Control of Haptic Systems Based on Input-to-State Stability

Discretization of signals often generates additional energy in the haptic systems, and makes them unstable. The currently popular controls based on the passivity stabilize the systems by limiting the rendered force of the haptic systems so that the generated energy from the system stays below zero. The passivity-based methods are, however, often conservative and sacrifice the performance of haptic rendering. This paper proposes a control method to adjust the change rate of the stiffness of virtual environment connected to the haptic systems to satisfy the input-to-state stability (ISS) for better stability and transparency. The ISS conditions for the systems are derived by modeling the system as a linear time-varying system. The systems become dissipative if they satisfy the ISS conditions. The generated surplus energy of the dissipative system is less than a positive finite value while maintaining stability. Since the passive system is a special case of the dissipative system, the proposed ISS-based control is less conservative than the passivity-based approaches. Performance of the proposed control is experimentally compared with the virtual coupling and the force-bounding method that are widely used passivity-based approaches. The energy generated from the system using the proposed method is positive finite whereas the generated energy using the passivity-based approaches is less than zero. This means that more energy is transferred to the operator. Increased stiffness corresponding to this additionally transferred energy can be rendered. Root-mean-square and maximum errors of the rendered forces are, therefore, reduced by at least 86 % and 50 %, respectively.