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Optimal Joint TDPA Formulation for Kinematically Redundant Robot Manipulators

The accomplishment of a successful teleoperation task requires guaranteeing system stability and transparency. Communication delay (in particular variable time delay), quantization and discretization negatively affect system stability and might be overcome with Time Domain Passivity Approach (TDPA), a model-free and robust way to cope with energy injection due to communication delay. However, this method degrades the transparency of the teleoperation system and worsens tracking performance, introducing in particular position drift error at the slave side and high frequency vibration (jittering) at the master side. In this work, we propose a new joint passivity controller formulation for kinematically redundant manipulators. Our approach stabilizes the system guaranteeing minimal performance loss by privileging the dissipation of the observed energy in the Jacobian null-space. The residual energy (if any) is dissipated in an orthogonal subspace. This is achieved by the solution of an optimization problem with appropriately defined cost functions and constrained to dissipate the energy observed by the passivity observer, guaranteeing the stability of the system. The effectiveness of our algorithm is tested in simulation with both constant and variable time delays.