1. Tactile perception Haptics

2. Haptic exploration by Lederman and Klatzky
In series experiments in the late 80’s Lederman and Klatzky studied haptic
Identification of objects and discovered that the hand movements employed by
their subjects were not random but could be divided into a small number of stereotypical movements which they termed Exploratory Procedures (EP). A small object will usually be first enclosed in the fingers and palm giving a broad range of object properties which, if not enough to identify straight away can be used to select subsequent procedures. For example, scissors would further be examined by attempting to use them, in this case by opening and closing the scissor blades. The principle exploratory procedures identified by L&K were:
- See more at: procedures/#sthash.qVu2vCW9.dpuf

3. Exploratory procedures

4. EP: Exploratory Procedures
EP: Lateral Motion Pressure Static Contact Unsupported Holding Principle Feature Identified: Texture Hardness Temperature Weight EP: Enclosure Contour Following Function Test Part Motion Test Principle Feature Identified: Global Shape & Volume Global Shape, Exact Shape Specific Function Mechanical Application, e.g. turning a handle - See more at: procedures/#sthash.qVu2vCW9.dpuf

5. Dynamic Touch
A related touch experience, though not directly an EP as far as I know, is called Dynamic Touch. Certain physical properties of an object can be discerned by moving it around and sensing its dynamic behaviour. For example, it is possible accurately determine the length of a uniform rod without vision by swinging it around from one end and perceiving the rotational inertia. - See more at: procedures/#sthash.qVu2vCW9.dpuf

6. EP,cont.
Final quip for this post, active touch demonstrates an exceptional ability to transcend the contact medium and extend perception beyond the corporal. If a tool is used to poke or prod it is the interaction between the tool and the object that is perceived, not the skin-tool interaction. Try it, pick up a pencil and explore the world with it, do you notice the contact between your fingers and the pencil where the forces are being sensed, or do you notice the contact between the pencil and other object where the forces are originating? - See more at: procedures/#sthash.qVu2vCW9.dpuf

7. The robotic implications
Bajcsy, R., Lederman, S.J., & Klatzky, R.L. (1987). Object exploration in one and two fingered robots.
Proceedings of the 1987 IEEE International Conference on
Robotics & Automation 3, New York: Computer Society Press.
The psychological studies imply that attributes such as hardness, surface texture, temperature, are acquired by a stereotypical hand movements.

8. One finger and two finger sensors
One finger scenario was investigated in P.Allen’s Ph.D dissertation 1985, where a combined vision and one finger tactile manipulator was able to discriminate surface, holes and cavities.
The two fingered scenario allows one to estimate the size of the object depending if the object can be enclose or not by the extend of the two fingers.
In addition the graspable object can be estimated for its weight.

9. Hand Dynamics, chapt. 6th Lagrange Equations with Constraints
A) find generalized coordinates which completely and minimally parametrize the configuration space of the system;
B) for Multifingered robot hand , the configuration of system depends on joint angles for the fingers and the position and orientation of the object;
C) they are not independent since their velocities are related by grasping constraints. We have configuration space
Q= {q[1],…..q[n]}

10. Pfaffian Constaints
A constraint on a mechanical system restricts the motion of the system, limiting the set of paths with the system can follow.
A simple example is the case of two particles {p[1],p[2]}attached to with a massless rod of length L. The constraint acts through the application of constraint forces which modify the Motion of the system. The constraint below is an example of holonomic constraint.
More generally a constraint is holonomic if it restricts the motion of the system to a smooth hypersurface in the unconstraint configuration space.

11. Holonomic Constraint ,cont.
It can be represented as an algebraic constraint on Configuration space:
H[i](q) =0 for i=1,…k
We assume that constraints are linearly independent

12. Holonomic define a smooth hypersurface
In the Configuration space, it is possible to eliminate the constraints by choosing a set of coordinates for this surface. These new coordinate parameters will be a linear combination of gradients of
The constraint function h[i]. If h represents the vector –valued constraint function, we can write the constraint force (GAMA)as shown below and Lambda is the vector of the relative magnitude of the Constrained forces

13. Constraint forces are normal to constraint surface
Now work is done by the constraint forces when the system moves along feasible trajectories.
The equation says that Gama (constrained force) dot product with
Velocity of joints is equal to zero. Hence no work!

14. Constraint during mutifingered GRASP
Here the allowable motions of the system are restricted by the velocity constraint
More generally the set of velocity constraints A(q), denoted by
A(q)q*=0. This type of constraint is called Pfaffian constraint. We assume that A(q) is a full rank .
q=(theta, x) where theta is the angle of joint of the hand/fingers and x is the local coordinate for the object position and orientation:

15. Constraint for multifingered hand, .
A(q) is matrix composed of the Jacobian Hand and the GRASP map.
Integrable Pfaffian constraint is equivalent to a holonomic constraint.

16. Lagrange Multipliers
Let L(q,dq/dt) represent lagrangian for unconstrained system and the constraint is represented by
A(q).dq/dt=0 equation (6.3)
A(q) is a matrix made of k rows representing forces and n columns representing degrees of freedom .
The dynamics then is equation (6.4)

17. Lagrange multipliers,cont
In the previous equation it is the standard Lagrange formulation of dynamic but added the constraint matrix transposed A(q) multiplied with lambdas ,called Lagrange multipliers which represent the magnitude of the constraint forces and Gama which represents (as before) the non conservative and externally applied forces.
The Lambda[i] s are determined by solving both equations (6.3) and (6.4).
In general each Lambda[i] will be a function of q,dq/dt, Gama.since constraint forces vary with configuration q, velocity dq/dt and exernal forces Gama.

20. Idealized planar pendulum

21. Dynamics of an idealized pendulum

22. The Unconstrained Lagrange formulation

23. Computing Lagrange multipliers

24. Tension
While we have one degree freedom system, we have two variables x ad y.

25. Lagrange-d’Alembert Formulation
We need to introduce Virtual displacement
If F is a generalized force applied to the system,
then we call Virtual Work
D’Alambert principle state that forces of constraint do NO Virtual Work, hence (Delta q is not equivalent to dq/dt!). The generalized velocity dq/dt satisfies both the velocity constraints and the equations of motion, while virtual displacement satisfies only
the constraints.

26. Motion equation projected into A(q) subspace
Then we get the motion equation with virtual displacement
We call the equations (6.7) and (6.8) as Lagrange-D’Alembert equation

27. Dynamics of a Rolling Disk

28. The configuration of the disk is given by xy position in the..

29. Kinetic energy-Lagrangian and Langrange-D’Alambert equations