The problem of the control of flexible joint robots is considered. Motion and torque control of robot joints, especially those equipped with harmonic drive (HD) transmission, is a challenging task due to the inherent nonlinear characteristics and joint flexibility of such systems. Two issues related to the control of flexible joint robots are investigated. The first is the development of a systematic scheme for selecting uncertainty bounds of robot joint nonlinearity and flexibility for control design purposes. The second is the development of motion and torque control schemes that guarantee robust performance in the presence of model uncertainties.

We propose a twofold robust control design for flexible joint robots with HD:​ an actuator-level torque control and a link-level motion control. We utilize multivariable H∞-based optimal control laws supported entirely by frequency domain measures at both levels. The proposed method provides a unified framework for achieving the desired performance requirements and for preserving robust stability in the presence of model uncertainties. Using simulation it is shown that the proposed method is more robust than conventional methods because the uncertainties due to the actuator-transmission nonlinearity are explicitly considered in the control design procedure.

In the design of the actuator level torque control, we analyze nonlinear harmonic drive phenomena that have been widely observed in experiments. The focus is on incorporating into the control design process a knowledge of the mismatch between the physical system and its mathematical models. The describing function and conic-sector-bounded nonlinearity methods are used to build into the control design process the effects of mismatch between hysteresis, friction and nonlinear stiffness of HD transmission and their mathematical models. In the design of the link level motion control, a nonlinear compensator based on the computed torque technique is derived. It is shown that the closed-loop system achieves robust performance using the proposed control design technique.

Using the Small Gain theorem and the Lyapunov Function method, the stability of the proposed control scheme is verified. Finally, in order to illustrate the proposed technique two control designs are presented for the IRIS-facility experimental testbed (a versatile, modular, and reconfigurable prototype robot developed at the Robotics and Automaton Laboratory of the University of Toronto) together with simulation and experimental results