Claims:We claim:
1. A system for providing rapidness and precision in control of robotic structure by obtaining the optimum inverse kinematic solution through training of Artificial Neuro-Fuzzy Inference System (ANFIS) network with reduced data set, said system (S) comprising of at least one robotic structure (100), at least one capturing unit (110), at least one actuating unit (120), at least one control unit (200) and at least one training unit (300),
wherein
- said robotic structure(100) comprises of
? Origin (O) at the proximal end, at least one End Effector Unit (EEU) at the distal end,
? at least three segments (S1,S2,S3…. Sn) being deployed between said Origin (O) and said End Effector Unit (EEU) through corresponding Joint members (J1, J2, J3, J4… Jn)
- said capturing unit (110) comprises of at least one input device for capturing data including data pertaining to Origin, target position (X,Y,Z), mechanical constraints of arms and work-space constraints.
- said control unit (200) comprises of at least one memory unit (210) coupled to processor unit (240), said memory unit (210) comprises of at least one Geometric Module (212) capable of obtaining orientations ((?1,?2) of proximal joint members(J1, J2) as well as distance of target position from origin, at least one capturing module (211) for storing inputs from the capturing unit (110) and at least one data module (214) for storing trained Artificial Neuro Fuzzy Inference System (ANFIS) networks being capable of obtaining the orientation of said distal joint members (J2,J3 and J4) using said distance of target position from the origin, at least one storage module (213) for storing the computed orientation of proximal member (J1), at least one module_D (215) to obtain precise orientation (?1, ?2+??2,?3,?4) of said joint members (J1,J2,J3,J4), and communicating it to said actuating unit (120),
- said training unit (300) comprises of at least one predetermined data module (310) for storing predetermined reference information (PRI), at least one training data generator (320), at least one data storage unit (330), and at least one ANFIS training Module (340), wherein said End Effector unit (EEU) is constrained to move in predetermined straight line motion in a manner that said training data generator is capable of obtaining the reduced data {DS} in said data storage unit (330) by communicating with said actuating unit (110), capturing unit (120) and said PRI module (310),
wherein said ANFIS training module (340) is capable of training at least three ANFIS network (AN1,AN2,AN3) with the help of said reduced data set {D} and thereafter deploying said trained ANFIS networks in said data module (214) of said control unit (200).

2. The system for providing rapidness and precision in control of robotic structure by obtaining the optimum inverse kinematic solution through training of Artificial Neuro-Fuzzy Inference System (ANFIS) network with reduced data set as claimed in claim 1 wherein said predetermined reference information (PRI) comprising of information selected individually or in combination from robotic structure type, origin information, number of joint members, number of segments of robotic structure, length and width parameter of segments, mechanical constraints of robotic structure and work constraint of application.

3. The system for providing rapidness and precision in the control of robotic structure by obtaining optimum inverse kinematic solution through training of Artificial Neuro-Fuzzy Inference System (ANFIS) network with reduced data set as claimed in claim 1, wherein axes of rotations of Joint members (J1 and J2) are orthogonal to each other.

4. A method for providing rapidness and precision in the control of the robotic structure by obtaining optimum inverse kinematic solution through training of ANFIS network with reduced data, said method comprising of training phase and control phase,
wherein
said training phase comprises the steps of :
- extracting the information including information of Origin (O), the type of robotic structure (100), joint member (J1,J2,J3) mechanical constraint of robotic structure (100) and work constraints of application and user’s choice of right or left handedness from the PRI module (310), [1101]
- setting the orientation of at least one proximal member (J1) to any arbitrary orientation from said origin (O) in a manner that said joint member (J1) facilitates the radial motion of said robotic structure (100), [1102]
- identifying set of angles (?2,?3,?4) for said facilitation of radially outward or inward motion of said robotic structure (100) while retaining the orientation of said joint member (J1) to angle (?1 ), [1103]
- computing End effector unit (EEU) positions by applying said set of angles on said robotic structure (100) in a manner that the End Effector unit (EEU) of robotic structure move in straight line motion by using actuating unit (120) and capturing unit (110) [1104],
- converting computed EEU positions data set D{(X,Y,Z)} into distances(L) from origin (O), [1105],
- generating reduced data set {L, ( ??2,;?3;?4)} by pairing the computed distance with respected orientation of each joint member (L, ??2), (L, ?3), (L, ?4) [1106],
- training of at least three ANFIS networks (AN1, AN2, AN3) by ANFIS training system with corresponding reduced data set (L, ??2), (L, ?3), (L, ?4) [1107],
- deploying the trained ANFIS network (AN1, AN2, AN3) in the module (214) of control unit (200), [1108],
said control phase comprising a steps of
- capturing of target position (X) by at least one capturing unit (110), [1201]
? storing said target position (X,Y,Z) in capturing module (211), [1202]
? storing mechanical constraint of robotic structure (100), work constraints of work application and origin (0) extracted from PRI module in capturing module(211), [1203]
? computing the orientation (?1, ?2) of said proximal joint member (J1, J2) in GM (212) on the basis of target position (X) and extracted information from said PRI module (310), [1204]
? storing said computed proximal joint member orientations (J1,J2) in storage module (213), [1205]
? computing distance of said target position (X) from Origin (O) in GM module (221) (1206) and inputting it to a data module (214), [1206]
? computing the precise orientation ((??2,?3,?4)) of said distal members (J2, J3 and J4) by the trained ANFIS networks being deployed in data module (224) using said computed distance as input, [1207]
? retrieving the computed orientation (?1, ?2) of said proximal joint members (J1, J2) from said stored module (213) as well said computed orientation of the distal joint member (J2,J3,J4) from said data module (214) in Module_D to obtain the precise orientation (?1, ?2 +??2, ?3, ?4) of said joint members and thereafter communicating it to said actuating unit (120), [1208].
5. A method for providing rapidness and precision in the control of robotic structure by obtaining the optimum inverse kinematic solution through training of ANFIS network with reduced data as claimed in claim 4 wherein said positions of the EEU are computed by applying forward kinematics on said sets of Joint angles.
, Description:FIELD OF THE INVENTION:
The present invention relates to the system and method for providing rapidness and precision in the control of robotic structure. More particularly the invention relates to a system and method for providing rapidness and precision in the control of robotic structure by obtaining the optimum inverse kinematic solution through training of Adaptive Neuro-Fuzzy Inference System (ANFIS) networks with reduced data set.

BACKGROUND OF THE INVENTION:
The advancement in the capabilities of the robotic machines in the last three decades is largely attributed to the continuous ongoing research and new innovations in the field of computational engineering, mechanical engineering and electrical engineering.

Robotics word is derived from the Slavic word “Robota” which means “to do labor”. As suggested by its meaning, the reasons for using robotic machines are immense, for instance they are ideal for carrying out jobs which are repetitive and require precise movements. They are also suitable for handling the products which can be damaged by human presence or for performing tasks which requires enormous physical efforts. Further the robotic machines are also useful for carrying out scientific research in an environment or regions which are inaccessible to human beings, such as outer space or environments with extreme weather conditions.

The robotic machines can be classified in many ways. One way of classifying robotic machines is the type of applications for which they are designed. For example in households, the robotic machines may be designed for use as vacuum cleaner or surveillance robots while industrial robotic machines are mostly used as articulated arm whose purpose is to perform spraying, welding, picking etc.

The robotic machine generally comprises of a programmable mechanical structure which is constructed by connecting different joints together with rigid segments. The mechanical structure has end-effector unit at its terminal end which can be configured to perform varied activities as per the nature of an application.

Robotic kinematics is the analytic study of robotic motion of robotic machine and a very important field of research. This analytical study examines the relationship between the position, velocity and acceleration of the joint members of a robotic structure. The robotic kinematics can be divided into Forward Kinematics (FK) and Inverse Kinematics (IK). In the FK the end-effector displacements and orientations are determined on the basis of joint member orientation and displacement. Conversely in the IK the orientation and displacement of the joint members are computed on the basis of the orientation and displacement of the end-effector unit.

Since the FK always has a definite solution for the robotic machine so it is straight forward and there are no complexities involves in it. In contrast, the IK provides infinite solutions for the robotic manipulator; and finding its optimum solution is computational heavy and time consuming tasks.

However, practically the IK model is more important than the FK model because any manipulation task is always described in term of position of target points and orientation of the end-effector unit rather than in the form of joint member orientation and displacement.

Several mathematical models such as iterative, geometric and algebraic methods have been reported in the prior art for finding the solution of IK model. These traditional methods are quite effective when the robotic structure is simple i.e. limited to two or three joints. However due to their inherent mathematical nature these methods become inefficient and slow as the robotic structure becomes complex.

In order to overcome the drawbacks associated with the mathematical models in solving IK problem for the complex robotic structure ANFIS based model has also been reported in various research papers. In comparison to traditional mathematical models the ANFIS based models are limited in term of mathematical representation and have ability to learn from the training data. One example of such ANFIS based model is disclosed by the research paper titled “ANFIS implementation for Robotic manipulator” which was published in the IJERT on June 2012. Another research paper “Solution of inverse Kinematic for SCARA manipulator using ANFIS network” published in IJSC on November 2011 also discloses ANFIS based solution to the IK problem.

The training data for the ANFIS model is based on the target points i.e. coordinates of the target points. The forward kinematic relations are used for obtaining the data for the training of the ANFIS network. The drawback of this type of target point based training is that it demands huge sets of data and therefore very time consuming. In addition it is also not very precise in positioning.

Hence in view of above there is still a scope for a system and method which is capable of providing training to the ANFIS model in a manner which is rapid, more efficient and precise in its positioning.
OBJECT AND SUMMARY OF THE INVENTION:
In order to overcome the drawbacks in the prior art the main object of the present invention is to provide a system capable of rapid and precise control of robotic structure and method for providing rapidness and precision in the control of said robotic structure.

Another object of the present invention is to provide a system and method capable of providing rapidness and precision in the control of robotic structure by employing a combination of geometric approach and Adaptive Neuro-Fuzzy Inference system (ANFIS) in which orientation of joints of robotic structure are partly computed by geometric method and partly computed by training of ANFIS networks.

Yet another object of the present invention is to provide a system and method which is capable of providing rapidness and precision in the control of robotic structure by obtaining optimum Inverse Kinematic solution at higher speed by training the ANFIS system through reduced data which is formed by pairing End Effector Unit (EEU) positional distances from the origin with the respected orientation of joint member.

Yet another object of the present invention is to provide a system and method which can provide right and left handedness to the robotic structure.

Accordingly the present invention relates to a system and method for providing rapidness and precision in control of robotic structure by obtaining the optimum inverse kinematic solution through training of Artificial Neuro-Fuzzy Inference System (ANFIS) network with reduced data sets. The system comprises of at least one robotic structure, at least one capturing unit, at least one actuating unit, at least one control unit and at least one training unit. The robotic structure comprises of Origin at the proximal end, at least three Joint members, at least one End Effector Unit at the distal end, at least 3 segments and at least one capturing unit. Said three segments are deployed between the Origin and the End Effector Unit (EEU) through corresponding Joint members. The capturing unit comprises of at least one input device for capturing data including data pertaining to Origin, target position, mechanical constraints of arms and work-space constraints. The control unit comprises of at least one memory unit coupled to processor unit. The memory unit comprises of at least one Geometric Module, at least one capturing module, at least one storage module and a module_D. The Geometric Module is capable of obtaining orientations of proximal joint members as well as distance of target position from origin. The capturing module is capable of storing inputs from the capturing unit. The data module is capable of storing a trained Artificial Neuro Fuzzy Inference System (ANFIS) which is capable of obtaining the orientation of the distal joint members using the distance of target position from the origin. The function of the storage module is to store the computed orientation of proximal member. The function of the module_D is to obtain precise orientation (?1, ?2+??2, ?3, ?4) of the Joint members (J1, J2, J3 and J4), and then communicating it to the actuating unit. The training unit comprises of at least one predetermined data module for storing predetermined reference information, at least one training data generator, at least one data storage unit, and at least one ANFIS training Module.

The EEU of the robotic structure is constrained to move in predetermined straight line motion in a manner that the training data generator is capable of obtaining the reduced data {DS} in the data storage unit by communicating with the actuating unit, capturing unit and the PRI module. The ANFIS training module is capable of training at least three ANFIS network with the help of the reduced data set {DS} and thereafter deploying the trained ANFIS networks in the data module of the control unit.

BRIEF DESCRIPITION OF DRAWINGS:
Fig 1 illustrates the overview of the system for providing the rapidness and precision in the control of robotic structure.
Fig 2 depicts the overview of the training unit and the control unit of the system.
Fig 3 depicts the method for obtaining the reduced data set in the training unit.
Fig. 4 depicts the method for controlling the robotic structure with the trained ANFIS system.
Fig 5 illustrates the one example of robotic structure.
Fig 6 illustrates the six DOF robotic arms in Cartesian coordinate system.
Fig 7 illustrates the conventional ANFIS training results in tabulated form.
Fig 8 illustrates the comparison of the conventional ANFIS training results with the standard ANFIS IK solution.
Fig 9 illustrates the training results of the ANFIS system employed by the present invention in the tabulated form.
Fig. 10 illustrates the comparison of the present system ANFIS training results with the standard ANFIS IK solution.

DETAIL DESCRIPTION OF THE INVENTION WITH DRAWINGS AND ILLUSTRATIONS:
The present invention relates to a system and method for providing rapidness and precision in the control of complex structure of robots. More particularly the invention relates to the system and method for providing rapidness and precision in the control of robotic structure by obtaining the optimum inverse kinematic solution through training of ANFIS networks with reduced data set.

The system primarily works in two phases namely training phase and control phase. In the training phase the system generates the reduced data sets and trains the ANFIS networks by utilizing the generated reduced data set. In the control phase the system controls the robotic structure using the trained ANFIS network systems and geometrical module.

Unlike the prior art system where the target points for robotic structure are identified by employing either geometric approach or by employing ANFIS networks, the system and method of the present invention employs a combination of geometric approach and ANFIS training approach.

The ANFIS training based on target points is computationally heavy and less accurate for off grid positions. The present system overcomes these drawbacks in the state of art system by providing the training to the ANFIS network using the length of arm i.e. the distance of the target point from the reference point or predetermined origin. This method drastically reduces the computational complexities and is accurate even in off grid positions. Further the present system is also capable of imparting the left handedness or right handedness to the robotic structure which is lacking in the current state of art.

The term “predetermined reference information” (PRI) in the specification means information pertaining to the mechanical constraints, work constraint fed by the user. Additionally it may also include the information pertaining to the number of joints, type of joints, length and width of segments.

The term “mechanical constraints” in the specification refers to those constraints which are imposed by the joint members, segments with regard to their capacity in carrying out any application. More specifically mechanical constraints refer to the extent to which each joint can move in its own degree of freedom. This can vary as per mechanical structure of robotic arm. For example human elbow cannot rotate more than 1800. Mechanical constraints are predefined as per the structure of robotic arm or robotic structure.

The term “work constraints” refers to those constraints which are imposed by permanent obstacle in the working environment. More specifically the work constraints are those static and permanent obstacles which restricts the movement of the arm or robotic structure in the fixed workspace. The “work constraint” information in the form of limits on joint angles may be fed by user directly (pre-determined) or may be captured by actuating unit with appropriate image processing algorithm.

Fig 1 illustrates the schematic diagram of a system. As shown in Fig. 1 the system (S) comprises of at least one robotic structure (100), at least one actuating unit (120), at least one capturing unit (110), at least one control unit (200) unit and at least one training unit (300).

The robotic structure (100) comprises of at least one Origin (O) at proximal end, at least one end-effector unit (EEU) at distal end and at least three segments (S1, S2, S3,…SN) with corresponding joint members (J1,J2,J3). The segments (S1, S2, S3, SN ) are deployed between the origin point (O) and End-Effector Unit (EEU) and are interconnected to each other.

The Origin (O) may be fixed on to the platform or supporting structure (P) which may be movable or fixed at one place.

Fig 1 illustrates serial connected robotic structure or manipulator (100). However, robotic structure may be parallel connected or combination of serial –parallel combination.

The capturing unit (110) may be any input device such as camera or sensor unit which is capable of capturing the EEU positions with in working area of the system. In Fig 1, the capturing unit (110) is deployed at remote location from the robotic structure (100) or on to the platform (P) of the robotic structure (100). However the capturing unit (110) may be deployed on the End-Effector Unit (EEU). The actuating unit (120) of the present system may be servomotors being deployed on the robotic structure (100) for actuating its joint members (J1, J2 and J3).

Fig. 2 illustrates the control system (200) and training unit (300) in details. As shown in Fig. 2 the training unit (300) comprises of at least one predetermined data module (310), at least one training data generator (320) for generating reduced data set {DS}, at least one data storage unit (330) for storing the reduced data set {DS} and at least one ANFIS training Module (340) for training at least three ANFIS networks (AN1, AN2, AN3).

The control unit comprises of at least one memory unit (210) coupled with at least one processing unit (240). The memory unit (210) comprises of least one Geometric Module (212), at least one capturing module (211) for storing inputs from capturing unit (110), at least one storing module (213) for storing outputs of GM modules, at least one data module (214) for storing trained ANFIS networks (AN1, AN2, AN3), and module_D (215) for retrieving the net orientation of joint member computed by GM (212) and ANFIS networks and communicating it to the actuating unit (120).

As shown in Fig.2 the function of the training data generator (320) of training unit (300) is to generate the reduced data set {DS} and then is to store the generated reduced data set {DS} in the data storage unit.

The training data generator (320) performs this function by extracting predetermined information from PRI module (310) and by communicating with actuating unit (120) and capturing unit (110). The extracted predetermined information from PRI may comprise of right and left handedness of the robotic structure and other definition such as predetermined set of joint angles of work constraints chosen by user. In order to generate the reduced data set, the training generator needs to acquire the set of positions of End Effector Unit (EEU) for the predetermined specific joint angles in a manner that constraints the robotic structure to move in straight line motion.
The training data generator (320) may acquire these positions by using forward kinematics model of robot (less precise) or by communicating with actuating unit and capturing unit in real time (more precise). Once the data is acquired by training generator in (x,y,z) coordinates then it is converted into the lengths from origin to generate the reduced data set {DS}. The obtained reduced data set {DS} is then stored into the data storage unit (330).
The tasks of ANFIS training module (340) are to train at least three ANFIS network (AN1, AN2 and AN3) with the help of reduced data {DS} stored in data storage unit (330) and to deploy the trained ANFIS networks in the data module (214) of the control unit (200) for the control operation.

During the control operation, the control unit (200) computes the precise orientation of the robotic structure (100) by using the GM (212) and the trained ANFIS networks (AN1, AN2, AN3).

As shown in Fig. 2, the GM (212) is deployed in control unit (200) for performing mainly two functions on the basis of the target positions and captured information stored in the module (211). Firstly computing the orientations (?1, ?2) of the proximal joint members (J1, J2) and then storing them into the module (213). Secondly computing the distances of target points from the origin point and then inputting them into the storing module (214).

The function of the trained ANFIS networks which are being deployed in the module (214) is to compute the orientation of the distal joint members (J2, J3, J4) i.e. (?2, ?3, ?4) using calculated length as input from GM (212) and then outputting them to the module_D (215). The module_D (215) is configured to retrieve the orientation of proximal joint members (J1, J2) from the storing module (213) as well as the orientation of distal joint member from the Module (214) and then pairing the computed orientation of distal and proximal members (?1, ?2 +??2, ?3, ?4) and thereafter communicating it to the actuating unit (120) for joints members actuation.

Fig. 3 and Fig 4 provide the flow chart depicting the method involves in the rapidness and precision in the control of robotic structures. The method comprises of two phases namely training phase and control phase. Fig 3 illustrates the training phase of the present system while Fig. 4 depicts the control phase in detail. The training phase is one time process.

As shown in Fig 3, the training phase initiates with the extractions of predetermined parameters from the PRI module (310) in the step (1101). The extracted information from the PRI module includes origin (O) information, type of robotic structure, joint member information, and mechanical constraints of robotic structure and user’s choice of right or left handedness which is based on work constraints.

After that in the step (1102) the orientation of proximal joint member (J1) is set to the arbitrary angle (?1). Fixing the orientation of proximal joint member (J1) enables the radial motion of the robotic structure (100).

In the step (1103) the robotic structure (100) is provided with the radially outward or inward motion in order to identify the sets of angles (?2, ?3, ?4). During this step the orientation of the joint member (J1) is retained to value (?1).

In the step (1104), EEU positions are obtained by applying the sets of angle on the system (100) using the actuating unit (more accurate) or by applying the forward kinematics on the sets of identified angles (?2, ?3, ?4 (less accurate). In this step (1104) the sets of predetermined angles are applied on the joints members (J1, J2, J3 and J4) of robotic structure (100) in a manner that results in the straight line motion of robotic structure.

In the step (1105) the captured end positions of the EEU are converted into the distances from the origins {L}. In the next step (1106) reduced data set {DS} is generated by forming a pair of computed distances of end effector position (EEU) with respected orientation of each joint angles member ({L, ??2} , { L, ?3 }, { L ,?4} ).

Further in the step (1107), ANFIS training system (340) trains at least three ANFIS network (AN1, AN2, AN3) with corresponding data set {L, ??2}, {L, ?3}, {L, ?4}. In the subsequent step (1108), the trained ANFIS networks (AN1, AN2 and AN3) are deployed into the data module (214) of the control unit (200) for the control phase.

As shown in Fig. 4, the control phase initiates with steps (1201) and (1202) in which the capturing unit (110) captures at least one target point (X) and stores it in the module (211).

In the next step (1203), the orientations of the proximal joint member (J1) and (J2) are computed in the Geometric module (GM) (212) and are stored in the module (213).

Further in the next step (1205), GM (212) computes the distances or length of the target position from the origin point (X) and sends it as input to the module (213). In the following step (1206) the trained ANFIS networks deployed in the data module (214) obtain the precise orientation of the distal joint members (J2, J3 and J4) on the basis of computed distances of target from the origin.

In the next step (1207) the precise orientation () of all joint members are retrieved in the module D (215) and thereafter are communicated to the actuating unit (120) for the control of robotic structure (100).

The advantages of the method and system disclosed by the present invention can be understood by the following example:

EXAMPLE:
As mentioned earlier the precision and rapidness of robotics system depends upon the manner in which it computes the joint angle while solving Inverse Kinematics equation. In the current state of art if manufacturer wishes to train the artificial right arm then manufacturer constraints the movements of the arm both in the mechanical movement and also in the calculation of joint angles while solving inverse kinematics which is a costly and complicated approach. In contrast to it the present invention adopts a methodology in which there is no need to constrain the motions of arm by the manufacturer to obtain the solution of Inverse Kinematics; instead the control unit of the system naturally provides all joint angles which are feasible for the right handed motion. This can be been achieved by the present invention in the following manner.

The manufacturer feeds the restrictions of the joint movements of robotic right arm in PRI unit in terms of min and maximum degrees of rotations of each servo motor as work constraints (following sign standards for right handed coordinate system). For instance consider that the right handed coordinate system is attached to base joint (J0) as shown in Figure 4. To obtain the right handedness manufacture can provide the restriction in the movement of the joint angles as positive angles J1 (0-900), J2 (0 -900), J3 (0 - 1200), where as for left handedness restrictions need to be written with negative sign.

Now given the minimum and maximum angles for base joint J1 and joint J2 (axes of J1 and J2 should be orthogonal to each other) the training generator sweeps the angles of Joints (J2, J3 and J4) from minimum to maximum limits to create a set of joint angles. The training generator also simultaneously applies these created set of joint angles to respective joints and computes the positions of End Effector Unit (EEU). The training generator applies the sweep of angle over the joints (J1, J2 and J3) of robotic arms in a manner that it results in straight line motion of robotic arm or structure. If any obstacle is detected in this line of movement, then the base angle (?1) is incremented and the aforementioned process with identical set of angles for joints (J1, J2 and J3) is repeated again from the beginning. This iteration of movements can be avoided by user if the user manually feeds the appropriate work constraints (suitable angle of the joints J1 and J2) so that the movement of arm or structure is not restricted to move straight in motion.

The advantage of moving the robotic arm or structure (EEU of robotic structure) in straight line lies in the fact that the relationship between the end effector positions to the joint angles in straight line motion is more obvious than in any other arbitrary motion of robotic arm. The proportionality in the increment of a joint angle to increment in distance from origin helps ANFIS to quickly converge to appropriate gain. “n” number of such individual proportional gains (via “n” ANFIS networks) between angels of “n” joints and end effector positions could be achieved precisely and quickly by training with significantly less number of samples (in the experiment described below, there were altogether 100 such points). The proportionality gains shown by these ANFIS networks is equally valid even for off trained positions as they also lie on the same straight line. That is why straight line motion in training ANFIS is the main requirement to reduce computational complexity and improve performance.
Fig 4 and Fig 5 provide the example of implementation of system on the 6 Degree of Freedom (DOF) arm. Fig 4 shows the actual six DOF robotic structure while Fig 5 shows the 6 DOF robotic structure in the Cartesian space.
As shown in Fig 4 the robotic arm or structure comprises of 3 links or segments and 4 joints (J0, J1, J2, and J3). The length of segment 1 between J1 and J2, segment 2 between J2 and J3 is 10 cm while the length of the segment 3 which lies between end effector and J3 is 4 cm. The robotic arm or robotic structure is constrained to move through the predefined path first by using conventional ANFIS IK solution and then by using the ANFIS IK solution of the present invention. For the sake of simplicity the predefined path is chosen in a manner that the orientation of joint (J0) can be kept at a constant angle.

Conventional ANFIS IK method:
Four ANFIS networks have been trained where training data comprises of all the possible positions in the reachable set of robotic arm or structure at a resolution of 1 cm and corresponding joint angles (?0, ?1, ?2, ?3).

Total 8192 data pairs are formulated where reference output set is { ?(j)} and input set is {x(i),y(i),z(i)}, i varies from 1 to 8192. Four ANFIS networks corresponding to each joint angle (j = 0 to 3) are trained. Fig 7 shows the table which depicts the ANFIS training result. The IK solutions obtained from conventional mathematical expressions (standard IK solution) and the IK solution obtained from the trained ANFIS are compared and errors are plotted in Figure 8. The result shows that on an average the error for (?1, ?2 and ?3) are 0.2, 0.01 and 0.4 radians respectively. As the path of robotic arm is chosen in a manner that the Joint angle (?0) is constant, therefore only three errors have been shown along the path.

The ANFIS IK method of the present invention:
On similar grounds the method of the present invention is tested. In this method only 3 ANFIS networks (AN1, AN2 and AN3) corresponding to each Joints (J1, J2 and J3) are necessary. The Joint angles (?0 and ?1) are obtained using formulas presented for given position. The training data is obtained by moving end effector of arm along Z axis from top to bottom towards J0. The maximum length of arm or robotic structure is 24 cm.

The ANFIS training results of the present invention are tabulated in table as shown in Fig 9. The table shows a drastic improvement in training time. The ANFIS networks are less complex, more accurate and with less number of data pairs.

Fig 10 shows the comparison of the ANFIS training results with the standard IK solution for predefined path. The result shows that the average error for all joint angles (?1, ?2, ?3) corresponding to Joints (J1, J2 and J3) are less than 0.02cm i.e. 20mm. For the joint J0 the error is zero as it is formulated using standard IK formula itself.