Programming by Demonstration: Some recent challenges Aude G. Billard LASA Laboratory EPFL http://lasa.epfl.ch
Generalizing: Learning a control law Learning a control law that ensures that you reach the target even if perturbed and that you follow a particular dynamics http://lasa.epfl.ch
Learn a control law from examples & & ( ) * * x f x 0. x f x ( ) Time-invariant DS with stable attractor = = = x*: target x 2 x http://lasa.epfl.ch 1
Learn a control law from examples & { i i } Make N observations of the state of the system x x , , i 1... . N = K & & ( k k ) Learn p x x , = w N x x µ , ; , : joint density (mixture of Gaussians) ( ) ∑ Σ k k 1 = describing the distribution of velocity in state space. x 2 x http://lasa.epfl.ch 1
Learn a control law from examples & { i i } Make N observations of the state of the system x x , , i 1... . N = K & & ( k k ) Learn p x x , = w N x x µ , ; , : joint density (mixture of Gaussians) ( ) ∑ Σ k k 1 = describing the distribution of velocity in state space. x 2 x http://lasa.epfl.ch 1
Learn a control law from examples & { i i } Make N observations of the state of the system x x , , i 1... . N = K & & ( k k ) Learn p x x , = w N x x µ , ; , : joint density (mixture of Gaussians) ( ) ∑ Σ k k 1 = describing the distribution of velocity in state space. p x ( ) ~ N x µ Σ ( ; , ) x 2 x http://lasa.epfl.ch 1
Learn a control law from examples & { i i } Make N observations of the state of the system x x , , i 1... . N = K & & ( k k ) Learn p x x , = w N x x µ , ; , : joint density (mixture of Gaussians) ( ) ∑ Σ k k 1 = K describing the distribution of velocity in state space. & Compute (analytical expression for f ) k ( ) ( k k ) { } f x E p x x | = h x A x b ( ) ( ) ∑ = + k 1 = x 2 x http://lasa.epfl.ch 1
Learn a control law from examples & { i i } Make N observations of the state of the system x x , , i 1... . N = K & & ( k k ) Learn p x x , = w N x x µ , ; , : joint density (mixture of Gaussians) ( ) ∑ Σ k k 1 = K describing the distribution of velocity in state space. & Compute (analytical expression for f ) k ( ) ( k k ) { } f x E p x x | = h x A x b ( ) ( ) ∑ = + k 1 = x Stability Constraints in terms of Gaussian Parameters 2 1 − ⎧ ( ) k k k k a ) 0 µ + ∑ ∑ µ = & & x xx xx x ⎪ k 1,... K ∀ = ⎨ T ( ) 1 1 − − k ( k ) k ( k ) p b ) 0 ⎪ ∑ ∑ + ∑ ∑ & & xx xx xx xx ⎩ Determine the parameters of the density as a constrained optimization problem (maximize likelihood under stability constraints). x http://lasa.epfl.ch Khansari and Billard, SEDS, IEEE TRO 2011 1
Generalizing: Learning a control law Other examples of complex dynamics that can be estimated through SEDS. Stability at attractor x 2 x 1 http://lasa.epfl.ch Khansari and Billard, IEEE TRO 2011 Khansari and Billard, SEDS, IEEE TRO 2011
Generalizing: Learning a control law Other examples of complex dynamics that can be estimated through SEDS. Stability at attractor x 2 x 1 http://lasa.epfl.ch Khansari and Billard, IEEE TRO 2011 Khansari and Billard, SEDS, IEEE TRO 2011
Learning motion with non-zero velocity at target Extend the SEDS model with modulation in speed at target http://lasa.epfl.ch Kronander, Khansari and Billard, IROS 2011, JTSC Best Paper Award
Learning coupling across dynamical systems Learn separately stable control laws to control for arm and fingers. Couple the two systems to allow adequate adaptation to perturbations. http://lasa.epfl.ch Shukla and Billard, RSS 2011
Learning coupling across dynamical systems Learn separately stable control laws to control for arm and fingers. Couple the two systems to allow adequate adaptation to perturbations. http://lasa.epfl.ch Shukla and Billard, RSS 2011
Catching Objects in Flight http://lasa.epfl.ch
What to Imitate? Learning a skill is more than simply replaying a trajectory. It requires to understand what a skill is. To learn this, one needs to show several demonstrations to generalize across sets of examples. http://lasa.epfl.ch Billard et al, Rob. and Aut. Systems, 2005; Calinon et al. IEEE SMC 2007
How to Imitate? Imitator Demonstrator ? à à Find the closest solution according to some cost function http://lasa.epfl.ch
Statistical model of the data Key Idea: The world is uncertain; learn about its uncertainty through probabilistic modeling of information. K & & p x x , w N x x µ , ; , ( ) ( ) ∑ = Σ i i i i 1 = & Computing the variance provides crucial information x & { } var p x x | ( ) & { } E p x x | ( ) x The expectation gives a reference trajectory http://lasa.epfl.ch
Generalizing To generate new trajectories that depart from the reference trajectory while remaining within the total variance. & Computing the variance provides crucial information x x The variance à provides a notion of feasible space of solutions à is used to compute new path in the face of changes in the context http://lasa.epfl.ch
Generalizing − ) ) & & & H x x x & & & ( ) min H x x x Cost function ( ) = = − & & u.c. J x (inverse kinematics) θ = & x ) & & { } x E p x x | ( ) = x The variance à provides a notion of feasible space of solutions à is used to compute new path in the face of changes in the context http://lasa.epfl.ch
Generalizing − ) ) & & & H x x x & & & ( ) min H x x x Cost function ( ) = = − & & u.c. J x (inverse kinematics) θ = & x Impossible solution x The variance à provides a notion of feasible space of solutions à is used to compute new path in the face of changes in the context http://lasa.epfl.ch
Generalizing ) ) T & min H x 1 ( ) ( ) ( ( ) ( ) ) & & & & − & & H x x x x x x Cost function = − Σ − & & u.c. J x (inverse kinematics) θ = & x & & { } x var p x x | ( ) ( ) Σ = x The variance à provides a notion of feasible space of solutions à is used to compute new path in the face of changes in the context http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Grasping usually solved by searching for the optimal placement of fingers onto an object. http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Grasping usually solved by searching for the optimal placement of fingers onto an object. Knowing the extent to which one can adapt this grasp is useful for safe manipulation. Learn how comply with external perturbations while maintaining a firm grasp. http://lasa.epfl.ch Sauser, Argall and Billard, Autonomous Robots, 2012
Adap%ve ¡Grasping ¡ Teaching through tactile sensing http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Teaching through tactile sensing http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Learn a probabilistic mapping p , , s between contact ( ) φ θ signature of the object (normal force and tactile response ) s φ and fingers' posture . θ http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Learn a probabilistic mapping p , , s between contact ( ) φ θ signature of the object (normal force and tactile response ) s φ and fingers' posture . θ i { i i i } ° 47 Make N observations of the state of the system , s , , i 1... . N ξ = φ θ ∈ = K ( ) k k p = w N ; , : joint density (mixture of Gaussians) describing ( ) ∑ ξ ξ µ Σ k k 1 = the observations and the correlation across the variables o f the system. Can be used to predict the appropriate joint posture when perceiving a change in contact signature: ˆ ˆ E p { | , s } , s E p s { | , } ( ) ( ) θ = θ φ = θ φ http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ ˆ ˆ E p { | , s } , s E p s { | , } ( ) ( ) θ = θ φ = θ φ http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ After Training http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Another Example http://lasa.epfl.ch
Adap%ve ¡Grasping ¡ Another Example http://lasa.epfl.ch
Adap%ve ¡Manipula%on ¡ Teaching through teleoperation using Interface for direct joint motion transfer (Xsens motion sensors) Refining knowledge using tactile interface (5 touchpads mounted on robot’s arm and wrist)
Adap%ve ¡Manipula%on ¡ Reuse: To avoid re-learning a new task from scratch when the new task bears similarities with the old task http://lasa.epfl.ch
Adap%ve ¡Manipula%on ¡ Reuse preserves variability learned in the previous task. This may be a drawback à Use tactile feedback to adapt locally this variability After Reuse Before Reuse http://lasa.epfl.ch
Adap%ve ¡Manipula%on ¡ Reuse: One more example http://lasa.epfl.ch
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