Symbolic differentiation algorithm for inverse dynamics of serial robots with flexible joints

A new symbolic differentiation algorithm is proposed in this paper to automatically generate the inverse dynamics of flexible joint robots in symbolic form, and results obtained can be used in real-time applications. The proposed method with 𝒪(n) computational complexity is developed based on the recursive Newton-Euler algorithm, the chain rule of differentiation, and the computer algebra system. The input of the proposed algorithm consists of symbolic matrices describing the kinematic and dynamic parameters of the robot. The output is the inverse dynamics solution written in portable and optimized code (C-code/Matlab-code). An exemplary, numerical simulation for inverse dynamics of the Kuka LWR4 robot with seven flexible joints is conducted using Matlab, in which the computational time per cycle of inverse dynamics is about 0.02 millisecond. The numerical example provides very good matching results versus existing methods, while requiring much less computation time and complexity.

Vibration Control of Flexible Joint Robots Using a Discrete-Time Two-Stage Controller Based On Time-varying Input Shaping and Delay Compensation

Most industrial serial robots use decentralized joint controllers assuming rigid body dynamics. To prevent exciting the flexible mode, gains are kept low, resulting in poor control bandwidth and disturbance rejection. In this paper, a two-stage flexible joint discrete controller is presented, in which the decentralized approach is extended with a stiffness to take into account the dominant coupling mode. In the first-stage, an input shaping feedforward shapes the rigid closed-loop dynamics into desired dynamics that does not produce link vibrations. Robotic dynamic computation based on a recursive Newton-Euler Algorithm is conducted to update the feedforward link inertia parameter during robot motion. A second-stage is added to increase disturbance rejection. A generalized Smith predictor is developed to compensate for delay and feedback sensor filtering. An effective methodology is presented to optimize the control loop gains. Numerical simulations and experiments on a six-joint robot manipulator confirm that the proposed controller improves control performances in terms of bandwidth, vibration attenuation, and disturbance rejection.