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Studies on motion control of robot manipulators with elastic joints are basically aimed at improving robot performance in tracking or regulation tasks. In the interaction between robots and environment, instead, the main objective of a control strategy should be the reduction of the vibrational and chattering phenomena that elasticity in the robot joints can cause. This work takes into account working environments where unexpected interactions are experienced and proposes a compliance control scheme in the Cartesian space to reduce the counter effects of elasticity. Two theoretical formulations of the control law are presented, which differ for the term of gravity compensation. For both of them the closed-loop equilibrium conditions are evaluated and asymptotic stability is proven through the direct Lyapunov method. The two control laws are applied to a particular class of elastic robot manipulators, i.e., cable-actuated robots, since their intrinsic mechanical compliance can be successfully utilized in applications of biomedical robotics and assistive robotics. A compared experimental analysis of the two formulations of compliance control is finally carried out in order to verify stability of the two closed-loop systems as well as the capability to control the robot force in the interaction.
Zollo et al. (2004) studied this question.