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Adaptive Control System for a Robotic Arm

(check back for videos and more schematics)

(This was an undergrad project, done in the pre-inect era!

The project aims to capture human arm motion and translate this motion into correspondingmovement of the robotic arm, to be used as a manipulator for interaction with the environment.

Here, the human arm motion is estimated from the positioning of the palm which then controlsthe end effector of the robotic arm. The intermediate system consisting of the other links of the

robotic arm is controlled using inverse kinematics with the help of Neuro!u""y hybrid system.The concept is divided into two aspects#

$)%mage &rocessing to capture human arm motion

')%nverse inematics to move obotic *rm

A "ew Concepts#

$ahalanobis %istance#

+onsider the problem of estimating the probability that a test point in Ndimensional uclideanspace belongs to a set, where we are given sample points that definitely belong to that set. -ur

first step would be to find the average or center of mass of the sample points. %ntuitively, the

closer the point in uestion is to this center of mass, the more likely it is to belong to the set.However, we also need to know if the set is spread out over a large range or a small range, so

that we can decide whether a given distance from the center is noteworthy or not. The simplistic

approach is to estimate the standard deviation of the distances of the sample points from the

center of mass. %f the distance between the test point and the center of mass is less than onestandard deviation, then we might conclude that it is highly probable that the test point belongs

to the set. The further away it is, the more likely that the test point should not be classified as

 belonging to the set.This intuitive approach can be made uantitative by defining the normali"ed distance between

the test point and the set to be . /y plugging this into the normal distribution we can derive the

 probability of the test point belonging to the set.The drawback of the above approach was that we assumed that the sample points are distributed

about the center of mass in a spherical manner. 0ere the distribution to be decidedly non

spherical, for instance ellipsoidal, then we would e1pect the probability of the test point

 belonging to the set to depend not only on the distance from the center of mass, but also on the

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direction. %n those directions where the ellipsoid has a short a1is the test point must be closer,

while in those where the a1is is long the test point can be further away from the center.&utting this on a mathematical basis, the ellipsoid that best represents the set2s probability

distribution can be estimated by building the covariance matri1 of the samples. The 3ahalanobis

distance is simply the distance of the test point from the center of mass divided by the width of

the ellipsoid in the direction of the test point.!ormally, the 3ahalanobis distance of a multivariate vector from a group of values with mean

and covariance matri1 4 is defined as#

&nitial Conditions and Assumptions#

The screen and camera position at the user would be arranged as depicted in the picture below#

4ince the 4kin 4egmentation Techniue may identify both the hand and the face, the camera is positioned to focus on the lower region of the body i.e neckdown. 4ince this position and

location of the camera are fi1ed, the input video stream will have a constant background therebymaking the use of background subtraction a viable option.

&mage 'rocessing to capture human arm motion 

ac)ground Subtraction and S)in Colour Segmentation

fig$ fig'fig5

%n order to reduce the region of interest, the static background is eliminated using background

subtraction.

* set of background images are normalised and the variace and mean are computed. verysubseuent test frame which is obtained is then compared with the background image set, with

the regions of high variance being retained while the others are removed. The subseuent image

obtained (fig$) is then converted to the 6+b+r colour space and used to calculate themahalanobis distance with respect to the sampleset obtained from the skin samples made

available in the previous steps.

The hand contour , thus, e1tracted in form of a binary image(fig'). The image is then subject to a

series of morphological operations to eliminate noise(fig5) if any and create a much moreconcrete hand shape. Then simple heuristics are used to obtain features such as fingertips,palm

centroid and boundary region.The segmented image i.e rather only the boundary of interest is

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 plotted along with the fingers marked with red circles. (*s shown in the image below, however

the te1t here is added in &icasa ). The algorithm works well in illuminated areas and gives

satifactory results in dimly lit areas(if the background isnt too similar to skin shade.)

fig 7. This is the gui. Here only the region of the palm above the centroid is displayed. Nounnecessary region boundaries are reuired. (% added the profiles section after getting fedup of

constantly taking skin samples for every run. *lso the te1t (eg.thumb etc)was added in picasa. %

had to brighten the image cause the red markings on the fingers werent visible in the image. The

fingers are detected by the algorithm.)

 Now that the fingers and palm is detected this information is sent to the 8ucas anade optical

flow algorithm in order to track the palm.

(n1t update will include# use of lucas kanade 9 palm rotation:arm depth control9anfis)