The unique exoskeleton system (EXO-UL7) in UCSC is controlled in two levels. The lower-level uses standard PID control. Three force sensors in the upper-level send desired trajectories to the lower-level. The impedance/admittance control can is limit both internal and contact forces. It is impossible to design a model-based impedance/admittance control when the model of theexoskeleton is unavailable. In this paper, a model-free PID type admittance control is applied, whose parameters can be designed by human impedance properties. The inverse kinematics are required when the desired trajectories generated by admittance control in task space. It is difficult to solve the inverse kinematics problem especially when the robots are redundant, such asexoskeleton system. In this paper, we put both the upper-level PID admittance control and the lower-level linear PID control in task space. Novel sufficient conditions of semiglobal asymptotic stability are proposed via stability analysis in task space. These conditions give an explicit selection method of PID gains.

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