Design and Implementation of an Adaptive Control for a Robot

Abstract: This research investigates the performance of an adaptive controller for five-bar linkage robot. The proposed controller was entirely independent on the physical specifications of the robot. The controller was examined as the dynamics of the mechanical system varies for various environment conditions, which make it an ambiguous system. In this study, the introduced controller was designed based on the governing ideal Euler-Lagrange equations on the robot but assessed using the on-line dynamic simulation of the mechanism for different target configurations which guarantees the high performance and effectiveness of the designed controller.


INTRODUCTION
Self tuning controller should be very convenient way for nonlinear system such as robot manipulator. There are many references in this regard [1][2][3][4][5][6][7][8][9][10] . In our study, we proposed an adaptive controller which entirely independent of physical aspects of Manipulator such as center of mass, size and more importantly load variations. Also, the effectiveness of proposed method is investigated to overcome the sever nonlinearity of Robot dynamic problems. Although the results are not extensive, yet they can be used to establish some investigations related to the design of adaptive controller for a robot.

Dynamics of five-bar linkage:
Consider the manipulator shown in Fig. 1. It is clear from the figure that even though there are four links being moved, there are in fact only two degrees-of-freedom, identified as 1 ϕ and 2 ϕ . As the mechanism is a closed kinematics chain, Jacobian matrices are employed to work out the dynamic equations of the mechanism. The coordinates of the centers of mass of four links as a function of the generalized coordinates are calculated as follows [3] : By differentiating equations (1) The inertia matrix is given by Substituting equation (5) into (6), we obtain If the following simplification is assumed Based on Euler-Lagrange equation, the dynamic system of five-bar linkage robot can be represented as follow: Space-state model of equation (10) is expressed by which will be used to design the adaptive controller.
Design of adaptive controller: The dynamic system of the robot can be represented by two identical SISO models hence it is sufficient to design an adaptive controller.
Theorem: Control input and adaptive laws (13) will guarantee the stability of assumed SISO model (12).
Simplifying and rewriting (16), it can be shown that which can be reduced to As this expression holds true, the stability of the SISO model (12) with the given adaptive laws and control input (13) will be assured.

RESULTS
The CAD model of a real five-bar linkage robot was designed using Solidworks ® which is used for manufacturing and translation into SimMechanics ® . Figure 2 and 3 depict SimMechanics and the manufactured models respectively.
The proposed realistic and practical SimMechanics model is further employed to simulate the designed controller which is implemented using Simulink. The complete model of the system with random input is illustrated in Fig. 4.
Simulation results are shown for a desired configuration of 1 30 ϕ = o and 2 10 ϕ = − o in Fig. 5. Figure 6 demonstrates the target tracking capability of the proposed system for random inputs. From Fig. 6 it can be easily realized that tracking error is infinitesimal which assures high performance of the designed controller.

CONCLUSION
In this study the performance of an adaptive controller for five-bar linkage robot was investigated. The proposed controller is entirely independent on the physical specifications of the robot. Also, the stability of the proposed controller was verified. Simulation results have shown effectiveness of his controller. One of the most interesting things of this controller is that it is independent of the robot specifications in a wide range of variations as well as unstructured environment. IN the future we will implement the proposed method using HIL methods, i.e., XPC® target and RTWINT® toolboxes. Also it is extended to the third joint.