Variable impedance control improves compliance and robustness in robot-environment interaction through variation of the desired stiffness and the desired damping. This paper proposes neural approximation-based variable impedance controllers for robots in robot-environment interaction. Constraints on variable impedance parameters are given to ensure the exponential stability of the desired first- and second-order variable impedance dynamics. Adaptive neural network controllers are proposed to ensure the achievement of the desired first- and second-order variable impedance dynamics through convergence of variable impedance errors. In the neural networks, deadzone modifications are utilized to enhance robustness by turning off adaptation when auxiliary tracking errors enter the constructed small neighbourhoods of zero. The proposed variable impedance control methods in this paper guarantee the stability and achievement of the desired variable impedance dynamics. Theoretical analysis and simulation results validate the effectiveness of the proposed variable impedance control methods.
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