A ChebyShev-based computational method for the dynamic analysis of robotic manipulators
The objective of this study is to develop and evaluate a procedure based on ChebyShev Polynomial expansion for the inverse dynamics of robotic manipulators. This approach was consisted of the following procedure and methodology as implemented for this purpose: Formulation of equations to calculate the torques of the joints of a robotics manipulator, using conventional methods of mechanics of robotics manipulators. A computer program in C language was developed to calculate the torques and the computer time, CPU, to compute these torques. Using the ChebyShev Polynomials ( CSP) methods, an algorithm was developed to calculate the coefficients by introducing the torques’ equations appropriately into the CSP, and then, using these coefficients, an approximation technique algorithm was also developed. Based on these algorithms a computer program in C language was developed to calculate the torques using CSP approximation and interpolation ( CSPAIM ) methods. CPU Time was also calculated, by the provisions into the computer program, taken by the computer to calculate these values. The CPU times taken by the conventional mechanics equations for the torques and by the CSP approximation methodology were compared and evaluated for time optimization and accuracy at different values of the degree of CSP and subintervals between the intervals determined by velocities in radians. It has been found that the ChebyShev Polynomial Approximation formula has been very effective not only to calculate values with minimum error, but also it is very time efficient as much as sixteen times as compared to the conventional methods. Hence, we can efficiently use CSP approximation methodology to calculate torques at the joints of a robotics manipulator up to a certain degree of accuracy, and we can also obtain time reduction in the computer calculation process, by the application of ChebyShev Polynomial Approximation Methodology.