUSH-BACK
JOINT-LIMIT AVOIDED?
initial
final
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Higher Level Controllers
Look-ahead controller
Joint-limit controller
Obstacle controller
Occlusion controller
…
CO
LLIS
ION
PR
ED
ICT
ED
?
Push-back controller
OB
ST
AC
LE
AV
OID
ED
?
Look-ahead controller
LO
CA
L M
INM
A?
D
EA
D L
OC
K?
Add a specific task
Add a removed taskRemove a task
e1
ei-1
ei
STACK
en
constraints
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Higher Level Controllers
Examples
Desired position
REMOVE
PUSHBACKRECONFIGURE
PUSHBACK
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Global task Positioning (6 DOF)
Define a set of tasks Tasks to be realized
Centering Zoom Rotation Perspective
Constraints to be respected Joint limits Occlusion Obstacles
High level controller Constraint controller Push-back controller Reconfiguration controller
Applications Afma6 manipulator robot
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Centering
Zoom
Perspective
Z-rotation
Stack of Tasks
CONSTRAINTS
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Centering
Zoom
Perspective
Z-rotation
Stack of Tasks
CONSTRAINTS
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Applications Non-holonomic robot
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Applications Non-holonomic robot
Depending from controller state+1,-1
-1,+1
+1,+1
-1,-1
[Promete94]
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Global task Positioning (no obstacles)
Define a set of tasks Tasks to be realized
Positioning: second order approximation Positioning toward a virtual position
High level controller Virtual goal controller
Applications Non holonomic robot
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Applications Non-holonomic robot
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Applications Humanoid robot
Application of the previous work Catching a ball while walking
Define a set of tasks
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Applications Humanoid robot
Global task Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Task centering:
Input dim=2
Output dim = 10
Rank = 2
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Task grasping:
Input dim=3
Output dim = 14
Rank = 3
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Subtask distance:
Input dim=1
Output dim = 14
Rank = 1
Subtask orientation:
Input dim=2
Output dim = 14
Rank = 2
divideTask grasping:
Input dim=3
Output dim = 14
Rank = 3
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Task walking:
Input dim=12
Output dim = 12
Rank = 12
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Constraint Joint Limits:
Input dim=28 → 14
Output dim = 14
Rank = 0 to 14
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Constraint Manipulability:
Input dim = 6
Output dim = 6
Rank = 1
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Constraint Chest:
Input dim = 2
Output dim = 2
Rank = 2
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
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Applications Humanoid robot
Application of the previous work Catching a ball while walking
Define a set of tasks Tasks to be realized
Centering Grasping Walking
Constraints to be respected Joint limits Arm manipulability Chest (immobile)
High level controller Joint-limits control Reachability control
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Conclusion
Low level Stack of task: a new tool for task-level control Directional redundancy Varying-feature-set task
High level Task-level controllers to ensure multiple constraints during the displacement Application for humanoid robotic An alternative to path planning?
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Perspectives
Multiple short-term perspective Application for multi sensors Integration of the varying-feature-set control laws
Non-holonomic robots control
Generalization of the method for humanoid robot
Integration of the path planning solutions
Learning by imitation
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Merci à …
Many thanks to …
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Appendix 1
State of the Art
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Appendix 1
State of art Sensor-based control + constraints
Singularity [Nelson95], joint limits [Chan95] Redundancy formalism [Liegeois77],[Hanafusa84], [Siciliano91], [Samson91]
Switching control law Visual servoing 2D / 3D [Gans03] Positioning / Visibility [Chesi03] Positioning / Obstacle avoidance [Soueres03, Folio06]
Ad-hoc sequencing [Peterson01] [Chiaverini05]
High-level control Behavior control [Brooks87],[Mataharic01] Humanoid task-level control
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Appendix 2
Calibration-robust Stack of Tasks
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1. Centering
2. Rotation
Appendix 2
Calibration-robust Stack of Tasks
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56robust not robust
Centering not respected
1. Centering
2. Rotation
Appendix 2
Calibration-robust Stack of Tasks
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The redundancy formalism is not robust to jacobian misestimation
We have an initial estimation of J … Analytical solution
… and then we estimate J on-line Learning Correction of the perturbation
[Hosoda94],[Jagersand96]
[Piepmeier99]
[Lapreste04]
Appendix 2
Calibration-robust Stack of Tasks
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58
Two cameras on mobile Pan-Tilt Fixed head for the experiments
Eye-To-Hand servoing Markers on the hand
Flexible robot No real zero-position Difficult to calibrate Approximation of the Jacobian
Appendix 2
Calibration-robust Stack of Tasks
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Analytical matrices On-line estimated matrices
Appendix 2
Calibration-robust Stack of Tasks
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Appendix 3
Pseudo-linear Control for Non-holonomic Robots
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+
Appendix 3 Pseudo-linear Control for Non-holonomic Robots
BUT
?=
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where
In our case
+ =
[Hettlich98]
Appendix 3 Pseudo-linear Control for Non-holonomic Robots