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1 Archives of Control Sciences

1 2002

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Feed-forward torques and reference trajectory for an arm with flexible joints

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Aoustin Y. , Formal'sky A.

tom Vol. 12, no. 1/2

125-149

We propose a design method of the feed-forward torques and the reference trajectory for an arm with flexible joints and unknown stiffiness coefficients. The bounds on the control torque are included explicitly. The designed commanded feed-forward torques and the corresponding reference trajectory are close to be time-optimal. The control law for each drive torque is composed with the commanded feed-forward torque and linear angular position and velocity feedback. The torques and the trajectory are used as input signals of PD-controllers. In a case of one-link flexible arm it is proved that so-called 'fluent' control torque enables to reach the desired motion with a small error and without large vibrations in the flexible joint. Designed fluent commanded feed-forward torque is successfully implemented in numerical experiments. The stiffness coefficient is assumed to be unknown so the mathematical model of the flexible arm is not known exactly. In two-link flexible arm the stiffness coefficients are also assumed unknown. Due to discontinuities of the optimal control functions and not acceptable jumps in the optimal control torques a 'trapezoidal' fluent control technique is proposed. Numerical experiments show that the designed control is close to time-opitimal. The approach presented in the paper can be extended to systems with more links and can take the gravity into consideration. however, in this case a time-optimal or a quasi-time-optimal control for the associated rigid system have to be designed.