Stochastic parameter identification for precise motion control

1. Dynamic equation and minimum set of dynamics parameters

Robot dynamics is represented by;

　　

and it is also represented by;

　　

using minimum set od dynamics parameters. The minimum set of dynamics parameters are the minimum number of physical parameters to express the dynamic equations, and consist of mass, moment of inertia, and so on.

2. Parameter identificaion via Least Square Method

The parameters p are normally identified from the data of joint angles, angular velocities, angular accelerations and torques obtained by moving the robot based on Least Square Method minimizing the following evaluation function.

　　

However, this is a minimization of the difference between the left and right sides of the equation of motion and cannot evaluate thet error of p.

3. Stochastic parameter identification

Therefore, in this research, the equation of motion is assumed to be satisfied, and the inconsistency of the equation of motion is regarded due to stochastic variation of the parameter.

　　

Based on this concept, the following equations are delived.

　　

From this result, the error of p is representd by the following equation using a free parameter.

　　

The free parameter is determind so that the self covariance will be the reference value.

　　

4. Snsitivity analysis

Here, we specify the self-covariance of the parameter error based on the sensitivity to the robot's end-effector positioning. This allows parameter identification to be accurate for an certain robot motion. This is verified by applying it to the periodic motion of a planar 3-link manipulator.

　　


e-mail : .m.aa@m.titech.ac.jp