Trajectory planning for energy minimization of industry robotic manipulators using the Lagrange interpolation method

We propose to use Lagrange interpolation method to express each joint trajectory function to realize trajectory planning for energy minimization of industrial robotic manipulators. We give the position constraints to the industrial robotic manipulators and the stability of the industrial robotic manipulators should be satisfied. In order to avoid Runge's phenomenon of Lagrange interpolation method, we use the Chebyshev interpolation points for our approach. Through derivation, the angular velocity functions and angular acceleration functions can be obtained. Lagrange interpolation method can satisfy position constraints, and ensure the smoothness of joint angular positions, velocities, accelerations, and joint torques. By taking these functions into the Performance Index (PI) of energy minimization, as well as the direct iteration method used for optimization of energy consumption, we can obtain the optimal trajectory for industrial robotic manipulators.